Question

The domestic demand for portable radios is given by \\[ Q=D(P)=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=S(P)=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

In summary, the domestic equilibrium for portable radios is at a price of $20 and a quantity of 3000 radios per year. When free trade is introduced, the new market equilibrium price drops to $10, and the total quantity increases to 4000 radios, with 2500 radios imported. With the implementation of a $5 tariff, the new market equilibrium shifts to a price of $15 and a total quantity of 3500 radios, with 1250 radios imported. At this point, the tariff revenue equals $6250, the consumer surplus transferred is $5000, and the deadweight loss is $3125. In the case of voluntary export restraints, the market will experience a similar effect as the tariff scenario, with an increase in domestic price and a decrease in imported radios. However, the deadweight loss would be larger compared to the tariff scenario, as there will be no tariff revenues to compensate for the increase in prices caused by voluntary restraints.

Step-by-step solution

a. Domestic Equilibrium

To find the domestic equilibrium, we need to equate the domestic demand and supply functions: $$ 5000 - 100 P = 150 P $$ Now let's solve for \(P\): $$ 5000 = 250 P $$ $$ P = 20 $$ Now, let's calculate the equilibrium quantity \(Q\) by substituting the price \(P\) into either the demand or supply function: $$ Q = 5000 - 100(20) = 3000 $$ The domestic equilibrium in the portable radio market is \(P = \$ 20\) and \(Q = 3000\) radios per year.

b. New Market Equilibrium with Free Trade

With free trade, the world price is \(P_W = \$ 10\). To find the new market equilibrium, we need to calculate the domestic demand and supply at this price: Demand at \(P_W = 10\): $$ Q_D = 5000 - 100(10) = 4000 $$ Supply at \(P_W = 10\): $$ Q_S = 150(10) = 1500 $$ Since domestic demand is greater than domestic supply, portable radios will be imported. The new market equilibrium is \(P = \$ 10\) and \(Q = 4000\) radios, with 2500 radios imported (\(4000 - 1500\)).

c. Market Equilibrium with $5 Tariff

With a \(5 tariff, the import price becomes \)P_T = \$ 15$. We need to calculate the new domestic demand and supply at this price: Demand at \(P_T = 15\): $$ Q_D = 5000 - 100(15) = 3500 $$ Supply at \(P_T = 15\): $$ Q_S = 150(15) = 2250 $$ The new market equilibrium with the tariff is \(P = \$ 15\) and \(Q = 3500\) radios, with 1250 radios imported (\(3500 - 2250\)). Now let's find the tariff revenues, consumer surplus transferred, and deadweight loss: Tariff revenues: \((\$ 5) \times (1250) = \$ 6250\). Consumer surplus transferred: The price increased from \(\$ 10\) to \(\$ 15\), so the consumers lose \(\$ 5\) per radio on 1000 radios (the increased quantity of domestic production). Thus, the consumer surplus transferred is \(\$ 5 \times 1000 = \$ 5000\). Deadweight loss: The rectangle's width and height denote the change in price (from \(\$10\) to \(\$15\), or \(\$5\)) and the change in import quantity (from 2500 to 1250, or 1250), respectively. The deadweight loss is: $$ Deadweight\, Loss = \frac{1}{2} \times 5 \times 1250 = \$ 3125 $$

d. Voluntary Export Restraint

If the government reaches an agreement with foreign suppliers to voluntarily limit the portable radios they export to 1,250,000 per year (we assume 1 unit = 1000 radios, so 1250 units per year), this would affect the market equilibrium by restricting the quantity supplied by foreign suppliers. With a constrained supply of imported radios, the domestic price will increase due to the reduced competition from imports. The effects on the market will be similar to those of a tariff, with an increase in the domestic price and a decrease in the quantity of imported radios. However, the major difference is that instead of tariff revenues collected by the government, there will be no added income, as prices are only increased due to the voluntary restraint agreement. This results in a larger deadweight loss compared to the case with a tariff, as the domestic market faces even higher prices without the benefit of tariff revenues.

Key concepts

Market Equilibrium

Market equilibrium is a core concept in microeconomic theory where the quantity demanded by consumers meets the quantity supplied by producers, resulting in a stable market price. For example, consider the case of portable radios where the demand is represented by the equation \( Q=D(P)=5,000-100P \), and supply is \( Q=S(P)=150P \). To find where the market rests without any outside intervention, we equate the demand and supply to find the equilibrium price \( P \). Solving \( 5000 - 100P = 150P \) gives us \( P = 20 \), and at this price, the equilibrium quantity is 3000 thousand radios per year. It's at this point that the market naturally balances itself; no excess supply or unmet demand exists.

Understanding equilibrium helps to predict the consequences of market changes, such as introducing tariffs or trade agreements. When changes arise, like a world market price or an imposed tariff, the market strives to reach a new equilibrium, giving us insight into how such disruptions can affect both producers and consumers.

Tariffs and Trade

In the context of tariffs and trade, when a country allows its citizens to trade freely, the world price dictates market dynamics. In the example of portable radios, if they could be imported at a world price of \( P_W = \(10 \), below the domestic equilibrium of \( \)20 \), consumers would opt for the cheaper imports. This causes a new market equilibrium where domestic supply decreases, demand increases, and the import of additional radios becomes necessary to satisfy the excess demand.

When tariffs are introduced, such as a \( \(5 \) tariff per radio, this raises the world price to \( P_T = \)15 \), reducing imports and raising domestic prices, altering the market equilibrium again. Tariffs serve as a tool to protect domestic industries by making imported goods more expensive but also result in higher prices for consumers. It illustrates the delicate balance policymakers must maintain while considering tariffs on trade, where protecting domestic industries can have far-reaching implications on market equilibrium and consumer costs.

Consumer Surplus

Consumer surplus is the difference between what consumers are willing to pay and what they actually pay. It represents the economic benefit to consumers, as they can purchase products for less than their maximum willingness to pay. For the portable radios, when the price is at the world market level of \( \(10 \), the consumer surplus is at its peak, because consumers enjoy lower prices.

When a tariff is imposed, raising the price to \( P_T = \)15 \), the consumer surplus is reduced. This is because buyers now pay more for the same product, reducing the economical benefit they previously enjoyed. The consumer surplus that is 'transferred' to domestic producers, measured as the increase in price times the increase in the quantity of domestic production due to the tariff, is one way to gauge the cost of such trade policies to consumers. The reduction in consumer surplus is a significant consideration when evaluating the impact of tariffs.

Deadweight Loss

Deadweight loss occurs when market inefficiency creates a loss of economic welfare. In cases where tariffs are applied, such as the \( \(5 \) tariff on portable radios, a deadweight loss arises. This loss is quantified by the loss in consumer and producer surplus that is not offset by the gain in tariff revenue. It represents the economic value that is simply lost to society because the tariff reduces the quantity traded below what the market would have determined in a free trade scenario.

The calculation of the deadweight loss involves the area of a triangle formed by the price increase and the reduction in trade volume. For instance, with the tariff, a rectangle's area under the demand curve represents lost consumer surplus, while a triangle's area represents the deadweight loss due to decreased imports. Specifically, the deadweight loss resulting from the \( \)5 \) tariff on portable radios would be \( \frac{1}{2} \times 5 \times 1250 = $3125 \), reflecting the inefficiency and reduced consumer welfare imposed by the tariff.