Question

The domestic demand for portable radios is given by $$Q=5,000-100 \mathrm{P}$$ where price \(\mathrm{(P)}\) is measured in dollars and quantity \(\mathrm{(Q)}\) is measured in thousands of radios per year. The domestic supply curve for radios is given by $$Q=150 \mathrm{P}$$ a. What is the domestic equilibrium in the portable radio market? b. Suppose portable radios can be imported at a world price of $$\$ 10$$ per radio. If trade were unencumbered, what would the new market equilibrium be? How many portable radios would be imported? c. If domestic portable radio producers succeeded in having a $$\$ 5$$ tariff implemented, how would this change the market equilibrium? How much would be collected in tariff revenues? How much consumer surplus would be transferred to domestic producers? What would the deadweight loss from the tariff be? d. How would your results from part (c) be changed if the government reached an agreement with foreign suppliers to "voluntarily" limit the portable radios they export to \(1,250,000\) per year? Explain how this differs from the case of a tariff.

Short answer

In summary, the domestic equilibrium in the portable radio market is initially P=$20 and Q=3,000 radios per year. With free trade, the market equilibrium shifts to P=$10 and Q=4,000 radios per year, with 2,500 portable radios being imported. When a $5 tariff is implemented, the new equilibrium is P=$15 and Q=3,500 radios per year, with $6,250 collected in tariff revenues, $6,250 transferred from consumer surplus to domestic producers, and a deadweight loss of $3,125. Under a voluntary export restraint, the prices, quantities, and deadweight losses are the same as in the tariff scenario. The main difference is the distribution of revenues, with export restraint revenues going to foreign suppliers instead of the domestic government.

Step-by-step solution

a. Finding the domestic equilibrium

To find the domestic equilibrium, set the demand and supply equations equal to each other, and solve for \(\mathrm{P}\) and \(\mathrm{Q}\): $$5,000 - 100P = 150P$$ Then, $$5,000 = 250P$$ $$P=20$$ Now use either the demand or supply equation to find the equilibrium quantity: $$Q = 5,000 - 100(20) = 5,000 - 2,000 = 3,000$$ The domestic equilibrium in the portable radio market is \(\mathrm{P} = \$20\) and \(\mathrm{Q} = 3,000\) radios per year.

b. Analyzing the impact of free trade on market equilibrium

If trade were unencumbered, portable radios would be imported at a world price of \(\$10\) per radio. In this case, the demand equation remains the same, but now quantity supplied decreases since \(\mathrm{P}\) decreases: $$Q^s = 150(10) = 1,500$$ To find the imported quantity of radios, we need to evaluate the domestic demand at this lower world price: $$Q^d = 5,000 - 100(10) = 5,000 - 1,000 = 4,000$$ The imported quantity is the difference between the domestic demand and the domestic supply: $$Q^I = Q^d - Q^s = 4,000 - 1,500 = 2,500$$ Therefore, with free trade, the new market equilibrium is \(\mathrm{P} = \$10\) and \(\mathrm{Q} = 4,000\) radios per year, with \(2,500\) portable radios being imported.

c. Analyzing the impact of a \(\$5\) tariff on the market equilibrium

If a \(\$5\) tariff is implemented, the new market price would increase to \(\$15\). Thus, the quantity supplied would increase and the domestic demand would decrease: $$Q^{s'} = 150 (15) = 2,250$$ $$Q^{d'} = 5,000 - 100(15) = 5,000 - 1,500 = 3,500$$ The imported quantity is the difference between the new domestic demand and the new domestic supply: $$Q^{I'} = Q^{d'} - Q^{s'} = 3,500 - 2,250 = 1,250$$ 1. Tariff revenues: The government would collect tariff revenues based on the tariff per radio and the quantity of radios imported: $$\$5 * 1,250 = \$6,250$$ 2. Change in consumer surplus: The increase in price from \(\$10\) to \(\$15\) redistributes consumer surplus to domestic producers. The transferred consumer surplus can be calculated as a result of the price increase multiplied by the decrease in imported quantity: $$(\$15 - \$10) * 1,250 = \$6,250$$ 3. The deadweight loss from the tariff can be calculated as the difference in imported quantities between the free trade and tariff scenarios, multiplied by the tariff: $$(\$5 * (2,500 - 1,250)) / 2 = \$3,125$$ The new equilibrium with the tariff is \(\mathrm{P}=\$15\) and \(\mathrm{Q}=3,500\) radios per year, with $$\$6,250$$ collected in tariff revenues, $$\$6,250$$ transferred from consumer surplus to domestic producers, and $$\$3,125$$ of deadweight loss.

d. Analyzing the effect of voluntary export limits on the market equilibrium

If the government reached an agreement with foreign suppliers to voluntarily limit their portable radio exports to \(1,250,000\) per year, the effect would be similar to that of a tariff, but with some crucial differences: 1. Price impact: With a voluntary export restraint, there will be a new effective world price equivalent to the domestic price that equates the quantity supplied by importing country producers with the voluntary restraint quantity. Let's denote this new price by \(\mathrm{P'}\). In this case, \(Q^{I'} = 1,250\). Assuming all other things being equal, this would have a price effect similar to the tariff. 2. Revenue impact: Unlike the case of a tariff, the revenue generated by the higher price under voluntary export restraints would accrue to the foreign suppliers rather than to the domestic government. So, there would be no tariff revenue collected by the government. 3. Deadweight loss: Since the quantity of imported radios is the same as in the tariff scenario, the deadweight loss would also be the same, at $$\$3,125$$. The main difference between the tariff and the voluntary export restraint is the distribution of the collected revenues: tariff revenues go to the domestic government, while revenues under voluntary export restraints go to foreign suppliers. The prices, quantities, and deadweight losses in both scenarios are the same.