1.    Prove the following proposition: Free trade is better than no trade.
While a general equilibrium proof may be better, I present a partial equilibrium proof consistent with the presentation in Chapter 6:

Let PA = \$6/bushel be the autarky price, and let PW = \$3/bushel be the free trade price. When the country moves from autarky to free trade, domestic consumption increases from 4 to 7 million bushels of grapes per year, while domestic production decreases from 4 to 1 million bushels of grapes per year. The quantity imported, M = Qd - Qs = 7 - 1 = 6 million bushels of grapes per year.

With free trade, consumers gain the added consumer surplus \$(a+b+c), while producers lose \$a. Subtracting the value of the loss from the gains leaves a net gain in the amount \$(b+c). Therefore, free trade is better than no trade (autarky).

Using the illustration below, let PW +T = \$5/bushel be the free trade price plus the tariff. When the country moves from autarky to restricted trade, domestic consumption increases from 4 to 5 million bushels of grapes per year, while domestic production decreases from 4 to 3 million bushels of grapes per year. The quantity imported, M = Qd - Qs = 5 - 3 = 2 million bushels of grapes per year.

With restricted trade, consumers gain the added consumer surplus \$(d+e), while producers lose \$d. Subtracting the value of the loss from the gains leaves a net gain in the amount \$e. Therefore, restricted trade is better than no trade (autarky).

3.    Suppose that a country imposes a pure revenue tariff. Calculate the welfare effects of this tariff. How do these effects differ from the usual deadweight costs analyzed in the chapter?

An example of a pure revenue tariff is shown below. There is no domestic supply curve in this illustration since domestic producers are unwilling to market the item at any price consumers are willing to pay. This is equivalent to a "supply curve" lying on the vertical axis, since the supply will be zero at any price shown. Let PW be the free trade price, and PW+t the free trade price plus the tariff.

When the country moves from autarky to free trade, domestic producers still sell the same amount (none!), but consumption jumps from zero to 7 million bushels per year, all in the form of imports, with the net gain in consumer surplus of \$a+b+c. When the government places a tariff on the good, the price rises and consumers cut back consumption of imports to 5 million bushels per year. Consumer surplus decreases from \$a+b+c to just \$a. Government revenues are \$b, and deadweight cost is \$c.

The deadweight cost of a pure revenue tariff differs from the case analyzed in the chapter because there are no domestic producers. Therefore, the portion of deadweight cost that would result from producers increasing production in the higher cost domestic industry does not occur. In this case, consumer deadweight cost constitutes the total deadweight cost.

4. The less elastic (i.e. the steeper) is the domestic supply curve, the lower is the production deadweight cost of any tariff. True or false? Demonstrate and explain.

This is a difficult question if the country under consideration is large. Let's begin by adopting the small country assumption. This is a true statement for a small country. To see why, go to Figure 6.7 in the text and rethink the analysis assuming that the domestic supply curve continues to pass through the point (PW,Q1) but is now steeper. Triangle b measuring the production deadweight loss would have the same height as before, but it would have a shorter base. Its area must be smaller.

The economic rationale for this result is as follows. The deadweight cost arises from the fact that by artificially distorting domestic prices, tariffs cause output to expand in inefficient industries. Inelasticity in supply indicates an absence of production flexibility in the first place, so the price distortions are of less consequence.

World welfare can be readily analyzed using the following diagram. The rest of the world's (RoW) export supply is found by subtracting its demand curve from its supply curve. Home's import demand curve is found by subtracting its supply curve from its demand curve. A less elastic supply curve in the importing country means that its import demand curve (M) will also be less elastic. Here the inelastic M is shown in blue, the elastic M in red. The world deadweight cost may be calculated as 1/2 x tariff x change in imports. The less the elasticity, the smaller the change in imports. The sum of areas f and g is smaller as a consequence.

5. The more elastic (i.e. the flatter) is the domestic demand curve, the lower is the consumption deadweight cost of any tariff. True or false? Demonstrate and explain.

This is a false statement. The analysis parallels that in question 4 above.

6. Use the data in the table in Item 6.1 to calculate U.S. tariff revenues on rubber footwear, women's shoes, and luggage.

The answer to this question involves the following identity:
consumer cost = producer gain+
Solving this for the tariff revenue yields:
tariff revenue = consumer cost - producer gain - deadweight cost.

The table provides information on everything but the tariff revenue. With the identity, we can figure out the revenue. The answers are:

a) Tariff revenue from footwear = \$141 million

b) Tariff revenue from shoes = \$295 million

c) Tariff revenue from luggage = \$169 million

7. Given the following information, calculate the cost to consumers, the benefit to producers, the change in government revenue, and the deadweight costs of a proposed 20% tariff on personal computers.

 price of computers (free trade) \$2,000 domestic production (free trade) 100,000 domestic production (after tariff) 120,000 domestic consumption (free trade) 150,000 domestic consumption (after tariff) 140,000

The tariff adds \$400 to the price of each computer, so the new price is \$2400.

Consumers: purchases decline and so does consumer surplus by the amount of \$58,000,000. (\$2,000,000 of this is consumer deadweight loss.)

Producers: increase output by 20,000 and raise prices on all units, including the 100,000 they would have sold at \$2000 before the tariff. They will increase total revenue by \$48,000,000, although \$4,000,000 of this will be increased costs of production (deadweight costs). Thus, increased producer surplus (profits) will be \$44,000,000.

Government: previous tariff revenues were \$zero. Tariff revenues rise to \$8,000,000.

Deadweight costs: \$6,000,000 in total: \$4,000,000 in production inefficiency(area b), plus the value of the lost consumption (net of its cost), area d, is \$2,000,000.

8. 'The optimal tariff for a small country is zero. Prove this statement geometrically and then explain your results.

Refer to the illustration for problem 1. By definition, a "small country" is one that is unable to influence the price of a good on the world market through buying or selling. This assures that the country will have a horizontal world supply curve at the price PW, regardless of its tariff policy. When a small country applies a tariff to a good, the world price will remain constant at Pw. Tariff revenue will simply be a transfer from consumers to the government. If the country's demand curve is downward sloping, the deadweight cost will always increase proportionately to tariff increases, even if there is no domestic supply (see problem 3).

9. Prove that the more elastic demand and supply conditions are in a country that is large in world markets, the greater the ability of that country to impose an optimal import tariff.

A country is more likely to gain by imposing an import tariff the less the tariff is reflected in the domestic price and the more it is reflected in the foreign price. To answer the question, let us show that a tariff will have a smaller effect on the domestic price the more elastic is domestic demand or supply. Refer to Figure 6.9 in the text and keep everything the same except, say, the demand curve in country A. Specifically, suppose the demand curve continues to pass through the point (PFT,Q2) but is more elastic. The free-trade equilibrium would be the same as before, with an international price PFT and country A importing Q1Q2. But with a new demand curve in country A, the with-tariff equilibrium would have to look different. At a price P", country A would want to consume less and, therefore, import less than before. There would be a surplus in the world market. For the market to be in equilibrium, the price in country A must lie below P", and the price in country B must lie below P'. This completes the proof.

10. Prove that the more inelastic demand and supply conditions are in the foreign country, the greater the ability for a country that is large in world markets to impose an optimal import tariff. Use this result to explain why the OPEC price increases of the 1970s had such devastating effects on the economies of the West.

The proofs are similar to those in question 9. For example, return to Figure 6.9 and imagine a supply curve in country B  that supports the original free-trade equilibrium (PFT,Q'2) but is otherwise more inelastic. The with-tariff equilibrium would have to involve a foreign price that is lower than P'. Why? Because of the new supply conditions, country B would want to export more than before. There would be a surplus in world markets at the old prices. To reach an equilibrium, prices must come down.

What does this have to say about OPEC? Think of the OPEC suppliers as country B and the industrialized nations as country A. The industrialized nations were largely unable to substitute away from petroleum-intensive consumption (they had very inelastic demand curves), and they had little ability, at least in the short run, to increase domestic supplies (inelastic supply). When OPEC reduced their exports to increase the price of petroleum it was our graphical equivalent of a very large tariff. The West's inability to adjust to the change forced it to pay the supplier's price. Hence, OPEC was very effective at shifting almost the entire burden of the "tariff" onto the consuming countries.

11. Given the following information, find the NRP and the ERP in the personal computer (PC) industry:

 World price of PCs \$2000 Cost of imported memory chips \$500 Domestic ' value added (free trade) \$1500 Tariff on PCs \$200 Tariff on memory chips \$0

Suppose the government were to impose a tariff of 30 percent on memory chips. What would happen to the NRP and the ERP in the PC industry? Derive and explain.

With no tariff on memory chips, the answers are:

NRP = 200/2000 = 10%

ERP = (1700-1500)/1500 = 13.3%.

With a tariff of 30 percent on memory chips, the rates of PC protection are:

NRP = 200/2000 = 10%

ERP = (1550-1500)/1500 = 3.3%.

12. Suppose a country imposed a specific export tariff of \$t on each unit of its exports of a certain product. Depict this situation graphically, and calculate the welfare cost of this policy.

As shown in the diagram above, the export tariff lowers the domestic price. Assuming the country is small in world markets, domestic price will fall by the full amount of the tariff. The welfare calculations will involve a consumer gain and a revenue gain but a producer loss that outweighs the two gains.
Specifically,
change in welfare    = consumer gain + tariff revenue - producer loss
= a + c - ( a+b+c+d)

= -(b+d)

13. In Argentina, there are export tariffs on both raw materials such as soybeans and on processed soybean products (e.g. oils). Use the theory of effective protection to explain which tariff is likely to be higher.

An export tariff on soybeans will cause the domestic price of soybeans to fall below the world price. This will create a cost advantage for processors who purchase their soybeans domestically. As we have seen, on the import side protection increases by stages of processing. An export tariff is like negative protection. Hence, we should expect to see a lower export tariff (i.e. less negative protection) on processed products. Indeed that has been the case. Why? Argentina's goal is to encourage the processing of their raw material export in Argentina, hoping to increase domestic value added. Unfortunately, Argentina's export tariffs also reduce its exports and its earnings of foreign currency. This unintended side effect contributed to Argentina's last macroeconomic crisis. Her recently increased export tariffs on food products are also contributing the the world's current food price inflation that has impoverished millions of people in the developing countries.

14. Prove that if a product is made with only domestic factors of production (i.e., there are no imported intermediate components), then NRP equals ERP.

The formulas for NRP and ERP are identical in this case since the domestic price of the product is completely accounted for by domestic value added. Remember that market price equals the sum of the value added across all stages of production, distribution, and retailing of the final good. If all of the inputs are domestic, then v=P. With the small country assumption, v'=P+T, so that:

15. Recently, the World Bank has been advising member countries to adopt uniform tariff rates on all imports. Suppose a country such as Chile adopts a uniform tariff of 20 percent ad valorem on all imports. Compare Chile's NRP and ERP under this policy. Why do you suppose the World Bank has been advocating uniform tariff rates?

As the example in Table 6 illustrates, if the nominal tariffs on both inputs and final products are equal, then the NRP equals the ERP. There are several reasons that the World Bank advocates uniform tariffs. First, uniform tariffs facilitate the process of trade liberalization. Tariff reductions are easy to implement and the loss of protection is spread equally across all import competing sectors. Second, uniform tariffs help countries avoid potential and possibly costly redistributions of resources brought on by complicated tariff structures where NRPs differ greatly from ERPS.

16. Use the data in Table 6.6 to compare U.S. protectionist policies with those of Japan. In what sectors are protection levels relatively equal? Where do they differ? Try to explain these patterns.

According to the table, on average Japan's tariffs are about twice as high as U.S. tariffs, but are relatively close to the mean tariff for developed countries. Japan's highest tariffs are on agricultural products and food, beverages, and tobacco. By contrast, these sectors rank among the least protected sectors in the United States. Clearly this pattern tells us something about the relative scarcity of farm land in Japan compared to the United States. Tariffs on most manufactured products are low in both countries, representing the fact that each is a significant exporter of manufactured goods. The highest U.S. tariff rate is found in apparel, a U.S. industry that has long history of competing with foreign imports.

17. (#18 in the 6th edition) Suppose that the domestic demand and supply for shoes in a small open economy are given by

P = 100 - 2Q (demand)

P= 5+Q (supply)

where P denotes price and Q denotes quantity.

a) What are the autarky price of shoes and quantity produced?

b) What are are the levels of domestic production, consumption, and imports if the world price is 10?

c) How would your answers in part b change if this country were to impose a tariff of 3?

Solution:

a) Q = 31.67, found by solving for Q: 5+Q=100-2Q
P = 36.67, found by substituting Q=31.67 into P=5+Q.

b) Production = 5, found by substituting P=10 into P=5+Q.
Consumption = 45; substitute P=10 into P=100-2Q.
Imports = 40, found as M = Qd - Qs = 45 - 5

c) Production = 8; Given the small country assumption, just substitute P=13 into the original supply equation: 13=5+Q
Consumption = 43.5; substitute P=13 into the original demand equation: 13=100-2Q
Imports = 35.5, found as M = Qd - Qs = 43.5 - 8

Question #17 from the sixth edition is for mathematically-advanced students. Suppose that a large country imports coffee. Let the import demand curve be given by

P = 200 - 2C

and the world's export supply curve for coffee be given by

P=10+C

where P is the price of coffee and C is the quantity of coffee.

a) Calculate the "optimum tariff" assuming no retaliation.

b) What would the revenue maximizing tariff rate be? How much revenue would be raised at this rate?

Diagram  of Export Supply & Import Demand

To understand the solution to this question, consider the diagram above. With free trade, the world price is determined by the intersection of import demand and world supply. The free trade solutions are:

C = 63.33
P=73.33

The effect of a tariff is to lower imports, raise the domestic price above the free trade price and lower the export supply price below the free trade price. The net gain to the importing country is given by the sum of the areas in the diagram:

Net gain = \$b - \$c.

To solve this problem express areas b and c in terms of free trade prices and quantities (which are constants), and variables that are functions of the parameter to be chosen (say the level of imports under protection). Then, use calculus (i.e., take the first derivative, set it equal to zero, and solve) to determine the level of imports that maximizes net gain:

Net Gain = (PFT PS(QT))QT -1/2*(QFT - QT)*(PD(QT) - PFT)

where:
PFT = the free trade price (here 73.33),
PS = the supply price that goes to the exporter,
QT = the level of trade under protection,
PD = the demand price paid in the import market.

The solution to this problem is:

QT = 47.5; optimal tariff = \$47.5

The maximum revenue tariff maximizes the area: \$a + \$b. To find its precise level, proceed as before. Here, choose QT to maximize

Revenue = (PD(QT) - PS(QT))QT.

The solution to this problem is:

QT = 31.67; maximum revenue tariff is \$95.

Note that the maximum revenue tariff is higher than the optimal tariff. This is a standard result that occurs because there is no consideration of the consumption deadweight costs that tariffs impose in the case of maximizing revenues.