Aggregating Supply Functions
An individual seller’s monthly supply of downloadable e-books is given by the equation
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.
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:
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.