Question

Use the following general linear supply function: Qs = 40 + 6P − 8PI + 10F where Qs is the quantity supplied of the good, P is the price of the good, PI is the price of an input, and F is the number of firms producing the good. Suppose PI = $40, F = 50, and the demand function is Qd = 700 − 6P, then if government sets a price of $50 what will be the result?

a) shortage of 120

b) a surplus of 120

c) a shortage of 160

d) a surplus of 160

Answer 1

Supply Function

Qs = 40 + 6P − 8PI + 10F

PI = 40

F = 50

Qs = 40 + 6P − 8(40) + 10(50)

Qs = 40 + 6P - 320 + 500

Qs = 220 + 6P

Demand Function

Qd = 700 − 6P

If the government sets the price of $50

Demand at $50 will be

Qd = 700 − 6P

Qd = 700 − 6(50)

Qd = 400

Supply at $50 will be

Qs = 220 + 6P

Qs = 220 + 6(50)

Qs = 520

So at a price of $50 demand is 400 units and supply is 520 units that means supply is more than demand so there is a surplus in the market at this price.

Surplus = Supply - Demand

Surplus = 520 - 400

Surplus = 120

Hence option B is correct