The demand for gasoline is given by P = 100 Q, while the supply (and private mar

Question

The demand for gasoline is given by P = 100 Q, while the supply (and private marginal costs) are given by P=20+Q. The marginal social costs of oil is given by P = 30 + Q. That is, each unit of oil consumed imposes $10 in extra cost on society, over and above the private cost of production. Assume that the gasoline market is perfectly competitive.

a) Find the price and quantity of gasoline sold in the market

b) What is the dead weight loss?

c) Because of new oil discoveries, the marginal private cost schedule shifts to P = 10 + Q. Calculate the new equilibrium price and quantity.

Explanation / Answer

           P=20+Q

          IN EQUILIBRIUM, 100-Q = 20+Q

          80 = 2Q OR Q=40

          P= 100-Q= 100-40 =60

          PRIVATE EQ, P=60, Q=40

2. SOCIAL COST, P=30+Q

SOCIAL EQ, 30+Q = 100-Q

2Q = 70 OR Q = 35

P = 100-Q = 100-35 =65

SOCIAL EQ, P=65, Q=35

DEADWEIGHT LOSS = AREA OF THE TRIANGLE

=1/2 * DIFFERENCE IN PRICE * DIFFERENCE IN QUANTITY

=1/2 * (65-55) * (40-35)

=1/2 * 10 * 5 = 5*5 = 25

3.P= 10+Q

IN EQUILIBRIUM, 100-Q=10+Q

90=2Q or Q=45

P=100-Q= 100-45=55

NEW PRIVATE EQ, P=55, Q=45

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