Problem on free trade equilibrium

Question

The domestic demand curve for portable radios is provided by Q^d = 5000 − 100P, here Qd is the number of radios which would be purchased whenever the price is P. The domestic supply curve for radios is provided by Q^s = 150P, where Q^s is the amount of radios which would be generated domestically when the price were P. Assume that radios can be received in the world market at a price of $10 per radio. The Domestic radio producers have effectively lobbied Congress to oblige a tariff of $5 per radio.

a) Sketch a graph stating the free trade equilibrium (with no tariff). Clearly state the equilibrium price.

b) By how much would tariff rise producer excess for domestic radio suppliers?

c) How much would govt. collect in tariff revenues?

d) Determine deadweight loss from the tariff?

Answer 1

a)

In free trade equilibrium, domestic demand is 4000, domestic supply is 1500, and import is 2500 units.

b) The producer excess with free trade would be 1/2(10-0)(1500). With the tariff, domestic supply will raise to 2250 and producer surplus will raise to 1/2(15-0)(2250) = 16875. Therefore producer surplus will rise by 9,375.

c) Through tariff, domestic demand will drop to 3500 units and domestic demand will rise to 2250 units.  Therefore, 1250 units will be imported.  The tariffs of $5 on each of such units will outcome in government receipts of 6,250.

d) The deadweight loss from tariff will come from two sources. First, the deadweight loss is related overproduction of domestic suppliers will be 1/2 (2250-1500)5 = 1875. Second, the deadweight loss is related with the reduction in consumption by consumers due to the tariff is 1/2 (4000-3500)5 = 1250.  Thus, the total deadweight loss with this tariff is 3,125.