Question

Suppose that, in the market for litres petrol, demand is given by P = 5 – 0.3Q, and supply is given by P = 1 + 0.1Q.

Further, suppose that the government provides a $1 per litre subsidy for petrol.

A. Calculate the effect of the subsidy on the equilibrium price and quantity.

B. Calculate the change in producer surplus and consumer surplus that result from the provision of the subsidy.

C. Does total surplus to everyone in the economy increase or decrease as a result of the subsidy? Explain why and calculate the amount of the change.

Answer 1

Demand: P = 5 - 0.3Q

Supply: P = 1 + 0.1Q

At equilibrium, demand equals supply

5 - 0.3Q = 1 + 0.1Q

Q = 10

At Q = 10, P = 2

a) If there is $1 subsidy, consumers would get benefit of $0.75 out of it while prodcers gets benefit of $0.25 per unit sold. Consumer would pay a price of $1.25 and producer recieve $2.25. Quantity traded at this price is 12.5 units.

b) Initial consumer surplus was area of portion A + B whose sum is (1/2) * (10 - 0) * (5 - 2) = 15

Initial producer surplus was area of portion C + D whose sum is (1/2) * (10 - 0) * (2 - 1) = 5

New consumer surplus was area of portion A + B + C + F + G whose sum is (1/2) * (12.5 - 0) * (5 - 1.25) = 23.43

New producer surplus was area of portion C + D + B + E whose sum is (1/2) * (12.5 - 0) * (2.25 - 1) = 7.81

Consumer surplus change by 23.43 - 15 = 8.43

Producer surplus change by 7.81 - 5 = 2.81

c) Government revenue is -(B + E + C + F + G + H) whose sum is (12.5 - 0) * (2.25 - 1.25) = 12.5

Change in Total surplus = Consumer surplus change + Producer surplus change - Government Revenue = 8.43 + 2.81 - 12.5 = -1.26