#cfa-level-1 #economics #microeconomics #reading-15-demand-and-supply-analysis-the-firm #section-3-analysis-of-revenue-costs-and-profit #study-session-4

A more general production function is stated as:

Equation (6)

Q = f (x1, x2, … xn)

where xi represents the quantity of the ith input subject to xi ≥ 0 for n number of different inputs.

If you want to change selection, open original toplevel document below and click on "Move attachment"

#### Parent (intermediate) annotation

Open it
n function , and it is represented generally as: Equation (5)  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. <span>A more general production function is stated as: Equation (6)  Q = f (x 1 , x 2 , … x n ) where x i represents the quantity of the ith input subject to x i ≥ 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

#### Original toplevel document

3. ANALYSIS OF REVENUE, COSTS, AND PROFITS
ationships among the revenue variables presented in Exhibit 7. Exhibit 8. Total Revenue, Average Revenue, and Marginal Revenue for Exhibit 7 Data <span>3.1.2. Factors of Production 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: Equation (5)  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: Equation (6)  Q = f (x 1 , x 2 , … x n ) where x i represents the quantity of the ith input subject to x i ≥ 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 (L 0 – L 1 ), TP is increasing at an increasing rate, typically because specialization allows laborers to become increasingly productive. In Region 2, however, (L 1 – L 2 ), 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 EXAMPLE 3 Factors of Production A group of business investor