#cfa-level-1 #economics #microeconomics #reading-15-demand-and-supply-analysis-the-firm #section-3-analysis-of-revenue-costs-and-profit #study-session-4
To fully comprehend the dimensions of profit maximization, one must have a detailed understanding of the revenue and cost variables that determine profit.
Revenue and cost flows are calculated in terms of total, average, and marginal. A total is the summation of all individual components. For example, total cost is the summation of all costs that are incurred by the business. Total revenue is the sum of the revenues from all the business’s units. In the theory of the firm, averages and marginals are calculated with respect to the quantity produced and sold in a single period (as opposed to averaging a quantity over a number of time periods). For example, average revenue is calculated by dividing total revenue by the number of items sold. To calculate a marginal term, take the change in the total and divide by the change in the quantity number.
Exhibit 3 shows a summary of the terminology and formulas pertaining to profit maximization, where profit is defined as total revenue minus total economic costs. Note that the definition of profit is the economic version, which recognizes that the implicit opportunity costs of equity capital, in addition to explicit accounting costs, are economic costs. The first main category consists of terms pertaining to the revenue side of the profit equation: total revenue, average revenue, and marginal revenue. Cost terms follow with an overview of the different types of costs—total, average, and marginal.Exhibit 3. Summary of Profit, Revenue, and Cost Terms
|(Economic) profit||Total revenue minus total economic cost; (TR – TC)|
|Total revenue (TR)||Price times quantity (P × Q), or the sum of individual units sold times their respective prices; ∑(Pi × Qi)|
|Average revenue (AR)||Total revenue divided by quantity; (TR ÷ Q)|
|Marginal revenue (MR)||Change in total revenue divided by change in quantity; (∆TR ÷ ∆Q)|
|Total fixed cost (TFC)||Sum of all fixed expenses; here defined to include all opportunity costs|
|Total variable cost (TVC)||Sum of all variable expenses, or per unit variable cost times quantity; (per unit VC × Q)|
|Total costs (TC)||Total fixed cost plus total variable cost; (TFC + TVC)|
|Average fixed cost (AFC)||Total fixed cost divided by quantity; (TFC ÷ Q)|
|Average variable cost (AVC)||Total variable cost divided by quantity; (TVC ÷ Q)|
|Average total cost (ATC)||Total cost divided by quantity; (TC ÷ Q) or (AFC + AVC)|
|Marginal cost (MC)||Change in total cost divided by change in quantity; (∆TC ÷ ∆Q)|
In free markets—and even in regulated market economies—profit maximization tends to promote economic welfare and a higher standard of living, and creates wealth for investors. Profit motivates businesses to use resources efficiently and to concentrate on activities in which they have a competitive advantage. Most economists believe that profit maximization promotes allocational efficiency—that resources flow into their highest valued uses.
Overall, the functions of profit are as follows:
Rewards entrepreneurs for risk taking when pursuing business ventures to satisfy consumer demand.
Allocates resources to their most-efficient use; input factors flow from sectors with economic losses to sectors with economic profit, where profit reflects goods most desired by society.
Spurs innovation and the development of new technology.
Stimulates business investment and economic growth.
There are three approaches to calculate the point of profit maximization. First, given that profit is the difference between total revenue and total costs, maximum profit occurs at the output level where this difference is the greatest. Second, maximum profit can also be calculated by comparing revenue and cost for each individual unit of output that is produced and sold. A business increases profit through greater sales as long as per-unit revenue exceeds per-unit cost on the next unit of output sold. Profit maximization takes place at the point where the last individual output unit breaks even. Beyond this point, total profit decreases because the per-unit cost is higher than the per-unit revenue from successive output units. A third approach compares the revenue generated by each resource unit with the cost of that unit. Profit contribution occurs when the revenue from an input unit exceeds its cost. The point of profit maximization is reached when resource units no longer contribute to profit. All three approaches yield the same profit-maximizing quantity of output. (These approaches will be explained in greater detail later.)
Because profit is the difference between revenue and cost, an understanding of profit maximization requires that we examine both of those components. Revenue comes from the demand for the firm’s products, and cost comes from the acquisition and utilization of the firm’s inputs in the production of those products.
This section briefly examines demand and revenue in preparation for addressing cost. Unless the firm is a pure monopolist (i.e., the only seller in its market), there is a difference between market demand and the demand facing an individual firm. A later reading will devote much more time to understanding the various competitive environments (perfect competition, monopolistic competition, oligopoly, and monopoly), known as market structure. To keep the analysis simple at this point, we will note that competition could be either perfect or imperfect. In perfect competition, the individual firm has virtually no impact on market price, because it is assumed to be a very small seller among a very large number of firms selling essentially identical products. Such a firm is called a price taker. In the second case, the firm does have at least some control over the price at which it sells its product because it must lower its price to sell more units.
Exhibit 4 presents total, average, and marginal revenue data for a firm under the assumption that the firm is price taker at each relevant level of quantity of goods sold. Consequently, the individual seller faces a horizontal demand curve over relevant output ranges at the price level established by the market (see Exhibit 5). The seller can offer any quantity at this set market price without affecting price. In contrast, imperfect competition is where an individual firm has enough share of the market (or can control a certain segment of the market) and is therefore able to exert some influence over price. Instead of a large number of competing firms, imperfect competition involves a smaller number of firms in the market relative to perfect competition and in the extreme case only one firm (i.e., monopoly). Under any form of imperfect competition, the individual seller confronts a negatively sloped demand curve, where price and the quantity demanded by consumers are inversely related. In this case, price to the firm declines when a greater quantity is offered to the market; price to the firm increases when a lower quantity is offered to the market. This is shown in Exhibits 6 and 7.Exhibit 4. Total, Average, and Marginal Revenue under Perfect Competition
|Average Revenue (AR)||Marginal Revenue (MR)|
The quantity or quantity demanded variable is the amount of the product that consumers are willing and able to buy at each price level. The quantity sold can be affected by the business through such activities as sales promotion, advertising, and competitive positioning of the product that would take place under the market model of imperfect competition. Under perfect competition, however, total quantity in the market is influenced strictly by price, while non-price factors are not important. Once consumer preferences are established in the market, price determines the quantity demanded by buyers. Together, price and quantity constitute the firm’s demand curve, which becomes the basis for calculating the total, average, and marginal revenue.
Total revenue (TR) is tabulated as price times the quantity of units sold. At 1 unit TR is 100 (calculated as 100 × 1 unit); at 10 units it is 1,000 (calculated as 100 × 10 units). At zero quantity, obviously, total revenue is always zero. Under perfect competition, for each increment in quantity, total revenue increases by the price level, which is constant to the firm. This relationship is shown in Exhibit 4—where the increase in total revenue from one quantity to the next equals 100, which is equal to the price.
Average revenue (AR) is quantity sold divided into total revenue. The mathematical outcome of this calculation is simply the price that the firm receives in the market for selling a given quantity. For any firm that sells at a uniform price, average revenue will equal price. For example, AR at 3 units is 100 (calculated as 300 ÷ 3 units); at 8 units it is also 100 (calculated as 800 ÷ 8 units).
Marginal revenue (MR) is the change in total revenue divided by the change in quantity sold; it is simply the additional revenue from selling one more unit. For example, in Exhibit 4, MR at 4 units is 100 [calculated as (400 – 300) ÷ (4 – 3)]; at 9 units it is also 100 [calculated as (900 – 800) ÷ (9 – 8)]. In a competitive market in which price is constant to the individual firm regardless of the amount of output offered, marginal revenue is equal to average revenue, where both are the same as the market price. Reviewing the revenue data in Exhibit 4, price, average revenue, and marginal revenue are all equal to 100. In the case of imperfect competition, MR declines with greater output and is less than AR at any positive quantity level, as will become clear with Exhibit 7.
Exhibit 5 graphically displays the revenue data from Exhibit 4. For an individual firm operating in a market setting of perfect competition, MR equals AR and both are equal to a price that stays the same across all levels of output. Because price is fixed to the individual seller, the firm’s demand curve is a horizontal line at the point where the market sets the price. In Exhibit 5, at a price of 100, P1 = MR1 = AR1 = Demand1. Marginal revenue, average revenue, and the firm’s price remain constant until market demand and supply factors cause a change in price. For instance, if price increases to 200 because of an increase in market demand, the firm’s demand curve shifts from Demand1 to Demand2 with corresponding increases in MR and AR as well. Total revenue increases from TR1 to TR2 when price increases from 100 to 200. At a price of 100, total revenue at 10 units is 1,000; however, at a price of 200, total revenue would be 2,000 for 10 units.Exhibit 5. Total Revenue, Average Revenue, and Marginal Revenue under Perfect Competition
Exhibit 6 graphically illustrates the general shapes and relationships for TR, AR, and MR under imperfect competition. MR is positioned below the price and AR lines. TR peaks when MR equals zero at point Q1.Exhibit 6. Total Revenue, Average Revenue, and Marginal Revenue under Imperfect Competition
Given quantity and price data in the first two columns of Exhibit 7, total revenue, average revenue, and marginal revenue can be calculated for a firm that operates under imperfect competition.Exhibit 7
|Quantity (Q)||Price (P)||Total Revenue (TR)||Average Revenue (AR)||Marginal Revenue (MR)|
Describe how total revenue, average revenue, and marginal revenue change as quantity sold increases from 0 to 10 units.
Total revenue increases with a greater quantity, but the rate of increase in TR (as measured by marginal revenue) declines as quantity increases. Average revenue and marginal revenue decrease when output increases, with MR falling faster than price and AR. Average revenue is equal to price at each quantity level. Exhibit 8 shows the relationships among the revenue variables presented in Exhibit 7.Exhibit 8. Total Revenue, Average Revenue, and Marginal Revenue for Exhibit 7 Data
Revenue generation occurs when output is sold in the market. However, costs are incurred before revenue generation takes place as the firm purchases resources, or what are commonly known as the factors of production, in order to produce a product or service that will be offered for sale to consumers. Factors of production, the inputs to the production of goods and services, include:
land, as in the site location of the business;
labor, which consists of the inputs of skilled and unskilled workers as well as the inputs of firms’ managers;
capital, which in this context refers to physical capital—such tangible goods as equipment, tools, and buildings. Capital goods are distinguished as inputs to production that are themselves produced goods; and
materials, which in this context refers to any goods the business buys as inputs to its production process.1
For example, a business that produces solid wood office desks needs to acquire lumber and hardware accessories as raw materials and hire workers to construct and assemble the desks using power tools and equipment. The factors of production are the inputs to the firm’s process of producing and selling a product or service where the goal of the firm is to maximize profit by satisfying the demand of consumers. The types and quantities of resources or factors used in production, their respective prices, and how efficiently they are employed in the production process determine the cost component of the profit equation.
Clearly, in order to produce output, the firm needs to employ factors of production. While firms may use many different types of labor, capital, raw materials, and land, an analyst may find it more convenient to limit attention to a more simplified process in which only the two factors, capital and labor, are employed. The relationship between the flow of output and the two factors of production is called the production function, and it is represented generally as:
Q = f (K, L)
where Q is the quantity of output, K is capital, and L is labor. The inputs are subject to the constraint that K ≥ 0 and L ≥ 0. A more general production function is stated as:
Q = f (x1, x2, … xn)
where xi represents the quantity of the ith input subject to xi ≥ 0 for n number of different inputs. Exhibit 9illustrates the shape of a typical input–output relationship using labor (L) as the only variable input (all other input factors are held constant). The production function has three distinct regions where both the direction of change and the rate of change in total product (TP or Q, quantity of output) vary as production changes. Regions 1 and 2 have positive changes in TP as labor is added, but the change turns negative in Region 3. Moreover, in Region 1 (L0 – L1), TP is increasing at an increasing rate, typically because specialization allows laborers to become increasingly productive. In Region 2, however, (L1 – L2), TP is increasing at a decreasing rate because capital is fixed, and labor experiences diminishing marginal returns. The firm would want to avoid Region 3 if at all possible because total product or quantity would be declining rather than increasing with additional input: There is so little capital per unit of labor that additional laborers would possibly “get in each other’s way”. Point A is where TP is maximized.Exhibit 9. A Firm’s Production Function
A group of business investors are in the process of forming a new enterprise that will manufacture shipping containers to be used in international trade.
What decisions about factors of production must the start-up firm make in beginning operations?
What objective should guide the firm in its purchase and use of the production factors?
The entrepreneurs must decide where to locate the manufacturing facility in terms of an accessible site (land) and building (physical capital), what to use in the construction of the containers (materials), and what labor input to use.
Overall, any decision involving the input factors should focus on how that decision affects costs, profitability, and risk—such that shareholders’ wealth is maximized.
Exhibit 10 shows the graphical relationships among total costs, total fixed cost, and total variable cost. The curve for total costs is a parallel shift of the total variable cost curve and always lies above the total variable cost curve by the amount of total fixed cost. At zero production, total costs are equal to total fixed cost because total variable cost at this output level is zero.Exhibit 10. Total Costs, Total Variable Cost, and Total Fixed Cost
Exhibit 11 shows the cost curve relationships among ATC, AVC, and AFC in the short run. (In the long run, the firm will have different ATC, AVC, and AFC cost curves when all inputs are variable, including technology, plant size, and physical capital.) The difference between ATC and AVC at any output quantity is the amount of AFC. For example, at Q1 the distance between ATC and AVC is measured by the value of A, which equals the amount of fixed cost as measured by amount B at Q1. Similarly, at Q2, the distance between ATC and AVC of X equals amount Y of AFC. The vertical distance between ATC and AVC is exactly equal to the height of AFC at each quantity. Both average total cost and average variable cost take on a bowl-shaped pattern in which each curve initially declines, reaches a minimum-cost output level, and then increases after that point. Point S, which corresponds to QAVC, is the minimum point on the AVC (such as 2 units in Exhibit 13). Similarly, point T, which corresponds to QATC, is the minimum point on ATC (such as 3 units in Exhibit 13). As shown in Exhibit 11, when output increases, average fixed cost declines as AFC approaches the horizontal quantity axis.Exhibit 11. Average Total Cost, Average Variable Cost, and Average Fixed Cost
Exhibit 12 displays the cost curve relationships for ATC, AVC, and MC in the short run. The marginal cost curve intersects both the ATC and AVC at their respective minimum points. This occurs at points S and T, which correspond to QAVC and QATC, respectively. Mathematically, when marginal cost is less than average variable cost, AVC will be decreasing. The opposite occurs when MC is greater than AVC. For example, in Exhibit 13, AVC begins to increase beyond 2 units, where MC exceeds AVC. The same relationship holds true for MC and ATC. Referring again to Exhibit 13, ATC declines up to 3 units when MC is less than ATC. After 3 units, ATC increases as MC exceeds ATC. Initially, the marginal cost curve declines, but at some point it begins to increase in reflection of an increasing rate of change in total costs as the firm produces more output. Point R (Exhibit 12), which corresponds to QMC, is the minimum point on the marginal cost curve.Exhibit 12. Average Total Cost, Average Variable Cost, and Marginal Cost
Exhibit 13 shows an example of how total, average, and marginal costs are derived. Total costs are calculated by summing total fixed cost and total variable cost. Marginal cost is derived by taking the change in total costs as the quantity variable changes.Exhibit 13. Total, Average, Marginal, Fixed, and Variable Costs
|Total Fixed Costa(TFC)||Average Fixed Cost (AFC)||Total Variable Cost (TVC)||Average Variable Cost (AVC)||Total Costs (TC)||Average Total Cost|
a Includes all opportunity costs.Exhibit 13 Data
Total costs (TC) are the summation of all costs, where costs are classified according to fixed or variable. Total costs increase as the firm expands output and decrease when production is cut. The rate of increase in total costs declines up to a certain output level and, thereafter, accelerates as the firm gets closer to full utilization of capacity. The rate of change in total costs mirrors the rate of change in total variable cost. In Exhibit 13, TC at 5 units is 400—of which 300 is variable cost and 100 is fixed cost. At 10 units, total costs are 1,650, which is the sum of 1,550 in variable cost and 100 in fixed cost.
Total fixed cost (TFC) is the summation of all expenses that do not change when production varies. It can be a sunk or unavoidable cost that a firm has to cover whether it produces anything or not, or it can be a cost that stays the same over a range of production but can change to another constant level when production moves outside of that range. The latter is referred to as a quasi-fixed cost, although it remains categorized as part of TFC. Examples of fixed costs are debt service, real estate lease agreements, and rental contracts. Quasi-fixed cost examples would be certain utilities and administrative salaries that could be avoided or be lower when output is zero but would assume higher constant values over different production ranges. Normal profit is considered to be a fixed cost because it is a return required by investors on their equity capital regardless of output level. At zero output, total costs are always equal to the amount of total fixed cost that is incurred at this production point. In Exhibit 13, total fixed cost remains at 100 throughout the entire production range.
Other fixed costs evolve primarily from investments in such fixed assets as real estate, production facilities, and equipment. As a firm grows in size, fixed asset expansion occurs along with a related increase in fixed cost. However, fixed cost cannot be arbitrarily cut when production declines. Regardless of the volume of output, an investment in a given level of fixed assets locks the firm into a certain amount of fixed cost that is used to finance the physical capital base, technology, and other capital assets. When a firm downsizes, the last expense to be cut is usually fixed cost.
Total variable cost (TVC), which is the summation of all variable expenses, has a direct relationship with quantity. When quantity increases, total variable cost increases; total variable cost declines when quantity decreases. At zero production, total variable cost is always zero. Variable cost examples are payments for labor, raw materials, and supplies. As indicated above, total costs mirror total variable cost, with the difference being a constant fixed cost. The change in total variable cost (which defines marginal cost) declines up to a certain output point and then increases as production approaches capacity limits. In Exhibit 13, total variable cost increases with an increase in quantity. However, the change from 1 to 2 units is 25, calculated as (75 – 50); the change from 9 to 10 units is 350, calculated as (1,550 – 1,200).
Another approach to calculating total variable cost is to determine the variable cost per unit of output and multiply this cost figure by the number of production units. Per unit variable cost is the cost of producing each unit exclusive of any fixed cost allocation to production units. One can assign variable cost individually to units or derive an average variable cost per unit.
Whenever a firm initiates a downsizing, retrenchment, or defensive strategy, variable cost is the first to be considered for reduction given its variability with output. However, variable cost is reducible only so far because all firms have to maintain a minimum amount of labor and other variable resources to function effectively.Exhibit 13 Data
Dividing total fixed cost by quantity yields average fixed cost (AFC), which decreases throughout the production span. A declining average fixed cost reflects spreading a constant cost over more and more production units. At high production volumes, AFC may be so low that it is a small proportion of average total cost. In Exhibit 13, AFC declines from 100 at 1 unit, to 20 at 5 units, and then to 10 at an output level of 10 units.
Average variable cost (AVC) is derived by dividing total variable cost by quantity. For example, average variable cost at 5 units is (300 ÷ 5) or 60. Over an initial range of production, average variable cost declines and then reaches a minimum point. Thereafter, cost increases as the firm utilizes more of its production capacity. This higher cost results primarily from production constraints imposed by the fixed assets at higher volume levels. The minimum point on the AVC coincides with the lowest average variable cost. However, the minimum point on theAVC does not correspond to the least-cost quantity for average total cost. In Exhibit 13, average variable cost is minimized at 2 units, whereas average total cost is the lowest at 3 units.
Average total cost (ATC) is calculated by dividing total costs by quantity or by summing average fixed cost and average variable cost. For instance, in Exhibit 13, at 8 units ATC is 125 [calculated as (1,000 ÷ 8) or (AFC + AVC= 12.5 + 112.5)]. Average total cost is often referenced as per-unit cost and is frequently called average cost. The minimum point on the average total cost curve defines the output level that has the least cost. The cost-minimizing behavior of the firm would dictate operating at the minimum point on its ATC curve. However, the quantity that maximizes profit (such as Q3 in Exhibit 17) may not correspond to the ATC-minimum point. The minimum point on the ATC curve is consistent with maximizing profit per-unit, but it is not necessarily consistent with maximizing total profit. In Exhibit 13, the least-cost point of production is 3 units; ATC is 75, derived as [(225 ÷ 3) or (33.3 + 41.7)]. Any other production level results in a higher ATC.
Marginal cost (MC) is the change in total cost divided by the change in quantity. Marginal cost also can be calculated by taking the change in total variable cost and dividing by the change in quantity. It represents the cost of producing an additional unit. For example, at 9 units marginal cost is 300, calculated as [(1,300 – 1,000) ÷ (9 – 8)]. Marginal cost follows a J-shaped pattern whereby cost initially declines but turns higher at some point in reflection of rising costs at higher production volumes. In Exhibit 13, MC is the lowest at 2 units of output with a value of 25, derived as [(175 – 150) ÷ (2 – 1)].EXAMPLE 4
The first three columns of Exhibit 16 display data on quantity, total fixed cost, and total variable cost, which are used to calculate total costs, average fixed cost, average variable cost, average total cost, and marginal cost. Interpret the results for total, average, marginal, fixed, and variable costs.Exhibit 16
a Includes all opportunity costs
Total fixed cost remains unchanged at 5,000 throughout the entire production range, while average fixed cost continuously declines from 5,000 at one unit to 500 by 10 units. Both average variable cost and marginal cost initially decline and then reach their lowest level at 3 units, with costs of 1,800 and 1,600, respectively. Beyond 3 units, both average variable cost and marginal cost increase, indicating that the cost of production rises with greater output. The least-cost point for average total cost is 3,200 at 5 units. At zero output, total costs are 5,000, which equal the amount of total fixed cost.
Exhibit 17 displays the firm’s supply curve, shutdown point, and breakeven level of operation under perfect competition in the short run. The firm’s short-run supply curve is the bold section of the marginal cost curve that lies above the minimum point (point A) on the average variable cost curve. If the firm operates below this point (for example between C and A), it shuts down because of its inability to cover variable costs in full. Between points A and B, the firm can operate in the short run because it is meeting variable cost payments even though it is unable to cover all of its fixed costs. In the long run, however, the firm is not able to survive if fixed costs are not completely covered. Any operating point above point B (the minimum point on ATC), such as point D, generates an economic profit.
A firm’s shutdown point occurs when average revenue is less than average variable cost (any output belowQshutdown), which corresponds to point A in Exhibit 17. Shutdown is defined as a situation in which the firm stops production but still confronts the payment of fixed costs in the short run as a business entity. In the short run, a business is capable of operating in a loss situation as long as it covers its variable costs even though it is not earning sufficient revenue to cover all fixed cost obligations. If variable costs cannot be covered in the short run (P < AVC), the firm will shut down operations and simply absorb the unavoidable fixed costs. This problem occurs at output Q1, which corresponds to point C where price is less than average variable cost. However, in the long run, to remain in business, the price must cover all costs. Therefore, in the long run, at any price below the breakeven point, the firm will exit the market, i.e., the firm will no longer participate in the market. Point D, which corresponds to output Q3, is a position where economic profit occurs because price is greater than ATC.Exhibit 17. A Firm’s Short-Run Supply Curve, Breakeven Point, and Shutdown Point under Perfect Competition
In the case of perfect competition, the breakeven point is the quantity where price, average revenue, and marginal revenue equal average total cost. It is also defined as the quantity where total revenue equals total costs. Firms strive to reach initial breakeven as soon as possible to avoid start-up losses for any extended period of time. When businesses are first established, there is an initial period where losses occur at low quantity levels. In Exhibit 17, the breakeven quantity occurs at output QBE, which corresponds to point B where price is tangent to the minimum point on the ATC. (Keep in mind that normal profit as an implicit cost is included in ATC as a fixed cost.)
Exhibit 18 shows the breakeven point under perfect competition using the total revenue–total cost approach. Actually, there are two breakeven points—lower (point E) and upper (point F). Below point E, the firm is losing money (economic losses), and beyond that point is the region of profitability (shaded area) that extends to the upper breakeven point. Within this profit area, a specific quantity (Qmax) maximizes profit as the largest difference between TR and TC. Point F is where the firm leaves the profit region and incurs economic losses again. This second region of economic losses develops when the firm’s production begins to reach the limits of physical capacity, resulting in diminished productivity and an acceleration of costs. Obviously, the firm would not produce beyond Qmax because it is the optimal production point that maximizes profit.Exhibit 18. A Firm’s Breakeven Points Using Total Revenue and Total Costs under Perfect Competition
Breakeven points, profit regions, and economic loss ranges are influenced by demand and supply conditions, which change frequently according to the market behavior of consumers and firms. A high initial breakeven point is riskier than a low point because it takes a larger volume and, usually, a longer time to reach. However, at higher output levels it yields more return in compensation for this greater risk.
In the case where TC exceeds TR, as shown in Exhibit 19, the firm will want to minimize the economic loss (as long as TR > TVC), which is defined as the smallest difference between TC and TR. This occurs at Qmin, where the economic loss is calculated as (TCM – TRN) on the vertical axis.Exhibit 19. Loss Minimization Using Total Revenue and Total Costs
The following revenue and cost information for a future period is presented in Exhibit 20 for WR International, a newly formed corporation that engages in the manufacturing of low-cost, pre-fabricated dwelling units for urban housing markets in emerging economies. (Note that quantity increments are in blocks of 10 for a 250 change in price.) The firm has few competitors in a market setting of imperfect competition.
How many units must WR International sell to initially break even?
Where is the region of profitability?
At what point will the firm maximize profit? At what points are there economic losses?
|Quantity (Q)||Price (P)||Total Revenue|
a Includes all opportunity costs
WR International will initially break even at 40 units of production, where TR and TC equal 360,000.
The region of profitability will range from 40 to 80 units. Any production quantity of less than 40 units and any quantity greater than 80 will result in an economic loss.
Maximum profit of 30,000 will occur at 60 units. Lower profit will occur at any output level that is higher or lower than 60 units. From zero quantity to 40 units and for quantities beyond 80 units, economic losses occur.
Given the relationships among total revenue, total variable cost, and total fixed cost, Exhibit 21 summarizes the decisions to operate, shut down production, or exit the market in both the short run and long run. As previously discussed, the firm must cover variable cost before fixed cost. In the short run, if total revenue cannot cover total variable cost, the firm shuts down production to minimize loss, which would equal the amount of fixed cost. If total variable cost exceeds total revenue in the long run, the firm will exit the market as a business entity to avoid the loss associated with fixed cost at zero production. By terminating business operations through market exit, investors escape the erosion in their equity capital from economic losses. When total revenue is enough to cover total variable cost but not all of total fixed cost, the firm can survive in the short run but will be unable to maintain financial solvency in the long run.Exhibit 21
|Revenue–Cost Relationship||Short-Run Decision||Long-Term Decision|
|TR ≥ TC||Stay in market||Stay in market|
|TR > TVC but TR < TFC + TVC||Stay in market||Exit market|
|TR < TVC||Shut down production to zero||Exit market|
For the most recent financial reporting period, a business domiciled in Ecuador (which recognizes the US dollar as an official currency) has revenue of $2 million and total costs of $2.5 million, which are or can be broken down into total fixed cost of $1 million and total variable cost of $1.5 million. The net loss on the firm’s income statement is reported as $500,000 (ignoring tax implications). In prior periods, the firm had reported profits on its operations.
What decision should the firm make regarding operations over the short term?
What decision should the firm make regarding operations over the long term?
Assume the same business scenario except that revenue is now $1.3 million, which creates a net loss of $1.2 million. What decision should the firm make regarding operations in this case?
In the short run, the firm is able to cover all of its total variable cost but only half of its $1 million in total fixed cost. If the business ceases to operate, its loss is $1 million, the amount of total fixed cost, whereas the net loss by operating is minimized at $500,000. The firm should attempt to operate by negotiating special arrangements with creditors to buy time to return operations back to profitability.
If the revenue shortfall is expected to persist over time, the firm should cease operations, liquidate assets, and pay debts to the extent possible. Any residual for shareholders would decrease the longer the firm is allowed to operate unprofitably.
The firm would minimize loss at $1 million of total fixed cost by shutting down compared with continuing to do business where the loss is $1.2 million. Shareholders will save $200,000 in equity value by pursuing this option. Unquestionably, the business will have a rather short life expectancy if this loss situation were to continue.
When evaluating profitability, particularly of start-up firms and businesses using turnaround strategies, analysts should consider highlighting breakeven and shutdown points in their financial research. Identifying the unit sales levels where the firm enters or leaves the production range for profitability and where the firm can no longer function as a viable business entity provides invaluable insight to investment decisions.
Profit maximization occurs when
the difference between total revenue (TR) and total costs (TC) is the greatest;
marginal revenue (MR) equals marginal cost (MC); and
the revenue value of the output from the last unit of input employed equals the cost of employing that input unit (as later developed in Equation 12).
All three approaches derive the same profit-maximizing output level. In the first approach, a firm starts by forecasting unit sales, which becomes the basis for estimates of future revenue and production costs. By comparing predicted total revenue to predicted total costs for different output levels, the firm targets the quantity that yields the greatest profit. When using the marginal revenue–marginal cost approach, the firm compares the change in predicted total revenue (MR) with the change in predicted total costs (MC) by unit of output. If MR exceeds MC, total profit is increased by producing more units because each successive unit adds more to total revenue than it does to total costs. If MC is greater than MR, total profit is decreased when additional units are produced. The point of profit maximization occurs where MR equals MC. The third method compares the estimated cost of each unit of input to that input’s contribution with projected total revenue. If the increase in projected total revenue coming from the input unit exceeds its cost, a contribution to total profit is evident. In turn, this justifies further employment of that input. On the other hand, if the increase in projected total revenue does not cover the input unit’s cost, total profit is diminished. Profit maximization based on the employment of inputs occurs where the next input unit for each type of resource used no longer makes any contribution to total profit.
Combining revenue and cost data from Exhibits 4 and 13, Exhibit 22 demonstrates the derivation of the optimal output level that maximizes profit for a firm under perfect competition. Profit is calculated as the difference between total revenue and total costs. At zero production, an economic loss of 100 occurs, which is equivalent to total fixed cost. Upon initial production, the firm incurs an economic loss of 50 on the first unit but breaks even by unit 2. The region of profitability ranges from 2 to 6 units. Within this domain, total profit is maximized in the amount of 100 at 5 units of output. No other quantity level yields a higher profit. At this 5-unit level, marginal revenue exceeds marginal cost. But at unit 6, marginal revenue is less than marginal cost, which results in a lower profit because unit 6 costs more to produce than what it generates in revenue. Unit 6 costs 150 to produce but contributes only l00 to total revenue, which yields a 50 loss on that unit. As a result, profit drops from 100 to 50. At unit 7 and beyond, the firm begins to lose money again as it passes the upper breakeven mark and enters a second economic loss zone.Exhibit 22. Profit Maximization under Perfect Competition
a Includes all opportunity costs
Exhibits 23 and 24 display the data from Exhibit 22 to illustrate profit maximization under perfect competition using the (TR – TC) and (MR = MC) approaches. Exhibit 24 highlights profit maximization based on comparing how much each unit of output costs to produce (MC) to how much each unit contributes to revenue (MR). Each unit up to and including unit 5 contributes to profit in that each unit’s marginal revenue exceeds its marginal cost. Starting at unit 6 and thereafter, the marginal revenue for each unit is less than the marginal cost. This results in a reduction in profit. Profit maximization occurs where MR equals MC. In this case, the optimal decision for the firm using a comparison of MR and MC is to produce 5 units.2Exhibit 23. Profit Maximization Using Total Revenue and Total Costs from Exhibit 22
Exhibit 24. Profit Maximization Using Marginal Revenue and Marginal Cost from Exhibit 22
It should be noted that under imperfect competition, the firm faces a negatively sloped demand curve. As the firm offers a greater quantity to the market, price decreases. In contrast, a firm under perfect competition has an insignificant share of the market and is able to sell more without impacting market price. Obviously, the type of market structure in which a firm operates as a seller has an impact on the firm’s profit in terms of the price received when output levels vary.EXAMPLE 7
Exhibit 25 shows revenue and cost data for a firm that operates under the market structure of imperfect competition.
At what point does the firm break even over its production range in the short run?
What is the quantity that maximizes profit given total revenue and total costs?
Comparing marginal revenue and marginal cost, determine the quantity that maximizes profit.
a Includes all opportunity costs.
The breakeven point occurs between unit 1 and unit 2, where profit increases from (5) to 480.
At an output level of 5 units, the firm maximizes profit in the amount of 1,275, calculated as the difference between TR of 4,875 and TC of 3,600.
Profit maximization occurs at 5 units, where MR of 955 exceeds MC of 800, which yields a profit contribution of 155. However, at 6 units, MR of 945 is less than the MC of 1,000, resulting in a loss of 55 and a reduction in profit from 1,275 to 1,220.
Exhibit 26 summarizes the (TR – TC) and (MR = MC) profit-maximization approaches for firms operating under perfect competition. (Profit maximization using inputs is discussed in Section 3.2.2.)Exhibit 26. Summary of Profit Maximization and Loss Minimization under Perfect Competition
|Revenue–Cost Relationship||Actions by Firm|
|TR = TC and MR > MC||Firm is operating at lower breakeven point; increase Q to enter profit territory.|
|TR ≥ TC and MR = MC||Firm is at maximum profit level; no change in Q.|
|TR < TC and TR ≥ TVC|
but (TR – TVC) < TFC (covering TVC but not TFC)
|Find level of Q that minimizes loss in the short run; work toward finding a profitable Q in the long run; exit market if losses continue in the long run.|
|TR < TVC|
(not covering TVC in full)
|Shut down in the short run; exit market in the long run.|
|TR = TC and MR < MC||Firm is operating at upper breakeven point; decrease Q to enter profit territory.|
Profit acts as an efficient allocator of equity capital to investment opportunities whereby shareholders’ wealth is increased. Equity flows from low-return business investments to high-return business investments as it seeks the greatest return potential on a risk-adjusted basis. Basic economic theory describes how consumer choice voiced through the price mechanism in competitive markets directs resources to their most efficient use according to what consumers need and want. In the end, it is profitability—which evolves from the interactions of demand and supply factors in product and resource markets—that decides where financial capital is employed.
Rational behavior dictates that the firm select an operating size or scale that maximizes profit over any time frame. The time frame for the firm can be separated into the short run and long run based on the ability of the firm to adjust the quantities of the fixed resources it employs. The short run is defined as a time period in which at least one of the factors of production is fixed. The most likely inputs to be held constant in defining the short run are technology, physical capital, and plant size. Usually, a firm cannot change these inputs in a relatively short period of time given the inflexible nature of their use. The long run is defined as a time period in which all factors of production are variable, including technology, physical capital, and plant size. Additionally, in the long run, firms can enter or exit the market based on decisions regarding profitability. The long run is often referred to as the planning horizon in which the firm can choose the short-run position or optimal operating size that maximizes profit over time.
The time required for long-run adjustments varies by industry. For example, the long run for a small business using very little in the way of technology and physical capital may be less than a year. On the other hand, for a capital-intensive firm, the long run may be more than a decade. However, given enough time, all production factors are variable, which allows the firm to choose an operating size or plant capacity based on different technologies and physical capital. In this regard, costs and profits will differ between the short run and long run.
The fixed-input constraint in the short run along with input prices establish the firm’s short-run average total cost curve (SRATC). This defines what the per-unit cost will be for any quantity in the short run. The SRATC and the demand for the firm’s product determine short-run profit. The selection of technology, physical capital, and plant size is a key determinant of the short-run cost curve for the firm. As the firm switches to newer technologies and physical capital, a corresponding change in short-run costs occurs. In the long run, a firm has the opportunity for greater profit potential based on the ability to lower its costs through choices of more-efficient technology and physical capital and a wider selection of production capacities.
Exhibit 27 displays the long-run average total cost curve (LRATC), which is derived from the short-run average total cost curves that are available to the firm.3 The business has a choice of five technology-physical capital options and plant capacities over the long run, each with its own short-run cost curve. The LRATC consists of sections of these individual short-run cost curves. For example, from zero production to Q1 output, SRATC1yields the lowest per unit cost. Between Q1 and Q2, the lowest cost per unit is attainable with SRATC2, which represents a larger production capacity. SRATC3 and SRATC4 would provide for the lowest average cost over time for output levels of Q2 – Q4 and Q4 – Q5, respectively. For any output greater than Q5, SRATC5 becomes the preferred curve for minimizing average total cost. Tangentially connecting all of the least-cost SRATC segments by way of an envelope curve creates the LRATC. (Assuming an unlimited number of possible technologies, plant sizes, and physical capital combinations—and therefore a theoretically unlimited number of SRATC—the LRATC becomes a smooth curve rather than a segmented one as indicated by the bold segments of the five SRATC’s in Exhibit 27.) The LRATC shows the lowest cost per unit at which output can be produced over a long period of time when the firm is able to make technology, plant size, and physical capital adjustments. If the same technologies and physical capital are available and adaptable to every firm in the industry, then all firms would have the same LRATC. However, firms could be at different positions on this homogenous LRATC depending on their operating size that is based on output.Exhibit 27. Long-Run Average Total Cost Curve
Over the long run, as a business expands output, it can utilize more efficient technology and physical capital and take advantage of other factors to lower the costs of production. This development is referred to as economies of scale or increasing returns to scale as a firm moves to lower cost structures when it grows in size. Output increases by a larger proportion than the increase in inputs. The opposite effect can result after a certain volume level at which the business faces higher costs as it expands in size. This outcome is called diseconomies of scale or decreasing returns to scale, where the firm becomes less efficient with size. In this case, output increases by a smaller proportion than the increase in inputs. Diseconomies of scale often result from the firm becoming too large to be managed efficiently even though better technology can be increasing productivity within the business. Both economies and diseconomies of scale can occur at the same time; the impact on long-run average total cost depends on which dominates. If economies of scale dominate, LRATC decreases with increases in output; the reverse holds true when diseconomies of scale prevail.
Referring back to Exhibit 27, economies of scale occur from Q0 (zero production) to output level Q3, where Q3 is the cost-minimizing level of output for SRATC3. It is evident throughout this production range that per-unit costs decline as the firm produces more. Over the production range of Q3 to Q5, diseconomies of scale are occurring as per-unit costs increase when the firm expands output. Under perfect competition, given the five SRATC selections that are available to the firm throughout the production range Q0 – Q5, SRATC3 is the optimal technology, plant capacity, and physical capital choice, with Q3 being the target production size for the firm that would minimize cost over the long term.
Perfect competition forces the firm to operate at the minimum point on the LRATC because market price will be established at this level over the long run. If the firm is not operating at this least-cost point, its long-term viability will be threatened. The minimum point on the LRATC is referred to as the minimum efficient scale (MES). The MES is the optimal firm size under perfect competition over the long run where the firm can achieve cost competitiveness.
As the firm grows in size, economies of scale and a lower average total cost can result from the following factors:
Division of labor and management in a large firm with numerous workers, where each worker can specialize in one task rather than perform many duties, as in the case of a small business (as such, workers in a large firm become more proficient at their jobs).
Being able to afford more-expensive, yet more-efficient equipment and to adapt the latest in technology that increases productivity.
Effectively reducing waste and lowering costs through marketable byproducts, less energy consumption, and enhanced quality control.
Better use of market information and knowledge for more-effective managerial decision making.
Discounted prices on resources when buying in larger quantities.
A classic example of a business that realizes economies of scale through greater physical capital investment is the electric utility. By expanding output capacity to accommodate a larger customer base, the utility company’s per-unit cost will decline. Economies of scale help to explain why electric utilities have naturally evolved from localized entities to regional and multi-region enterprises. Wal-Mart, the world’s largest retailer, is an example of a business that uses bulk purchasing power to obtain deep discounts from suppliers to keep costs and prices low. Wal-Mart also utilizes the latest in technology to monitor point-of-sale transactions to have timely market information to respond to changes in customer buying behavior. This leads to economies of scale through lower distribution and inventory costs.
The factors that can lead to diseconomies of scale, inefficiencies, and rising costs when a firm increases in size include:
So large that it cannot be properly managed.
Overlap and duplication of business functions and product lines.
Higher resource prices because of supply constraints when buying inputs in large quantities.
General Motors (GM) is an example of a business that has realized diseconomies of scale by becoming too large. Scale diseconomies have occurred through product overlap and duplication (i.e., similar or identical automobile models), where the fixed cost for these models is not spread over a large volume of output. (Recently, the company has decided to discontinue various low-volume product models that overlapped with other models.) GM has numerous manufacturing plants throughout the world and sells vehicles in over a hundred countries. Given this geographical dispersion in production and sales, the company has had communication and management coordination problems, which have resulted in higher costs. Also, GM has had significantly higher labor costs when compared with its competitors. By being the largest producer in the market, it has been a target of labor unions for higher compensation and benefits packages relative to other firms.
Strategically, when a firm is operating in the economies of scale region, expanding production capacity will increase the firm’s competitiveness through lower costs. Firm expansion is often facilitated with a growth or business combination (i.e., merger or acquisition) strategy. On the other hand, when a business is producing in the area of diseconomies of scale, the objective is to downsize to reduce costs and become more competitive. From an investment perspective, a firm operating at the minimum point of the industry LRATC under perfect competition should be valued higher than a firm that is not producing at this least-cost quantity.
The LRATC can take various forms given the development of new technology and growth prospects for an industry over the long term. Exhibit 28 displays examples of different average total cost curves that firms can realize over the long run. Panel A shows that scale economies dissipate rapidly at low output levels. This implies that a firm with a low volume of output can be more cost competitive than a firm that is producing a high output volume. Panel B indicates a lower and lower average cost over time as firm size increases. The larger the business, the more competitive it is and the greater its potential investment value. Finally, Panel C shows the case of constant returns to scale (i.e., output increases by the same proportion as the increase in inputs) over the range of production from Q1 to Q2, indicating that size does not give a firm a competitive edge over another firm within this range. In other words, a firm that is producing the smaller output Q1 has the same long-run average total cost as a firm producing the higher output Q2.Exhibit 28. Types of Long-Run Average Total Cost Curves
Exhibit 29 displays the long-run average total cost curve (LRATCUS) and the short-run average total cost curves for three hypothetical US-based automobile manufacturers—Starr Vehicles (Starr), Rocket Sports Cars (Rocket), and General Auto (GenAuto). The long-run average total cost curve (LRATCforeign) for foreign-owned automobile companies that compete in the US auto market is also indicated in the graph. (The market structure implicit in the exhibit is imperfect competition.)
To what extent are the cost relationships depicted in Exhibit 29 useful for an economic and financial analysis of the three US-based auto firms?Exhibit 29
First, it is observable that the foreign auto companies have a lower LRATC compared with that of the US automobile manufacturers. This competitive position places the US firms at a cost and possible pricing disadvantage in the market with the potential to lose market share to the lower-cost foreign competitors. Second, only Rocket operates at the minimum point of the LRATCUS, whereas GenAuto is situated in the region of diseconomies of scale and Starr is positioned in the economies of scale portion of the curve. To become more efficient and competitive, GenAuto needs to downsize and restructure, which means moving down the LRATCUS curve to a smaller, yet lower-cost production volume. On the other hand, Starr has to grow in size to become more efficient and competitive by lowering per-unit costs.
From a long-term investment prospective and given its cost advantage, Rocket has the potential to create more investment value relative to GenAuto and Starr. Over the long run, if GenAuto and Starr can lower their average total costs, they will become more attractive to investors. On the other hand, if any or all of the three US auto companies cannot match the cost competitiveness of the foreign firms, they may be driven from the market. In the long run, the lower-cost foreign automakers pose a severe competitive challenge to the survival of the US manufacturers and their ability to maintain and grow shareholders’ wealth.
No matter the time span, the firm’s supply behavior centers on the objective of profit maximization. In the short term, when technology and physical capital are fixed, maximum profit (or minimal loss) is determined where marginal cost equals marginal revenue (points A and B in Exhibit 30). Cases of profit maximization and loss minimization are illustrated in Exhibit 30 for a firm operating under perfect competition in the short run. In Panel A, the firm realizes economic profit because TR is greater than TC and price exceeds SRATC in the production range of Q1–Q2. Qmax is the output level that maximizes economic profit. Panel B shows the case of loss minimization because TC exceeds TR and SRATC is above the price level. Qmin yields the least loss of all possible production quantities. Note that in this case, the short-run loss is still less than fixed cost, so the firm should continue operating in the short run.Exhibit 30. Profit Maximization and Loss Minimization in the Short Run under Perfect Competition
Exhibit 31 illustrates long-run profit maximization under perfect competition given the long-run average total cost curve when economies of scale occur. In the long run under perfect competition, the firm will operate at the minimum efficient scale point on its long-run average total cost curve. This least-cost point is illustrated in Exhibit 31 as point E at output level QE. In comparison to the point of minimum efficient scale, any other output quantity results in a higher cost.
In the short run given SRATC1 and P1, the firm is making only normal profit because price equals average total cost at point A. By realizing economies of scale in the long run, the firm can move down the LRATC to SRATC2and produce QE. If the firm still receives P1, economic profit is forthcoming at QE in the amount of (B – E) per unit. However, economic profit with no barriers to entry under perfect competition leads to more competitors, a greater market supply, and, subsequently, a lower price in the long run. The price to the firm will decline to P2, and economic profit will disappear with the long-run equilibrium for the firm occurring at point E, the minimum efficient scale. At point E, the firm is making only normal profit because in the long run under perfect competition, economic profit is zero.Exhibit 31. Long-Run Profit Maximization and Minimum Efficient Scale under Perfect Competition
Exhibit 32 illustrates profit maximization and loss minimization in the long run when market prices change for a firm that is operating in a market of perfect competition at the minimum efficient scale point on its LRATC. (SRATC2, MC2, QE, and point E are the same in both Exhibit 31 and Exhibit 32.) Although point E represents the lowest production cost, the quantity that maximizes profit or minimizes loss is determined where marginal revenue equals marginal cost. (Under perfect competition, price equals marginal revenue.) If price is at P1 (which equals MR1), the firm will produce Q1 and accrue economic profit of (A – B) per unit in the short run because price is greater than average total cost. In the long run, economic profit attracts new competitors who drive price down, resulting in zero economic profit. Profitability declines to the level at P2, where price is tangent to average total cost at point E. If price is at P3 (which equals MR3), the firm will produce Q3 and realize an economic loss of (C – D) per unit in the short run because average total cost is greater than price. In the long run, firms will exit the market; as a result, price rises to P2, eliminating economic losses. Again, profitability for the firm returns to the normal level at point E, where price matches average total cost. The long-term equilibrium for the firm occurs at point E, which corresponds to Demand2, MR2, a price of P2, and an output level of QE.Exhibit 32. Profit Maximization and Loss Minimization in the Long Run under Perfect Competition
The long-run industry supply curve shows the relationship between quantities supplied and output prices for an industry when firms are able to enter or exit the industry in response to the level of short-term economic profit (i.e., perfect competition) and when changes in industry output influence resource prices over the long run. Exhibit 33 illustrates three types of long-run supply curves based on increasing costs, decreasing costs, and constant costs to firms competing under perfect competition.Exhibit 33. Long-Run Supply Curves for the Firm
An increasing-cost industry exists when prices and costs are higher when industry output is increased in the long run. This is demonstrated in Panel A. Assuming zero economic profit at E1, when demand increases from D0to D1, price rises and economic profit results at E2 in the short run. Over the long term in response to this economic profit, new competitors will enter the industry and existing firms will expand output, resulting in an increase in supply from S0 to S1 and a long-term equilibrium at E3. If the increase in demand for resources from this output expansion leads to higher prices for some or all inputs, the industry as a whole will face higher production costs and charge a higher price for output. As indicated by SLR in Panel A, the long-run supply curve for the industry will have a positive slope over the long run. The firm in an increasing-cost industry will experience higher resource costs so market price must rise in order to cover these costs. The petroleum, coal, and natural gas industries are prime examples of increasing-cost industries, where the supply response to long-run demand growth results in higher output prices because of the rising costs of energy production.
Panel B shows the case of a decreasing-cost industry, where the supply increase from S0 to S1 leads to a lower price for output in the market. Firms are able to charge a lower price because of a reduction in their resource costs. Decreasing costs can evolve from technological advances, producer efficiencies that come from a larger firm size, and economies of scale of resource suppliers (i.e., lower resource prices) that are passed on to resource buyers when industry output expands. The long-run supply curve for the industry will have a negative slope, as displayed by SLR in Panel B. As a result, the firm in a decreasing-cost industry will experience lower resource costs and can then charge a lower price.4 Possible examples of decreasing-cost industries are semiconductors and personal computers, where the rapid growth in demand over the past decade has led to substantially lower prices.
In some cases, firms in the industry will experience no change in resource costs and output prices over the long run. This type of industry is known as a constant-cost industry. This is displayed in Panel C, where the long-run supply curve (SLR) for the industry is a horizontal line indicating a constant price level when the industry increases output.EXAMPLE 9
Mirco Industries is a global manufacturer of outdoor recreational equipment in a market setting of easy entry and price competition. Company forecasts of total market demand for outdoor recreational products over the long run indicate robust growth in sales as families allocate more time to outdoor and leisure activities. This scenario looks promising for Mirco’s earnings and shareholders’ value. To assist Mirco in its assessment of this future scenario, industry analysts have presented Exhibit 34 to illustrate industry costs and the market supply curve over the long run.
Using Exhibit 34, what information would be of value to Mirco in identifying future production cost and price under a market growth scenario?Exhibit 34.
Note: Market demand increases from D0 to D1. The market responds with an increase in supply from S0 to S1. In the long run, the price of P2 will be higher than the original price of P1.
As indicated by the upward slope of the long-run industry supply curve, Mirco will experience an increase in production costs over the long run because of higher resource prices when the industry expands production and new firms enter the industry in response to an increase in market demand. To cover the higher production costs, Mirco will ultimately charge the higher market price of P2 relative to the current price of P1.
In general terms, productivity is defined as the average output per unit of input. Any production factor can be used as the input variable. However, it has been a common practice to use the labor resource as the basis for measuring productivity. In this regard, productivity is based on the number of workers used or the number of work-hours performed. In many cases, labor is easier to quantify relative to the other types of resources used in production. As such, productivity is typically stated as output per worker or output per labor hour.
Why is productivity important? Cost minimization and profit maximization behavior dictate that the firm strives to maximize productivity—that is, produce the most output per unit of input or produce any given level of output with the least amount of inputs. A firm that lags behind the industry in productivity is at a competitive disadvantage and, as a result, is most likely to face decreases in future earnings and shareholders’ wealth. An increase in productivity lowers production costs, which leads to greater profitability and investment value. Furthermore, productivity benefits (e.g., increased profitability) can be fully or partially distributed to other stakeholders of the business, such as consumers in the form of lower prices and employees in the form of enhanced compensation. Transferring some or all of the productivity rewards to non-equity holders creates synergies that benefit shareholders over time.
The benefits from increased productivity are as follows:
Lower business costs, which translate into increased profitability.
An increase in the market value of equity and shareholders’ wealth resulting from an increase in profit.
An increase in worker rewards, which motivates further productivity increases from labor.
Undoubtedly, increases in productivity reinforce and strengthen the competitive position of the firm over the long run. A fundamental analysis of a company should examine the firm’s commitment to productivity enhancements and the degree to which productivity is integrated into the competitive nature of the industry or market. In some cases, productivity is not only an important promoter of growth in firm value over the long term, but it is also the key factor for economic survival. A business that lags the market in terms of productivity often finds itself less competitive, while at the same time confronting profit erosion and deterioration in shareholders’ wealth. Whenever productivity is a consideration in the equity valuation of the firm, the first step for the analyst is to define measures of productivity. Typical productivity measures for the firm are based on the concepts of total product, average product, and marginal product of labor.
When measuring a firm’s operating efficiency, it is easier and more practical to use a single resource factor as the input variable rather than a bundle of the different resources that the firm uses in producing units of output. As discussed in the previous section, labor is typically the input that is the most identifiable and calculable for measuring productivity. However, any input that is not difficult to quantify can be used. An example will illustrate the practicality of using a single factor input, such as labor, to evaluate the firm’s output performance. A business that manually assembles widgets has 50 workers, one production facility, and an assortment of equipment and hand tools. The firm would like to assess its productivity when it utilizes these three types of input factors to produce widgets. In this case, the most appropriate method is to use labor as the input factor for determining productivity because the firm uses a variety of physical capital and only one plant building.
To illustrate the concepts of total product, average product, and marginal product, labor is used as the input variable. Exhibit 35 provides a summary of definitions and tabulations for these three concepts.Exhibit 35. Definitions and Calculations for Total, Marginal, and Average Product of Labor
|Total product||Sum of the output from all inputs during a time period; usually illustrated as the total output (TP or Q) using labor (L)|
|Average product||Total product divided by the quantity of a given input; measured as total product divided by the number of workers used at that output level; (TP ÷ L) or (Q ÷ L)|
|Marginal product||The amount of additional output resulting from using one more unit of input assuming other inputs are fixed; measured by taking the difference in total product and dividing by the change in the quantity of labor; (∆TP ÷ ∆L) or (∆Q ÷ ∆L)|
Measured on the basis of the labor input, total product (TP or Q) is defined as the aggregate sum of production for the firm during a time period. As a measure of productivity, total product provides superficial information as to how effective and efficient the firm is in terms of producing output. For instance, three firms—Company A, Company B, and Company C—that comprise the entire industry have total output levels of 100,000 units, 180,000 units, and 200,000 units, respectively. Obviously, Company C dominates the market with a 41.7 percent share, followed by Company B’s 37.5 percent share and Company A’s 20.8 percent portion of the market. This information says little about how efficient each firm is in generating its total output level. Total product only provides an insight into the firm’s production volume relative to the industry; it does not show how efficient the firm is in producing its output.
Average product (AP) measures the productivity of inputs on average and is calculated by dividing total product by the total number of units for a given input that is used to generate that output. Average product is usually measured on the basis of the labor input. It is a representative or overall measure of labor’s productivity: Some workers are more productive than average, and others are less productive than average.
Given the aforementioned production levels for the three firms, Company A employs 100 workers, and Company B and Company C utilize 200 and 250 workers, respectively. Calculating average product of labor for each of the three firms yields the following productivity results: Company A→1,000 units of output per worker, Company B→900 units per worker, and Company C→800 units per worker. It is apparent that Company A is the most efficient firm, although it has the lowest share of the total market. Company C has the largest portion of the total market, but it is the least efficient of the three. Given that Company A can maintain its productivity advantage over the long run, it will be positioned to generate the greatest return on investment through lower costs and higher profit outcomes relative to the other firms in the market.
Marginal product (MP), also known as marginal return, measures the productivity of each unit of input and is calculated by taking the difference in total product from adding another unit of input (assuming other resource quantities are held constant). Typically, it is measured in terms of labor’s performance; thereby, it is a gauge of productivity of the individual additional worker rather than an average across all workers.
Exhibit 36 provides a numerical illustration for total, average, and marginal products of labor.Exhibit 36. Total, Average, and Marginal Product of Labor
Total product increases as the firm adds labor until worker 7, where at that point total production declines by 70 units. Obviously, the firm does not want to employ any worker that has negative productivity. In this case, no more than six workers are considered for employment with the firm.
At an employment level of five workers, AP and MP are 80 units (400 ÷ 5) and 40 units [(400 – 360) ÷ (5 – 4)], respectively. The productivity of the fifth worker is 40 units, while the average productivity for all five workers is 80 units, twice that of worker 5.
A firm has a choice of using total product, average product, marginal product, or some combination of the three to measure productivity. Total product does not provide an in-depth view of a firm’s state of efficiency. It is simply an indication of a firm’s output volume and potential market share. Therefore, average product and marginal product are better gauges of a firm’s productivity because both can reveal competitive advantage through production efficiency. However, individual worker productivity is not easily measurable when workers perform tasks collectively. In this case, average product is the preferred measure of productivity performance.
Referring to the marginal product column in Exhibit 36, worker 2 has a higher output of 110 units compared with worker 1 who produces 100 units; there is an increase in return when employees are added to the production process. This economic phenomenon is known as increasing marginal returns, where the marginal product of a resource increases as additional units of that input are employed. However, successive workers beyond number 2 have lower and lower marginal product to the point where the last worker has a negative return. This observation is called the law of diminishing returns. Diminishing returns can lead to a negative marginal product as evidenced with worker 7. There is no question that a firm does not want to employ a worker or input that has a negative impact on total output.
Initially, a firm can experience increasing returns from adding labor to the production process because of the concepts of specialization and division of labor. At first, by having too few workers relative to total physical capital, the understaffing situation requires employees to multi-task and share duties. As more workers are added, employees can specialize, become more adept at their individual functions, and realize an increase in marginal productivity. But after a certain output level, the law of diminishing returns becomes evident.
Assuming all workers are of equal quality and motivation, the decline in marginal product is related to the short run, where at least one resource (typically plant size, physical capital, and/or technology) is fixed. When more and more workers are added to a fixed plant size-technology-physical capital base, the marginal return of the labor factor eventually decreases because the fixed input restricts the output potential of additional workers. One way of understanding the law of diminishing returns is to void the principle and assume that the concept of increasing returns lasts indefinitely. As more workers are added, or when any input is increased, the marginal output continuously increases. At some point, the world’s food supply could be grown on one hectare of land or all new automobiles could be manufactured in one factory. Physically, the law of increasing returns is not possible in perpetuity, even though it can clearly be evident in the early stages of production.
Another element resulting in diminishing returns is the quality of labor itself. In the previous discussion, it was assumed all workers were of equal ability. However, that assumption may not be entirely valid when the firm’s supply of labor has varying degrees of human capital. In that case, the business would want to employ the most productive workers first; then, as the firm’s labor demand increased, less-productive workers would be hired. When the firm does not have access to an adequate supply of homogenous human capital, or for that matter any resource, diminishing marginal product occurs at some point.EXAMPLE 10
Average product and marginal product can be calculated on the basis of the production relationship between the number of machines and total product, as indicated in the first two columns of Exhibit 37.
Interpret the results for total, average, and marginal product.
Indicate where increasing marginal returns change to diminishing marginal returns.
|Machines (K)||Total Product (TPK)||Average Product (APK)||Marginal Product (MPK)|
Total product increases to six machines, where it tops out at 7,500. Because total product declines from machine 6 to machine 7, the marginal product for machine 7 is negative 500 units. Average product peaks at 1,600 units with four machines.
Increasing returns are evident up to machine 3, where marginal product equals 2,000 units of output. Beyond machine 3, decreasing returns develop because MPK declines when more machines are added to the production process.
The data provided in Exhibit 38 show productivity changes for various US industries over the period 2000–2007. The coal mining and newspaper sectors have several years of negative changes in productivity, which do not reinforce prospects for long-term growth in profitability. Declines in productivity raise production costs and reduce profit. For the most part, the other industries have solid productivity increases from year to year, even though in some cases the change is volatile. On a trend basis, productivity increases appear to have peaked in the period 2002–2004 and then edged downward during the latter part of the period. Declining productivity makes a firm or industry less competitive over time; however, any adverse impact on profitability stemming from lower or negative productivity may be offset by rising demand for the product.Exhibit 38. Productivity Changes for Selected Sectors, 2000–2007
1North American Industry Classification System.
Note: Productivity is defined by the US Bureau of Labor Statistics as output per worker-hour.
Source: US Bureau of Labor Statistics, “Productivity and Costs by Industry: Annual Rates of Change.”
Productivity is a key element in the determination of costs and profit to the firm, especially over the long term. Although productivity can fluctuate widely in the short run (as indicated in Exhibit 38) for a variety of reasons, secular patterns in output per unit of labor denote more meaningful relationships among productivity, costs, profits, and the competitive status of the firm with respect to the industry. To summarize, the analyst should study the productivity levels of the firm over the long run and do an evaluation of how the firm’s efficiency compares with the industry standard. A firm that lags the industry in productivity may find itself at a competitive disadvantage with the end result of profit erosion and negative implications for shareholders’ wealth. Once evident, productivity issues cause the firm’s market value of equity to be discounted.
As previously discussed, a major determinant of the cost component of the profit equation is the degree of efficiency in which the firm uses resources in producing output as defined by the firm’s production function. Given the relationship between output and inputs, marginal product (MP) and average product (AP) form the basis for marginal cost (MC) and average variable cost (AVC). Actually, MC and AVC are respective mirror images of MP and AP. Exhibit 39 illustrates this relationship in the short run by showing three areas of interest.Exhibit 39. Relationship of Average Product and Marginal Product to Average Variable Cost and Marginal Cost in the Short Run
Area 1 shows an increasing MP from L0 to L1. The increases in MP result in declining marginal costs from Q0 to Q1. As MP or productivity peaks at L1, MC is minimized at Q1. Diminishing marginal returns take over in Areas 2 and 3, where a decreasing marginal product results in higher marginal costs. Not only does MP impact MC, but the shape of the AVC also is based on the pattern of AP. At L2, AP is maximized, while its corresponding output level of Q2 is consistent with the minimum position on the AVC curve. Note that when MP is greater than AP, AP is increasing; when MP is less than AP, AP is declining. A similar relationship holds true for MC and AVC. When MC is less than AVC, AVC is decreasing; the opposite occurs when MC is greater than AVC. In Area 3, AP is declining, which creates an upturn in the AVC curve.
Technology, quality of human and physical capital, and managerial ability are key factors in determining the production function relationship between output and inputs. The firm’s production function establishes what productivity is in terms of TP, MP, and AP. In turn, productivity significantly influences total, marginal, and average costs to the firm, and costs directly impact profit. Obviously, what happens at the production level in terms of productivity impacts the cost level and profitability.
Because revenue, costs, and profit are measured in monetary terms, the productivity of the different input factors requires comparison on a similar basis. In this regard, the firm wants to maximize output per monetary unit of input cost. This goal is denoted by the following expression:
where MPinput is the marginal product of the input factor and Pinput is the price of that factor (i.e., resource cost).
When using a combination of resources, a least-cost optimization formula is constructed as follows:
where the firm utilizes n different resources. Using a two-factor production function consisting of labor and physical capital, Equation 9 best illustrates this rule of least cost:
where MPL and MPK are the marginal products of labor and physical capital, respectively. PL is the price of labor or the wage rate, and PK is the price of physical capital. For example, if MPL/PL equals two and MPK/PK is four, physical capital yields twice the output per monetary unit of input cost versus labor. It is obvious that the firm will want to use physical capital over labor in producing additional output because it provides more productivity on an equivalent cost basis. However, as more physical capital is employed, the firm’s MP of capital declines because the law of diminishing returns impacts production. Physical capital is added until its ratio of MP per monetary unit of input cost matches that of labor: MPK/PK = MPL/PL = 2.5 At this point, both inputs are added when expanding output until their ratios differ. When their ratios diverge, the input with the higher ratio will be employed over the other lower ratio input when the firm increases production.EXAMPLE 11
Canadian Global Electronic Corp. (CGEC) uses three types of labor—unskilled, semi-skilled, and skilled—in the production of electronic components. The firm’s production technology allows for the substitution of one type of labor for another. Also, the firm buys labor in a perfectly competitive resource market in which the price of labor stays the same regardless of the number of workers hired. In the following table, the marginal productivity and compensation in Canadian dollars for each type of labor is displayed.
What labor type should the firm hire when expanding output?
|Type of Labor||Marginal Product|
per Day ($)
|Unskilled (U)||200 units (MPU)||100 (PU)||2 units per $|
|Semi-skilled (SS)||500 units (MPSS)||125 (PSS)||4 units per $|
|Skilled (S)||1,000 units (MPS)||200 (PS)||5 units per $|
The firm minimizes cost and enhances profitability by adding skilled labor over the other two types because it has the highest ratio of MP to input price. As the marginal product of skilled labor declines with additional workers, MPS/PS decreases. When it declines to the same value as semi-skilled labor, both skilled and semi-skilled workers are added because their productivity per Canadian dollar of input cost is identical. Again, a diminishing marginal product decreases both ratios. When all three labor inputs have the same MPinput/Pinput, the firm will add all three labor types at the same time when expanding output.
Equations 7, 8, and 9 derive the physical output per monetary unit of input cost. However, to determine the profit-maximizing utilization level of an input, the firm must measure the revenue value of the input’s MP and then compare this figure with the cost of the input. The following equations represent this relationship:
Marginal product × Product price = Price of the input
Marginal revenue product = Price of the input
Marginal revenue product (MRP) is calculated as the MP of an input unit times the price of the product. This term measures the value of the input to the firm in terms of what the input contributes to TR. It is also defined as the change in TR divided by the change in the quantity of the resource employed. If an input’s MRP exceeds its cost, a contribution to profit is evident. For example, when the MP of the last unit of labor employed is 100 and the product price is 2.00, the MRP for that unit of labor (MRPL) is 200. When the input price of labor is 125, the surplus value or contribution to profit is 75. In contrast, if MRP is less than the input’s price, a loss would be incurred from employing that input unit. If the MP of the next unit of labor is 50 with a product price of 2.00, MRPL will now be 100. With the same labor cost of 125, the firm would incur a loss of 25 when employing this input unit. Profit maximization occurs when the MRP equates to the price or cost of the input for each type of resource that is used in the production process.
In the case of multiple factor usage, the following equation holds true for n inputs:
When profit is maximized, MRP equals the input price for each type of resource used and all MRPinput/Pinput are equal to one.EXAMPLE 12
Using the data from the previous case of Canadian Global Electronic Corp., the table below shows the MRP per labor type when product price in Canadian dollars is $0.50. MRP per day is calculated as the MP per type of labor from Example 11 multiplied by the product price.
Which type of labor contributes the most to profitability?
|Type of Labor||Marginal Revenue Product (MRPinput)|
per Day ($)
per Day ($)
|Unskilled (U)||100 (MRPU)||100 (PU)||1.0|
|Semi-skilled (SS)||250 (MRPSS)||125 (PSS)||2.0|
|Skilled (S)||500 (MRPS)||200 (PS)||2.5|
Calculating the MRPinput/Pinput values for the different labor categories yields ratio numbers of 1.0, 2.0, and 2.5 for unskilled, semi-skilled, and skilled labor, respectively. The firm adds skilled labor first because it is the most profitable to employ, as indicated by MRPS/PS being the highest ratio of the three labor inputs. The contribution to profit by employing the next skilled worker is $300, calculated as ($500 – $200). However, with the employment of additional skilled workers, MRPS declines because of diminishing returns that are associated with the MP component. At the point where the skilled labor ratio drops below 2.0—for example, to 1.5—semi-skilled labor becomes feasible to hire because its MRP exceeds its compensation by more than that of skilled labor.6 Again, the diminishing returns effect decreases MRP when additional semi-skilled workers are hired. In the case of unskilled labor, MRPU equals the cost of labor; hence, no further contribution to profit accrues from adding this type of labor. In fact, adding another unskilled worker would probably reduce total profit because the next worker’s compensation is likely to exceed MRP as a result of a declining MP. The input level that maximizes profit is where MRPU/PU = MRPSS/PSS = MRPS/PS = 1.