Question

the inverse supply is p=.2Q-20 and inverse demand is P=40-.2Q. there is a price floor of $12, what is the producer and consumer surplus

Answer 1

Equating, the invese supply and demand we have

.2Q-20 =40-0.2Q

0.4Q=60

Q=60/0.4 = 150

P=0.2*150-20 = 10

The total surplus is (demand intercept-supply intercept)*quantity*0.5=(40+20)*150*0.5 = 4500

Since the price floor is 12>10, it is binding.

Now, the Quantity sold= quantity demanded

12=40-.2Q

Q=28*5 = 140

For a supply of 140, the price should be .2*140-20=8

The consumer surplus is (demand intercept-price)*quantity*0.5 = (40-12)*140*0.5 = 1960 (Ans)

The deadweight loss is 0.5*(change in quantity)*(Difference in price for supplier and demand for the same amount of quantity) = 0.5*(150-140)*(12-8) = 20

Thus, the producer surplus is Equilibrium Surplus - CS - DWL = 4500-1960-20 = 2520 (Ans)