Question

The inverse Demand is given by: P=40-0.2Q and the inverse supply is given by: P=0.2Q-20. If a price ceiling of $6 is imposed, then Producer surplus and DWL are:  (Hint: it helps to draw a graph for this question).

Answer 1

P=40-0.2Q

P=0.2Q-20

Equilibrium quantity is 40-0.2Q=0.2Q-20

Q=60/0.4 = 150

The price ceiling is $6

If the price is $6, the demand is 6=40-0.2*Q Q=34/0.2=170

If the price is $6, the supply is 6=0.2*Q-20 Q=26/0.2=130

Since the demand is higher than supply, it must be binding.

The producer surplus 0.5*(quantity supplied)*(P-Price at which supplier produces nothing) = 0.5*130*(6+20)

=1690(Ans)

We also have  P=40-0.2*130=$14 at which demand is 130

The dead weight loss is 0.5*(Difference in quantity)*(Difference in price for the quantity)

=0.5*(150-130)*(14-6)

=80 (Ans)