Question

Problem 6 Suppose that in the short run, demand for chicken sausage is given by Q = 100, 000 − 5, 000P and supply by Q = 80, 000 + 5, 000P , and that the equilibrium price and quantity in the market are $2/lb. and 90,000 lbs. respectively.

(i) (3 points) Suppose a $0.50 per-unit tax is imposed on consumers in the market. Find the post-tax quantity, the price paid by consumers, and the price received by producers.

(ii) (2 points) How much of the tax burden is borne by consumers in the long run? Explain.

Answer 1

i) Q = 100,000 − 5,000P

5,000P = 100,000 - Q

P = 20 - 0.0002Q               [This is inverse demand function]

Q = 80,000 - 5,000P

5,000P = -80,000 + Q

P = -16 + 0.0002Q             [This is inverse supply function]

When a tax of $0.50 per unit is imposed on consumer, the demand curve becomes,

P + 0.50 = 20 - 0.0002Q

P = 19.50 - 0.0002Q

The new equilibrium is

19.50 - 0.0002Q = -16 + 0.0002Q

0.0004Q = 35.5

Q = 35.5 / 0.0005 = 88,750

The price paid by consumers: P = 20 - 0.0002Q = 20 - 0.0002(88,750) = $2.25

The price received by the producers: P = -16 + 0.0002Q = -16 + 0.0002(88,750) = $1.75

ii) The tax burden borne by consumers in the long run = $2.25 - $2 = $0.25.

    The tax burden borne by producers in the long run = $2 - $1.75 = $0.25.