IPE W2015 Problem Set 1 Answer Key PDF

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Problem Set #1 ANSWER KEY Economics of International Trade 1. Home has 1,200 units of labor available. It can produce two goods, apples and bananas. The unit labor requirement in apple production is 3, while in banana production it is 2. a. Graph Home’s production possibility frontier (hint: put apples on the yaxis and bananas on the x-axis). To graph Home’s PPF, plot the y-intercept (0 bananas, 400 apples) and the xintercept (0 apples, 600 bananas) and connect these points with a line. (Calculations: 1200/3 = 400 apples; 1200/2 = 600 bananas.) This yields the blue PPF line below. These values represent the total amount of each good that can be produced if all units of labor are devoted to the production of that good.

Apples&

Home:&PPF&Before&Trade& 450" 400" 350" 300" 250" 200" 150" 100" 50" 0"

PPF"Before"Trade"

0"

200"

400" Bananas&

600"

800"

b. What is the most apples Home can consume? ANSWER: 400 c. What is the most bananas Home can consume? ANSWER: 600 d. What is the opportunity cost/price of apples in terms of bananas? ANSWER: Consuming an apple is equivalent to 3 labor units; consuming a banana is equivalent to 2 labor units. An apple in terms of bananas is 3/2 = 1.5 bananas. This represents the number of hours that Home would have to give up from the production of bananas in order to produce one apple.

2. There is another country, Foreign, with ! a labor force of 800. Foreign’s unit labor requirement in apple production is 5, while in banana production it is 1. a. Graph Foreign’s production possibility frontier (hint: as before, put apples on the y-axis and bananas on the x-axis). ANSWER: Calculation = 800/5 = 160 Apples. 800/1 = 800 bananas.

Apples&

Foreign:&PPF&Before&Trade& 180" 160" 140" 120" 100" 80" 60" 40" 20" 0"

PPF"Before"Trade"

0"

200"

400"

600"

800"

1000"

Bananas&

b. What is the most apples Foreign can consume? ANSWER: 160 c. What is the most bananas Foreign can consume? ANSWER: 800 d. What is the opportunity cost/price of apples in terms of bananas in Foreign? ANSWER: Foreign must give up 5 units of labor to make an apple, and those 5 units of labor could have made 5 bananas, so the opportunity cost for one apple is 5 bananas. This represents the number of hours that Home would have to give up from the production of bananas in order to produce one apple. 3. Assume that the demand for apples and bananas in both Home and Foreign is such ! that they negotiate a price that an apple is worth 2 bananas. a. On two separate graphs, redraw the production possibility frontier for Home ! and Foreign if they do not trade (Hint: these graphs will be identical to those you drew above). Then draw a line showing how much

each country can consume through a combination of production and trade. (The endpoints will be how much they can consume if they produce one product and don’t trade at all, and how much they can consume if they produce one product sell all of it to buy from the other country)

Home:&PPF&Before&and&After& Trade& 500"

Apples&

400" 300" 200"

PPF"Before"Trade"

100"

PPF"After"Trade"

0" 0"

200"

400"

600"

800"

1000"

Bananas&

Foreign:&PPF&Before&and&After& Trade& 500"

Apples&

400" 300" 200"

PPF"Before"Trade"

100"

PPF"After"Trade"

0" 0"

200"

400" 600" Bananas&

800"

1000"

For Home and Foreign, each country’s PPF in the absence of trade remains the same. With trade, each country will specialize in the production of a single good. At the extremes, Home has two options: produce 400 apples and trade them for 800 bananas (400 x 2); or produce 600 bananas and trade them for 300 apples (600 x ½). Home will choose the first option; this is because its opportunity cost of apples in terms of bananas is lower than that of Foreign. This new

PPF is plotted in red in the first graph above. Similarly, at the extremes, Foreign also has two options: produce 160 apples and trade them for 320 bananas; or produce 800 bananas and trade them for 400 apples. Foreign will choose the latter because its opportunity cost of bananas in terms of apples is lower than that for Home. This new PPF is plotted in red in the second graph above.

b. What is the most Apples Home can consume with trade? ANSWER: 400 c. What is the most Bananas Home can consume with trade? ANSWER: 800 d. What is the most Apples Foreign can consume with trade? ANSWER: 400 e. What is the most Bananas Foreign can consume with trade? ANWER: 800 f. Which country has improved its economic position (in absolute, not relative, terms) as a result of trade? Why? ANSWER: Both countries are made better off by trade because they can each consume a larger quantity of goods after trade than before. 4. Repeat the analysis from question 3, but now assume that the international price for apples in terms of bananas is 4 bananas per apple. (Hint: A country cannot import more than the other country can produce)

450" 400" 350" 300" 250" 200" 150" 100" 50" 0"

PPF"Before"Trade" PPF"After"Trade" 0" 120" 240" 360" 480" 600" 720" 840" 960" 1080" 1200" 1320" 1440" 1560"

Apples&

Home:&Before&and&After&Trade&

Bananas&

ANSWER: Home can now trade 400 apples for 4 x 400 = 1600 bananas, if 1600 bananas are available. But Foreign can only produce 800 bananas. So Home can trade for up to

800 bananas, which will “cost” 200 apples. Home still therefore would have the capacity to produce 200 apples, which would take up half of its labor force, 600 (200 x 3) labor units. If these labor units are dedicated to bananas, it could produce 600/2 = 300 bananas. So the maximum number of bananas possible is 800 bananas traded for plus 300 bananas produced directly = 1100 bananas.

Foreign&PPF&Before&and&After& Trade& 250"

Apples&

200" 150" PPF"Before"Trade"

100"

PPF"After"Trade"

50" 0" 0"

160"

320"

480"

640"

800"

Bananas&

Foreign can make 800 Bananas and trade for 800/4 = 200 Apples. Both are still better from trade than they would be without trade, because each can consume more with trade than without trade. 5. BONUS QUESTION: If a country changes its policies from closed to open, ! how will this affect economic growth in the short term vs. the long term? Why? In the short run, trade produces an increase in output via an outward expansion of the production possibilities frontier. In the long run, trade may influence the long run level of output, but will have no effect on the long run rate of growth of output – UNLESS countries increase their rate of technological improvement due to specialization. However, this goes beyond what has been introduced in the problem. Based on the information in the problem, the rate of growth will be high as each country shifts from autarky to trade, and then will settle at a new steady state of growth (which, based on the information available, is zero).

Practice with Simultaneous Games Find the (Pure Strategy) Nash Equilibrium/a for each of the following (Describe them as strategy for each player, not as payoffs). State whether each Nash Equilibrium is Pareto Efficient or not. Explain your reasoning. 1. Scarce dessert resources game Kid 2

Kid 1

Eat ice cream

Eat cake

Eat ice cream

4, 4

8, 10

Eat cake

10, 8

5, 5

ANSWER: For Kid 1, if Kid 2 eats ice cream, it is better to eat cake (10 > 4). If Kid 2 eats cake, it is better to eat ice cream (8 > 5). The same logic is true for Kid 2. There are two underlined payoffs in two cells, so the two Nash Equilibria are 1) Kid 1: Eat cake, Kid 2: Eat Ice cream, and 2) Kid 1: Eat ice cream, Kid 2: Eat cake. In each of these strategy combinations, neither player will want to unilaterally change his decision. In each of these strategy combinations, neither player will want to unilaterally change his decision. Each Nash Equilibrium is Pareto Efficient. In a Pareto Efficient outcome, there are no Pareto Improvements available, meaning there is no change in outcomes that would make at least one player better off and no players worse off. From payoff (10,8), any change in outcomes will make Kid 1 worse off, so there are no Pareto Improvements. From payoff (8,10), any change in outcomes will make Kid 2 worse off, so there are no Pareto Improvements. No Pareto Improvements available means the outcome is Pareto Efficient.

2. Odd Couple game Felix Clean

Relax

Clean

2, 8

0, 2

Relax

6, 4

8, 0

Oscar

ANSWER: Each player has a dominant strategy. Oscar always prefers to Relax (6 > 2 if Felix Cleans; 8 > 0 if Felix Relaxes) and Felix always prefers to Clean (8 > 2 if Oscar Cleans, and 4 > 0 if Oscar Relaxes). There is one Nash Equilibrium: 1) Oscar Relax, Felix Clean. Neither will want to unilaterally change his decision. In each of these strategy combinations, neither player will want to unilaterally change his decision. This Nash Equilibrium outcome is Pareto Efficient. In a Pareto Efficient outcome, there are no Pareto Improvements available, meaning there is no change in outcomes that would make at least one player better off and no players worse off. From payoff (6,4), any change in outcomes would make at least one player worse off, so there are no Pareto Improvements available. No Pareto Improvements available means the outcome is Pareto Efficient. 3. Texting while driving game Driver 2 Text

Don’t text

Text

-100, -100

1, -1

Don’t text

-1, 1

0, 0

Driver 1 " ANSWER: For Driver 1, if Driver 2 Texts, it is better to Don’t Text (-1 > -100). If Driver 2 chooses Don’t Text, it is better to Text (1 > 0). The same logic is true for Driver 2.

There are two underlined payoffs in two cells, so the two Nash Equilibria are 1) Driver 1: Don’t text, Driver 2: Text, and 2) Driver 1: Text, Driver 2: Don’t Text. In each of these strategy combinations, neither player will want to unilaterally change his decision. Each Nash Equilibrium is Pareto Efficient. In a Pareto Efficient outcome, there are no Pareto Improvements available, meaning there is no change in outcomes that would make at least one player better off and no players worse off. From payoff (-1, 1), any change in outcomes will make Driver 2 worse off, so there are no Pareto Improvements. From payoff (1, -1), any change in outcomes will make Driver 1 worse off, so there are no Pareto Improvements. No Pareto Improvements available means the outcome is Pareto Efficient.

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