Question

4. Please consider the following market:

Demand by P = 19 - 2Q

Supply by P = 5Q

a. Please solve the equilibrium Quantity and Price. and calculate the CS (consumer’s surplus), PS (producer’s surplus), DWL (if there is any), and ES (Economics surplus)

Suppose we now place a tax of $5 per unit of output on the seller.

b. What would the new supply curve is?

c. Please solve the new equilibrium quantity and price.

If the demand curve of a market become P = 14 - Q and the supply curve is P = 2 + 2Q, but a price ceiling of 6 is imposed:

d. Would there be a surplus or shortage? If yes, how much?

e. Please calculate PS, CS, DWL and ES

Answer 1

a) Equilibrium occurs when demand = supply

19 - 2Q = 5Q

Q = 2.71

At this Q, P = 13.57

Consumer surplus is area of portion A + B + C whose sum is (1/2) * (19 - 13.57) * (2.71 - 0) = 7.36\

Producer surplus is area of portion D + E + F whose sum is (1/2) * (13.57 - 0) * (2.71 - 0) = 18.39

b) When a tax of $5 is imposed, new supply curve would be P = 5Q + 5

c) Price paid by consumer rises to 15 and price received by producer falls by 10 which reduce quantity traded to 2 units

d) If there is a price ceiling at $6, there is quantity demanded of 8 units while supply of 2 units which result in shortage of 8 - 2 = 6 units.

e)

Consumer surplus before price ceiling is area of portion G + H + I whose sum is (1/2) * (14 - 10) * (4 - 0) = 8

Producer surplus before price ceiling is area of portion J + K + L whose sum is (1/2) * (10 - 2) * (4 - 0) = 16

After price ceiling:

Consumer surplus after price ceiling is area of portion G whose sum is (1/2) * (14 - 12) * (2 - 0) = 2

Producer surplus after price ceiling is area of portion J + K + H whose sum is (12 - 6) * (2 - 0) + (1/2) * (6 - 2) * (2 - 0) = 12 + 4 = 16

Deadweight loss is area of portion I + K whose sum is (1/2) * (12 - 6) * (4 - 2) = 6