Question

Suppose demand for automobiles in the United States is given by: P= 100−0.09QD where P is the price for new vehicles in dollars and QD is the quantity demanded per month. Assume the supply of automobiles is given by P= 4 + 0.03QS where again P is the price in thousands of dollars and QS is the quantity sold per month in hundreds of thousands.

a.) Solve for the market equilibrium price and quantity.

b.) Depict this market graphically, and compute consumer and producer surplus in this market.

c.) Suppose that the negative external cost of each automobile is $6. Add the social cost curve to your graph, and calculate the amount of the externality and the deadweight loss.

d.) Suppose we institute a tax on automobiles that fully internalizes the externality. Indicate how this affects the market graphically, and solve for consumer surplus, producer surplus, and the total amount of the tax revenue.

Answer 1

d)

The tax that internalizes the externality is $6 per unit tax. This changes the supply curve to shift to the left. the new supply curve coincides with the MSC curve and new equilibrium occurs at Q*=750 and P=32.5. The consumer and producers' surplus is

$\small CS=\frac{1}{2}\times (100-32.5)\times 750=25312.5$

$\small PS=\frac{1}{2}\times (32.5-4)\times 750=10687.5$

$\small Tax=6\times 750=4500$