Suppose the U.S is an importer of product X and that there are no trade restrictions. Let us assume that the U.S. consumers buy 1 million units of X each year, of which 400,000 are produced domestically and 600,000 are imported.

a) Suppose a technological advance in Japan causes the world price of X to fall by $100. Draw a graph to show how this change affects the well-being of U.S. consumers and U.S. producers of product X. (You can assume that the U.S. is a small country in the world market for product X.)
ii) After the fall in price, consumers buy 1.2 million units of X, of which 200,000 are produced domestically and 1 million are imported. Calculate the change in the consumer well-being and producer well-being from the price reduction. Which is larger? Why?
iii) If the U.S. government responded by imposing a $100 tariff on imported X, what would this do? Calculate the tariff revenue that would be raised and the deadweight loss of the tariff. Would the tariff be a good policy from the point of view of U.S. welfare? Who would support the tariff?
iv) Suppose the $100 price reduction is not due to a technological advance but to a $100 subsidy per unit of X produced in Japan. Would this additional information change your analysis or your conclusion regarding the desirability of the tariff? Explain.

a) With the technological advance causing the world price of X to fall by $100, the following changes can be observed:

- Demand Curve: The decrease in price will lead to an increase in quantity demanded by U.S. consumers. This can be shown by a rightward shift of the demand curve.
- Supply Curve: The decrease in price will likely lead to a decrease in quantity supplied domestically. However, the quantity supplied by imports may not change. This can be shown by a leftward shift of the supply curve for the domestic producers.

ii) After the fall in price, the new quantities are as follows:
- Consumers buy 1.2 million units of X: 200,000 produced domestically and 1 million imported.

To calculate the change in consumer and producer well-being, we need to compare two scenarios: before and after the price reduction.

- Consumer Well-being: Consumer well-being can be measured by Consumer Surplus, which is the difference between what consumers are willing to pay and what they actually pay. As the price decreased, consumer surplus will increase due to lower prices.
- Producer Well-being: Producer well-being can be measured by Producer Surplus, which is the difference between what producers receive and their costs. As the price decreased, producer surplus will decrease as they receive lower prices.

Based on this information, let's calculate the changes:

Consumer Well-being change = (New Consumer Surplus) - (Old Consumer Surplus)
Producer Well-being change = (Old Producer Surplus) - (New Producer Surplus)

The change in consumer well-being will be positive since consumer surplus increases. The change in producer well-being will be negative since producer surplus decreases. Consumer well-being change will be larger than the producer well-being change because the fall in price benefits consumers more than it harms producers.

iii) If the U.S. government imposes a $100 tariff on imported X, the following effects can be observed:

- The price of imported X will increase by $100 due to the tariff.
- Domestic producers may benefit from the tariff as they will face less competition from imports.
- Consumers will face higher prices due to the tariff.
- Tariff Revenue: The tariff revenue can be calculated as (Tariff rate x Quantity of imported X). In this case, the tariff rate is $100 and the quantity of imported X is 1 million units. Thus, the tariff revenue would be $100 million.
- Deadweight Loss: The deadweight loss is the loss of overall welfare due to the distortion caused by the tariff. It represents the economic inefficiency resulting from reduced trade. The size of the deadweight loss will depend on the elasticity of demand and supply for X and the size of the tariff.

The tariff may not be a good policy from the point of view of U.S. welfare because it will harm consumers by increasing prices and potentially reduce overall economic efficiency due to deadweight loss. Domestic producers who benefit from the tariff could potentially support it.

iv) If the $100 price reduction is due to a $100 subsidy per unit of X produced in Japan, it would make the analysis and conclusion regarding the desirability of the tariff different.

In this case, the subsidy to Japanese producers would incentivize them to increase production and lower the price of X. This would lead to higher quantities being supplied by Japan, including the imports to the U.S., compared to the previous scenario. The increased imports would further reduce the price that U.S. consumers pay for X.

Given this subsidy, the tariff's impact on the overall welfare and desirability might change. It would depend on the specific details of the subsidy and the dynamics between the subsidy and the tariff. Generally, subsidies can counteract the negative effects of tariffs by lowering costs for producers, but the analysis would require a more detailed examination of the specific circumstances.

To answer the given questions, we need to consider the impact of the technological advance in Japan on the world price of product X, and how it affects the well-being of U.S. consumers and producers. Let's break down the analysis step by step:

a) Graphical analysis:

First, we need to understand the concept of comparative advantage in trade. When the world price of X falls due to a technological advance in Japan, it means that Japan can now produce X more efficiently and at a lower cost. As a result, the world price of X decreases.

On a graph, we can represent the supply and demand for product X in the U.S. Before the technological advance, the domestic supply would be represented by a vertical line at 400,000 units (produced domestically), and the demand would be represented by a downward-sloping curve representing 1 million units. The difference between domestic supply and domestic demand (600,000 units) would be imported.

After the technological advance, the world price of X falls by $100. This decrease in price affects both domestic producers and consumers. The new equilibrium quantity of X is determined by the intersection of the domestic supply curve (now at 200,000 units) and the demand curve (now at 1.2 million units). Draw the new supply and demand curves, and you will see that U.S. consumers now demand more X (1.2 million units), of which 200,000 units are produced domestically, and the remaining 1 million units are imported.

ii) Calculation of change in consumer and producer well-being:

To calculate the change in consumer well-being, we need to find the area under the demand curve both before and after the price reduction.

Before the price reduction, consumer well-being is represented by the area between the demand curve and the horizontal axis, which can be calculated as (1 million units x (original price - 0)).

After the price reduction, consumer well-being is represented by the new area between the demand curve and the horizontal axis, which can be calculated as (1.2 million units x (new price - 0)).

To calculate the change in producer well-being, we need to find the difference between the revenue before and after the price reduction.

Before the price reduction, domestic producers were selling 400,000 units at the original price. So, the producer well-being was represented by (400,000 units x original price).

After the price reduction, domestic producers are selling only 200,000 units at the new price. So, the producer well-being becomes (200,000 units x new price).

To compare the changes in consumer and producer well-being, calculate the differences between the after and before values. The larger value indicates the greater impact on well-being.

iii) Analysis of the tariff imposition and its impact:

If the U.S. government imposes a $100 tariff on imported X, it means that for every unit of X imported, an additional cost of $100 is imposed.

This tariff would affect the equilibrium price and quantity of X. The new equilibrium price would be the world price of X plus the tariff ($100). The new equilibrium quantity would be determined by the intersection of the new supply curve (domestic supply remains the same) and the new demand curve (adjusted due to price increase).

To calculate the tariff revenue, multiply the tariff rate ($100) by the quantity of imports (1 million units).

The deadweight loss of the tariff represents the loss of total surplus (consumer and producer surplus) due to the distortion introduced by the tariff. The size of the deadweight loss can be measured as the triangular area between the new supply curve and the demand curve, within the range of quantity reduction caused by the tariff.

To evaluate the tariff's impact on the U.S. welfare, compare the total surplus (consumer surplus + producer surplus) before and after the tariff imposition, including the deadweight loss. If the total surplus decreases, the tariff may not be a good policy from the point of view of U.S. welfare.

The tariff could be supported by domestic producers who will benefit from reduced competition from imports, as well as some government officials who may see it as a means to protect domestic industries and preserve jobs.

iv) Impact of a $100 subsidy in Japan:

If the $100 price reduction is not due to a technological advance but to a $100 subsidy per unit of X produced in Japan, it would change the analysis and conclusion regarding the desirability of the tariff.

The subsidy would effectively lower the costs of production for Japanese producers, enabling them to sell X at a lower price in the global market. This would lead to an increase in imports and a further decrease in the world price of X.

In this scenario, the tariff would be less effective in raising the price of imported X because the subsidy offsets the cost increase. Therefore, the tariff's impact on the welfare of U.S. consumers and producers would likely be limited, and it may not be a desirable policy.