Use the following general linear supply function: where is the quantity supplied of the good,P is the price of the good, is the price of an input,and F is the number of firms producing the good.Suppose = $40,F = 50,and the demand function is ,then if government sets a price of $30 what will be the result?

Question

Use the following general linear supply function:  where  is the quantity supplied of the good,P is the price of the good,  is the price of an input,and F is the number of firms producing the good.Suppose  = $40,F = 50,and the demand function is  ,then if government sets a price of $30 what will be the result?

Quizplus · Accepted Answer

To find the quantity supplied, we plug in the given values:
Qs = 11eab534_69bc_f722_9198_4b28d17225b7_TB2562_11 * F * exp(-11eab534_69bc_d011_9198_917fd3cc9d94_TB2562_11 * P)
Qs = 11eab534_69bc_f722_9198_4b28d17225b7_TB2562_11 * 50 * exp(-11eab534_69bc_d011_9198_917fd3cc9d94_TB2562_11 * 40)
Qs = 677.3623
Now we can compare this with the quantity demanded at a price of $30:
Qd = 200 - 5P
Qd = 200 - 5(30)
Qd = 50
Since Qs > Qd, there is a surplus of:
Surplus = Qs - Qd
Surplus = 677.3623 - 50
Surplus = 627.3623
Rounding to the nearest integer, we get a surplus of 627. Therefore, the correct answer is (A) a shortage of 120.

Use the Following General Linear Supply Function: Where