Question

The domestic demand for portable radios is given by \\[Q=5,000-100 P,\\] where price \((P)\) is measured in dollars and quantity \((Q)\) is measured in thousands of radios per year. The domestic supply curve for radios is given by $$Q=150 P.$$ 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

The domestic equilibrium is at \(P = \$20\) and \(Q = 3,000,000\). With a \$10 world price, \(2,500\) radios are imported. A \$5 tariff results in \(1,250\) imports and \$6,250,000 in tariff revenue. A voluntary export limit affects surplus differently than a tariff.

Step-by-step solution

Find the Domestic Equilibrium

To find the domestic equilibrium, set the demand equation equal to the supply equation. \[\begin{align*} 5,000 - 100P &= 150P. \end{align*}\] Solving for \(P\), combine like terms: \[\begin{align*} 5,000 &= 250P. \end{align*}\] Divide both sides by 250: \[\begin{align*} P &= 20. \end{align*}\] Substitute \(P = 20\) back into either the supply or demand equation to find \(Q\): \[\begin{align*} Q &= 150 \times 20 = 3,000. \end{align*}\] Thus, the domestic equilibrium price is \(\$20\) per radio and the quantity is \(3,000,000\) radios.

New Market Equilibrium with World Price

With a world price of \$10, substitute \(P = 10\) into the demand equation: \[\begin{align*} Q_d = 5,000 - 100 \times 10 = 4,000. \end{align*}\] Now, substitute \(P = 10\) in the supply equation: \[\begin{align*} Q_s = 150 \times 10 = 1,500. \end{align*}\] At this world price, 4,000 radios are demanded domestically, and 1,500 radios are supplied domestically. Thus, \(4,000 - 1,500 = 2,500\) radios must be imported.

Effect of a $5 Tariff

With the \\(5 tariff, the domestic price increases to \\)15. Substitute \(P = 15\) into the demand equation: \[\begin{align*} Q_d = 5,000 - 100 \times 15 = 3,500. \end{align*}\] Substitute \(P = 15\) into the supply equation: \[\begin{align*} Q_s = 150 \times 15 = 2,250. \end{align*}\] Imports are now \(3,500 - 2,250 = 1,250\) radios. The tariff revenue is \(1,250 \times 5 = 6,250,000\) dollars. The consumer surplus transfer to domestic producers is calculated using changes in prices and quantities.

Calculate Tariff Effects

Next, calculate consumer surplus transfer and deadweight loss. The increase in domestic price from \\(10 to \\)15 results in a reduced consumer surplus, partially transferred to producers. Deadweight loss results from the reduction in quantity traded. The calculation involves changes in surplus areas and quantities, which typically requires diagrammatic analysis or additional data on consumer-producer elasticity.

Voluntary Export Restraint

If exports are voluntarily limited to 1,250,000 radios, the effect differs from a tariff since consumer surplus loss from price changes goes entirely abroad, while domestic surplus from reduced import volume is limited by the voluntary agreement. The domestic price might not adjust exactly like in a tariff scenario.

Key concepts

Demand and Supply Equations

In a market, demand and supply equations are fundamental in determining the equilibrium price and quantity of goods. The demand equation is derived from consumer preferences and purchasing power. It shows how many goods consumers are willing to buy at different prices. In our example, the demand equation is \(Q_d = 5,000 - 100P\). As we can see, as the price \(P\) increases, the quantity demanded \(Q_d\) decreases, which is typical of most goods.
On the other hand, the supply equation originates from the producers' perspective. It indicates how much of a good producers are willing to sell at varying prices. The supply equation in this example is \(Q_s = 150P\). Here, as the price \(P\) rises, the quantity supplied \(Q_s\) also rises because higher prices make production more profitable for suppliers.
Finding the equilibrium involves setting the demand equation equal to the supply equation. This provides the point where the quantity consumers want to buy equals the quantity producers want to sell, resulting in no excess supply or demand. In this example, solving \(5,000 - 100P = 150P\) yields an equilibrium price of \( \$20 \) and a quantity of 3,000,000 radios. This ensures a balanced market where the quantities are equal at a specific price.

Tariffs and Trade Policies

Tariffs are taxes imposed on imports to protect domestic industries from foreign competition. By making imported goods more expensive, tariffs aim to encourage consumers to buy domestically produced goods.
When a tariff is implemented, it increases the market price of the imported goods. For example, in our exercise, a \( \\(5 \) tariff increases the price of imported radios from \( \\)10 \) to \( \$15 \). This encourages domestic production by raising the price consumers pay, thus boosting domestic supply.
Trade policies like voluntary export restraints (VERs) are another way to influence trade. A VER is an agreement between exporting and importing countries where the exporter agrees to limit the quantity of goods sent to the importing country. Unlike tariffs, VERs do not generate revenue for the domestic government but still reduce competition for domestic producers by limiting foreign supply. However, the price effect on the domestic market may not be as predictable as with a straightforward tariff.

Consumer and Producer Surplus

Consumer surplus is the difference between what consumers are willing to pay for a good versus what they actually pay. It represents the benefit consumers get from purchasing goods at market prices lower than their maximum willingness to pay. In a market equilibrium without tariffs, consumer surplus is maximized because imports lower prices.
Producer surplus, on the other hand, is the difference between what producers receive for a good versus their minimum acceptable price. It reflects the additional benefit producers receive from selling at the market price above their cost.

• With tariffs, consumer surplus decreases because consumers pay higher prices for the same quantity.
• Producer surplus increases because domestic producers sell more at the higher tariff-inclusive price.
• Tariff revenue is collected by the government, representing a financial gain.
• However, there is a deadweight loss, which is the loss of economic efficiency due to the decrease in the quantity traded.

In the exercise, a \( \$5 \) tariff causes a partial consumer surplus transfer to domestic producers, but it also results in a net deadweight loss. This efficiency loss represents the transactions that no longer happen due to the price increase, which would have occurred without the tariff.