Suppose that the supply function for apples is Qs = 30 + 0.2Pa - 6 W (1.1) where

Question

Suppose that the supply function for apples is

Qs = 30 + 0.2Pa - 6 W (1.1)

where Qs is the quantity supplied of apples in millions of pounds. Pa is the market price of apples in cents and W is the hourly wage rate paid to agricultural workers. Currently the wage rate is $5 per hour. Substituting this value for W in equation 3.1, and solving for Pa produces this current supply curve

Pa = 5Qs (1.2)

Suppose that the demand function for apples is

Qd = 20 -1/3Pa + 0.002I (1.3)

where I is per capita income, and currently is $10,000.

What is the equilibrium Price and Quantity for apples? Show your work

Explanation / Answer

Supply equation: Pa = 5Q       or                     Q = .2Pa

Demand equation: Q = 20-(1/3)Pa + .002*10000 = 20- (1/3)Pa + 20

At equilibrium,

Demand = Supply

.2Pa = 40-(1/3)Pa

Pa = 40/(.2 + 1/3) = 75

Q = .2*75 = 15

So, equilibrium price of apple is 75 cents and equilibrium quantity is 15 millions of pounds.

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