Question

Suppose that the short-run supply and demand for pineapples in a certain town are described by the following two equations:

Q^S= 1,000,

Q^D= 2,000−200p.

Pineapples are an imported produce in this market, so the government imposes a tax of $1 per pineapple. Which of the following statements is true?

1. The after-tax equilibrium is given by p^S=5, p^B=6 and Q^T= 1,000.
2. The after-tax equilibrium is given by p^S=4, p^B=5 and Q^T= 1,000.
3. The deadweight loss of this tax is zero.
4. Only (a) and (c).
5. Only (b) and (c)

Answer 1

The correct option would be

• e. Only (b) and (c).

The pre-tax equilibrium in the market would be where or or or , and or or . But, if a tax is imposed on the producers, since the supply is inelastic (invariant to price), the tax would entirely be paid by producers. Hence, the price received to suppliers would be equilibrium price minus tax, ie $5 minus $1 or $4, while price paid by buyers would be the equilibrium price $5, and the equilibrium quantity would be same as before of 1000 units. The dead-weight loss occurs in case where the quantity traded in the market is reduced, which in this case is 0, and hence the dead-weight loss is zero.

The algebra is as follows. The quantity supplied is taken as , and in this case, as since the slope of supply curve is zero. The imposition of tax affects the supply curve as for t be the tax and p-t is price received by suppliers, and in this case it would be or . As can be seen, the supply curve is unaltered, and the market equilibrium quantity and price (price paid by buyers) is same as before. All that changes is the price received by sellers.