Economics 0115 Homework #4: Answers

 

1. Given the data on the production possibility frontiers for the US and Japan in Table 1-1, do the following:

 

a. Construct a table showing the opportunity costs for producing food and autos in each country. Which country has the comparative advantage in producing food? In producing autos? Explain.

Starting at F = 0, we note that a gain of 200 units of F occurs for a 100 unit loss of A. That means that 1 unit of F is gained when there is a loss of unit of A. This latter number is the opportunity cost of 1 more unit of F. Similar reasoning is used to compute the other numbers in Table 1-2.

 

 

 

 

 

 

 

 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

b. Draw each country's production possibility frontier (PPF) on a separate graph. Using autos on the vertical axis, calculate the slopes of these two PPFs.

 

 

 

 

Slope(US) = (-500)/1000 = -1/2 A per unit of F

 

Slope(Japan) = (-800)/400 = -2 A per unit of F

 

2. Assume that the terms of trade (TOT) are set at 1F = 1A.

 

a. Indicate the specialization point on each PPF.

 

For A, Japan is the low cost producer (1/2 F per unit of A vs 2 F per unit of A for the US). For F, the US is the low cost producer (1/2 A per unit of F vs 2 A per unit of F for Japan).

 

See the graphs in part c.

 

b. Given the TOT, indicate what will happen to the production of A and F in each country.

 

The US will specialize in the production of F by producing at (1000 F, 0 A) and Japan will specialize in the production of A by producing at (0 F, 800 A). This pattern of specialization occurs because the US must give up 2 F to obtain 1 A domestically but can obtain 1 A from Japan by giving up 1 F. Likewise, Japan must give up 2 A for 1 F domestically whereas it can obtain 1 F for 1 A from the US. As long as it is cheaper for the US to obtain A from Japan it will be willing to forego domestic production of A. Similar logic applies to Japan.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

c. Given the terms of trade, draw the consumption possibility frontiers (CPF) for the US and Japan.

 

 

 

 

 

 

d. Before trade and specialization, if the US consumed 600 F, it could only consume 200 A. After specialization and trade, how many units of A can be consumed if 600 F are consumed? Explain.

 

 

 

 

After specialization the US has (1000 F, 0 A). If it wants to consume 600 F then it can trade the remaining 400 F for 400 A (given that the TOT are 1 F for 1 A). Therefore its position after specialization and trade is (600 F, 400 A), a clear improvement over its initial position.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

e. Given the combination of F and A in the US after trade and specialization, what combination of F and A will be consumed in Japan? Explain.

 

 

Similar reasoning argues that Japan will specialize by producing (0 F, 800 A) and then trading 400 A for 400 F (again assuming the TOT are 1 A for 1 F). After specialization and trade, Japan has (400 F, 400 A), a clear improvement over its initial position of (200 F, 400 A).

 

f. What amounts of F and A do the US and Japan import and export? Explain.

 

Japan exports 400 autos and imports 400 units of food. The US exports 400 units of food and imports 400 autos. This is a model of simple bilateral trade, a situation that does not always occur in the real world (e.g. trade is triangular or even rectangular-or more).

 

 

 

 

 

 

 

 

 

 

3. Assume the TOT are 1F = 4A. Explain whether trade will occur with these TOT and who will benefit from them.

These terms would be very beneficial to the US because it could specialize in F and then trade 400 F for 1600 A, a very large improvement. (The slope of the CPF line would be -4.)

 

These terms would be very costly to Japan because it would specialize in A and then trade 400 A for 100 F, a definite loss. Since Japan could give up 400 A domestically and obtain 200 F, it would never engage in trade on these terms.

 

Note that when the TOT are outside the trading interval, one trader gains at the expense of the other.

 

 

 

 

 

 

 

 

 

 

 

 

4. Use the data in Table 2 to do the following:

a. If the world price of autos is $8, how many autos will the US import? Graph and explain this situation.

 

Since domestic suppliers will only produce 100 autos when the world price is $8, the US will import 800 more autos to satisfy its consumers who wish to purchase 900 autos at a price of $8.

b. Suppose the US government imposes a $2 tariff on autos. Graph and explain this situation, being sure to note what happens to:

(1) The price of autos

(2) The number of imports

(3) The domestic production of autos

(4) The revenue from the tariff and who collects it

(5) The welfare losses from the tariff

(1) The price of autos increases to $10.

 

(2) The number of imports decreases to 400.

 

(3) The domestic production of autos increases by 200.

 

(4) The revenue from the tariff is collected by the government and can be calculated by multiplying $2 tariff by the number of imports 400. Revenue is therefore $800.

 

 

 

 

 

 

(5) The welfare loss (WL) has two components. First, since domestic producers supplying the 200 extra autos (expanding output from 100 to 300) are less efficient than foreign producers extra resources will be attracted to the auto industry which could be used in other parts of the economy. The WL1 = 1/2(200)$2 = $200. Second, a higher price of autos (due to the tariff) will cause domestic consumers to purchase 200 fewer autos than they would have with free trade. The value of the lost consumption exceeds value of the resources gained by reduced production of autos in foreign countries. The WL2 is equal to 1/2(200)$2 = $200 also. Therefore the total welfare loss WL = $400.

 

c. Suppose the US government establishes a quota of 400 autos. Graph and explain this situation, being sure to note what happens to:

(1) The price of autos

(2) The domestic production of autos

(3) The revenue from the quota and who collects it

(4) The welfare loss from the quota

 


 

 

 

 

 

 

 

(1) The price of autos rises to $10.

 

(2) The domestic production of autos rises by 200.

 

(3) The revenue generated by the quota is $2(400) = $800. The import companies licensed by the government to import autos capture the extra revenue generated by the quota.

 

(4) The welfare loss calculations are the same: $400.

 

d. Suppose the US government negotiates a VER with the government of Japan limiting the number of Japanese exports to the US to 400. Graph and explain this situation, being sure to note what happens to:

(1) The price of autos

(2) The domestic production of autos

(3) The revenue from the VER and who collects it

(4) The welfare loss from the VER

(1) The price of autos rises to $10.

 

(2) Domestic production of autos rises by 200.

 

(3) The excess revenue is again $80. But the exporters in Japan will capture it this time. This is one reason why some countries may agree to a VER (their producers can capture its benefits) where they may not agree to a tariff or a quota.

 

(4) The welfare loss from the VER is the same: $400.

 

5. Answer the following questions on exchange rates:

 

a. If the exchange between the dollar and the mark is 2 DM per dollar [e($) = 2 DM/$], what is the exchange rate in dollars per mark? [e(DM) = ?]

 

e(DM) = $0.5/DM which is simply the inverse of the dollar exchange rate.

 

b. If a camera sells for 250 DM, what is the dollar price of the camera using the exchange rate from part a?

 

(250 DM)[e(DM)] = 250 DM ($0.5/DM) = $125

 

c. If a computer sells for $1000, what is the DM price of the computer using the exchange rate from part a?

 

($1000)[e($)] = ($1000)(2 DM/$) = 2000 DM

 

 

 

 

 

 

 

 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6. Using the data in Table 3, answer the following:

 

a. Compute the real exchange rate e*(Y) in the last column.

 

e*($) = [CPI(US)/CPI(J)]e($)

 

Year 1: e*($) = (100/100)100 /$ = 100 /$

 

Year 2: e*($) = (125/100)100 /$ = 125 /$

 

Year 3: e*($) = (125/100)80 /$ = 100 /$

 

b. What happens to e*($) when the price index in the US rises but e($) remains unchanged?

 

e*($) rises and purchasing power parity (PPP) is temporarily disrupted.

 

 

 

 

 

 

 

 

 

 

 

c. What happens to e*($) when the price index in the US rises and e($) falls proportionately?

 

e*($) remains constant. This is a reflection of the idea of purchasing power parity (PPP) which argues that exchange rates adjust in the long run so the prices of the same good in different countries is the same. This should make sense insofar as inflation will cause the US dollar to depreciate against other currencies such as the Yen. This depreciation occurs because inflation causes the demand for dollars (and dollar denominated assets) to decrease. This causes e($) to decrease.

 

For example, suppose that an item costs $5 in the US but 500 in Japan. When the e($) = 100/$, the item costs the same in both countries. But if the price level in the US rises by 25% the item now costs $6.25 in the US but still costs 500 in Japan (assuming the exchange rate stays constant in the short-run). But the exchange rate must change to maintain PPP. To see why, assume that the exchange rate does not change. Then the item costs $6.25 in the US but $5 = ($0.01/)500 in Japan; conversely, the item costs 500 in Japan but 625 = (100/$)$6.25 in the US. Therefore the dollar per yen price must fall to e($) = 80/$. At this exchange rate, the $6.25 and the 500 item will be the same price in both countries. That is, ($6.25)80/$ = 500 or (500)$0.0125/ = $6.25.


7. Suppose i(J) = interest rate in Japan = 4%/year and i(US) = interest rate in US = 9%/year. Also suppose that e($) = 100/$ today but is expected to be 95/$ in one year (the dollar is expected to depreciate against the yen). If a firm in the US has $1 million to lend:

 

a. How much will this firm receive in dollars in one year if it lends this money to an American firm?

 

In one year, this firm will be repaid $1,090,000 = $1M(1.09).

 

 

 

 

 

 

 

 

 

 

 

 

b. Suppose that this firm lends $1 million to a firm in Japan (assume that it converts $1 million into yen to do so). How much will this firm receive in yen in one year? Assuming that the exchange rate is 95/$ in one year, what is the dollar return on this firm's loan?

 

$1M(100/$) = 100M-. This amount will be loaned to a Japanese firm. In one year, the amount to be repaid in yen will be 104M-. Assuming this amount is then converted into dollars at e() = $0.010526/ (e($) = 95/$) the total dollar repayment on the loan is $1,094,704.

c. Where should the firm make its loan? Explain.

 

It should loan the money to the Japanese firm whenever the dollar exchange rate is expected to fall. This result occurs because the appreciation of the Yen is added to the interest on the loan to give the firm a higher rate of return on its money.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8. Suppose that the money markets for the US and Japan have reached equilibrium at e($) = 80 /$. Using this information, do the following:

 

a. Using two supply-demand graphs, illustrate this situation and briefly explain your graphs.

 

 

 

The yen price of the dollar is 80/$ and is the equilibrium price in the dollar market. The dollar price of the yen is $0.0125/ and is the equilibrium price in the yen market.


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

b. Assume that the demand for dollars increases so that the new exchange rate is e($) = 100/$. Illustrate this situation for both countries and explain your results. Be sure to explain what is occurring at the original exchange rate (increased imports or exports for the US and vice versa for Japan) and how the markets adjust.

 

 

 

 

 

 


 

As noted in lecture, the demand for dollars is equivalent to the supply of yen. The supply of yen expresses a desire on the part of the Japanese to convert their yen into dollars in order to purchase US goods. The demand for dollars ultimately represents the demand for US goods in Japan (US export/Japanese imports). An increase in the demand for dollars therefore represents an increase supply of yen and consequently increased US exports/Japanese imports. This occurs because the excess demand for dollars at e($) = 80/$ causes e($) (the yen price of the dollar) to rise 100/$ and e() to fall to $0.01/. In other words, the dollar appreciates and the yen depreciates in value when demand for dollars increases.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

c. Begin with the equilibrium established in part a. Then assume that the supply of dollars increases. Illustrate this situation for both countries and explain your results. Be sure to explain what is occurring at the original exchange rate (increased imports or exports for the US and vice versa for Japan) and how the markets adjust.

 

 

 

 

 

As noted in lecture, the supply of dollars is equivalent to the demand for yen. The demand for yen expresses a desire on the part of the Americans to purchase Japanese goods. The supply of dollars ultimately represents the demand for Japanese exports/US imports). An increase in the supply of dollars therefore represents an increase demand for yen and consequently increased Japanese exports/US imports. This occurs because the excess supply of dollars at e($) = 80/$ causes e($) (the yen price of the dollar) to fall and e(Y) to rise. In other words, the dollar depreciates and the yen appreciates in value when supply of dollars increases.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

d. Assume that the situation in part a is altered by the imposition of a fixed exchange rate regime where the exchange rate is fixed at fe($) = 120/$. Illustrate this situation for both countries and explain how the US central bank should act in this situation. Can the central bank maintain this fixed rate indefinitely? What is the danger it faces? Explain.

 

 

When the e($) is fixed above the equilibrium price that means that Japanese imports exceed US exports on the current account (a trade deficit). A fixed exchange rate in this situation commits the central bank to supplying yen reserves out of its holdings and demanding an equivalent amount of dollars to be taken off the market.

 

 

 

 

 

The danger here is that the central bank will run low on yen reserves. If that is the case, the central bank will ultimately have to devalue the dollar (lower the fixed rate of exchange) in order to preserve its reserves of yen. Any attempt to defend the fixed rate of exchange will allow speculators to enter the markets and cause a general flight from the dollar (no one wants to be holding a depreciating currency). This general flight from the dollar will force the central bank to devalue sooner than it wanted to.

 

The danger arises when participants in the market become aware that the central bank is running low on foreign reserves. In that case, these participants will anticipate a devaluation by fleeing the dollar--the demand for dollars will decrease and the supply will increase. As can be seen from the graph, this merely makes the situation worse and increases the likelihood that the central bank will devalue.