#cfa #cfa-level-1 #economics #microeconomics #reading-13-demand-and-supply-analysis-introduction #study-session-4
Aggregating Supply Functions

An individual seller’s monthly supply of downloadable e-books is given by the equation

Qseb=−64.5+37.5Peb−7.5W

where Qseb is number of e-books supplied, Peb is the price of e-books in euros, and W is the wage rate in euros paid by e-book sellers to laborers. Assume that the price of e-books is €10.68 and wage is €10. The supply side of the market consists of a total of eight identical sellers in this competitive market.

1. Determine the market aggregate supply function.

2. Determine the inverse market supply function.

3. Determine the slope of the aggregate market supply curve.

Solution to 1:

Aggregating supply functions means summing up the quantity supplied by all sellers. In this case, there are eight identical sellers, so multiply the individual seller’s supply function by eight:

Qseb=8(−64.5+37.5Peb−7.5W)=−516+300Peb−60W

Solution to 2:

Holding W constant at a value of €10, insert that value into the aggregate supply function and then solve for Peb to find the inverse supply function:

Qeb = –1,116 + 300Peb

Inverting, Peb = 3.72 + 0.0033Qeb

Solution to 3:

The slope of the supply curve is the coefficient on Qeb in the inverse supply function, which is 0.0033.

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3.5. Aggregating the Demand and Supply Functions
5Q eb Solution to 3: The slope of the market demand curve is the coefficient on Q eb in the inverse demand function, which is −0.0025. EXAMPLE 5 <span>Aggregating Supply Functions An individual seller’s monthly supply of downloadable e-books is given by the equation Qseb=−64.5+37.5Peb−7.5W where Qseb is number of e-books supplied, P eb is the price of e-books in euros, and W is the wage rate in euros paid by e-book sellers to laborers. Assume that the price of e-books is €10.68 and wage is €10. The supply side of the market consists of a total of eight identical sellers in this competitive market. Determine the market aggregate supply function. Determine the inverse market supply function. Determine the slope of the aggregate market supply curve. Solution to 1: Aggregating supply functions means summing up the quantity supplied by all sellers. In this case, there are eight identical sellers, so multiply the individual seller’s supply function by eight: Qseb=8(−64.5+37.5Peb−7.5W)=−516+300Peb−60W Solution to 2: Holding W constant at a value of €10, insert that value into the aggregate supply function and then solve for P eb to find the inverse supply function: Q eb = –1,116 + 300P eb Inverting, P eb = 3.72 + 0.0033Q eb Solution to 3: The slope of the supply curve is the coefficient on Q eb in the inverse supply function, which is 0.0033. <span><body><html>