Required Supplemental Problems for Homework

Supplemental Problem for HW #1 - There is a positive correlation between international trade and economic growth, but correlation does not prove causality.  What are some of the alternative interpretations of this statistical relationship?  Using Google Scholar or the Knowledge Center's subscription to EconLit, look up three different papers published in economics journals since 2000, and in a paragraph each, explain how their findings compare to the causality problem and the literature discussed in class.

Supplemental Problems for HW #2 -- Consider two countries, England and Germany, each producing two goods, sausages (S) and beer (B), with only one resource, labor, constant returns, and perfect competition. Assume that England has 40 million identical workers, and one worker can produce either 1500 kilos of sausages (per year) or 1200 liters of beer (that is, MPLs = 1500 and MPLb=1200).  Germany has 60 million workers, and one worker there can produce either 1200 kilos of sausages or 2000 liters of beer.
  1. In two separate diagrams, graph the PPFs for both England and Germany, putting sausages (in billions of kilos) on the horizontal axis, and beer (in billions of liters) on the vertical. What is the autarky relative price ratio (Ps/Pb) in each country?   Which country has the higher real per-capita income?
  2. Assume that, at autarky, each country allocates 40% of its labor to sausage production and 60% to beer. What is the autarky production combination of S and B for each country?  (Hint: first figure out how much 10% of the workers in each country could produce of each good.) Show these preferred combinations on your PPF graphs using indifference curves, and label them (A) for autarky.
  3. Which country has the comparative advantage in which good? What does the Ricardian Theorem predict would be the pattern of free trade?
  4. Prove that in this example, total production of S and B increases when each country specializes in its comparative advantage. At what values of the terms-of-trade (Ps/Pb) would each country be willing to specialize in its comparative advantage?
  5. Assume that the terms-of-trade for sausage are 4:3. Assume each country fully specializes, and they then trade 36 billion kilos of sausages for 48 billion liters of beer. How much S and B will each country consume? Show these new general equilibria on your PPF diagrams, labeling the new production points (Q), the consumption point (C), and the consumption possibility frontier (CPF).
  6. Using this spreadsheet, you may check some of your answers.  The model input goes in the blue boxes, and the spreadsheet makes the calculations.  This spreadsheet assumes that each country has total effective money supply (money times velocity) of $100 billion, and also calculates the nominal prices and exchange rate, along with the real wage rate and the average utility level.  Note however that the spreadsheet uses the constant-shares utility function.  What is the terms of trade and the amount of trade predicted by this spreadsheet?  Does trade make people in both countries better off?
  7. Using this spreadsheet, how would the terms of trade, the pattern of specialization, the pattern of trade (who exports which product), the volume of trade, and the gains from trade (measured as an increase in average utility) all change if:
    1. Germany's money supply doubled?  (What changed?)
    2. Germany became more productive in beer production, and MPL rose to 2200?
    3. Germany became more productive in sausage production, and MPL rose to 2000?
    4. Germany became much more productive in sausage production, and MPL rose to 3000?  

Supplemental Problems for HW #3
Assume that a country produces two goods, Crafts and Food, under perfect market conditions. Craft production uses labor with a constant (non-diminishing) marginal product, while Food production requires specific farmland, so labor has diminishing marginal product. 
  1. Using the four-quadrant diagram, graph the production functions and the labor allocation, and then show how to derive the PPF.
  2. Assume that Foreign has more significantly more labor, while Home has much more land. Which PPF would be more bowed out?
  3. In two separate diagrams, graph the PPFs for both countries, with Crafts on the horizontal axis, and use indifference curves to show the autarky equilibria. Assuming preferences are identical, how does the relative autarky price (PC/PF) differ internationally?  Which country has the comparative advantage in which good?  
  4. On your PPF diagrams, show how free trade would lead to new equilibria.  For each country, show the production point Q and the consumption point C, and compare this to the autarky equilibrium A.
  5. Using the labor allocation diagram for the Home country, show how the optimal labor allocation and the wage rate is determined.  Assume that trade only affects PC, and nominal Pdoes not change.  Show what happens to the nominal income of workers in each sector, and to landowners.  Assuming workers buy an equal amount of both goods, what happens to the real wage rate?
  6. Assume in #5 above that wages are rigid in the short-run.  Use the labor allocation diagram to show how free trade could create unemployment.

Supplemental Problems for HW #4

Consider an model of trade between China and the USA, in which the only resources are labor (L) and capital (K). Suppose the USA has 150 million workers and $12 trillion in capital, while China has 600 million workers and $1 trillion in capital. Each country produces only machines (M) and textiles (T) under perfect market conditions, using both labor and capital with constant returns to scale and diminishing marginal returns, though machine production is relatively capital-intensive. Assume preferences and available technologies are identical, and factors are equally productive between the two countries.
  1. In two separate diagrams, graph the PPFs for both countries, with M on the horizontal axis, and use indifference curves to show the autarky equilibria. How does the relative autarky price (PM/PT) differ internationally?
  2. Under perfect free trade between the two countries, what would the Heckscher-Ohlin theorem predict would be the pattern of trade?  How would this affect relative prices in each country?  
  3. According to the Stolper-Samuelson theorem, how would free trade affect the wage-rental (W/R) ratio in each country, and how would this in turn affect the (K/L) ratios in each sector, in each country? 
  4. On your PPF diagrams, show the free trade equilibria.  How does free trade affect overall welfare in each country?
  5. Use an Edgeworth box to show how free trade affects the allocation of capital and labor for the USA.
  6. Use an Edgeworth box to show that specialization increases the total production of M and T, while trade leads to a Pareto-optimal distribution.
  7. Assume instead that preferences are not identical, but instead each country had a strong preference bias for the good of its comparative advantage.  How might this change your answers to the first three questions?
  8. Assume that in the very short-run, neither factor (K,L) is mobile between sectors (M,T).  How would this affect your answers to the first three questions (assuming preferences were still identical)?
  9. In words, not graphs, explain how your predictions would be different if labor in the USA was five times as productive as in China.

HW #5 -- Assume that Spain and Portugal both have many producers of vino jerez (sherry), with free entry and exit, but product differences, brand-name recognition, and economies of scale keep the two markets from being perfectly competitive. Assume that Spanish and Portuguese sherry producers have similar cost structures, but that Spain is a much larger market.
  1. Explain how the number of firms in this hybrid case of “monopolistic competition” would affect the price of sherry. Explain how the number of firms and the size of the market would affect the average cost of production. Explain how free entry and exit would affect producer profits in the long-run.
  2. How would Spain and Portugal have differed, under autarky, in the number of producers and the price of sherry? 
  3. How would free trade between the two affect the price of sherry in each, the total number of producers, and the number of brands available to consumers? Show your predictions using the Krugman-Obstfeld monopolistic competition pricing (PP) and cost (CC) diagram.

HW #8 -- Consider a country we shall call “Home” that produces only two goods, X and Y, with only capital and labor resources under standard Heckscher-Ohlin production functions.  Assume Home is perfectly competitive and relatively capital-abundant, and good X is relatively capital-intensive. 
  1. Use a model of intertemporal trade (i.e., PPFs and indifference curves) to show the autarky amount of savings and investment for Home.  Assuming its marginal rate of return (R) on investment is higher at Home than in foreign countries, explain how savings would flow, and what would happen to domestic savings, investment, and future output at Home? What would happen to Home's trade balance?  What would then happen in the future?
  2. Assume Home has perfect competition.  Home doesn’t save very much, however, and borrows savings from the rest of the world.
    1. Use a standard trade model with a PPF and indifference curves, with X on the horizontal axis, to show how this inward transfer affects Home’s consumption in the current period (remember this is not an intertemporal model).  How this must affect Home’s trade balance?  Assume the transfer does not affect the terms-of-trade.  
    2. Use the model to show how Home’s consumption, and its trade balance, will be affected in the future, when Home has to repay its borrowing with interest.
    3. Assume that Home decides to use this borrowing to finance investment in its capital stock, instead of increasing its consumption.  Show how this investment would change its PPF in the future.
    4. If Home uses its foreign borrowing to finance investment instead of consumption, is it possible that Home will be able to consume more in the future than it could have without the borrowing?  Show this, if possible.
  3. Using a supply and demand model for Home’s market for foreign exchange (Forex):
    1. Why do we typically assume Forex supply is more elastic than demand? How would these elasticities change over time? How is the direct exchange rate E related to the value of Home’s currency?
    2. How would a transfer of savings from the foreign country to Home affect E and the trade balance?
    3. How would a transfer of savings from Home back to the foreign country affect E and the trade balance?
    4. How would a tariff by the Home country on its imports affect E and the trade balance?
  4. Assume that Home’s government imposes a tariff on all of its imports.
    1. Use a PPF and indifference curves to show how the tariff would affect Home’s welfare, assuming Home was a small economy.  Why is the terms-of-trade not tangent to either the PPF or the indifference curve?
    2. If Home were a large economy, how would this tariff affect its terms-of-trade?  Is it possible for the tariff to improve Home’s welfare?  Show this.
    3. Use a graph for the supply and demand of Forex, from Home's point of view, and assume (for simplicity) that the only reason for trade in currencies is trade in goods and services.  How would the tariff's effect on import demand affect the demand for Forex?  How would this affect E?  How would this affect exports?
    4. Suppose Home decided to impose this tariff to address its international trade imbalance.  Would this policy work?  Why or why not?
  5. Suppose Home puts a $2 tariff on a single good, imported toys.  Domestic production rises in response to the higher price, from 3 million to 5 million toys, while domestic consumption falls from 15 million to 12 million toys.
    1. What is the amount of the change in producer and consumer surplus? How much does government receive in tariff revenue from domestic consumers? No graph is necessary, and you should assume supply and demand are linear functions.
    2. Suppose our tariff lowered the price of toys on the international market by $1 (i.e., the tariff is actually $3, but we paid only $2 of it). Does the tariff improve or worsen our domestic welfare overall, and by how much?

HW #9 -- Suppose that the world price for oil was only $70 per barrel, and at that price the U.S. would produce 3 billion barrels (per year) and consume 10 billion barrels. Suppose there is an external cost of $60 per barrel consumed in the U.S., and a new administration decides to finally do something about it.
a)       Suppose that the U.S. government adds a $30 tariff to each barrel of imported oil, and the U.S. is a small part of the world oil market.  This then raises the domestic petroleum price to $100 per barrel, increases domestic production to 4 billion barrels, and decreases consumption to 8 billion barrels.  Show, calculate and explain the effects of this tariff on domestic producer surplus, domestic consumer surplus, and the government budget (all in billions of dollars per year). In the absence of an externality, would this tariff improve or worsen efficiency?  Adding in the savings from the reduced external cost, would the tariff improve or worsen efficiency?
b)       Suppose that the U.S. government instead puts a $30 tax on the consumption of each barrel of oil, regardless of whether the oil is imported or domestically-produced. Because we assume we are a price-taker, this would not affect the before-tax price of oil, but by making the effective after-tax price equal to $100, it would reduce consumption exactly as the tariff does. Calculate the effects of this consumption tax on domestic producer surplus, domestic consumer surplus, the government budget, and the consumption externality. Would this tax improve or worsen our net national welfare, relative to the $30 tariff?
c) Now make the same comparison between a tariff and a consumption tax of $60, assuming that the effects are linear, e.g., at a price of $130, domestic producers would supply 5 billion barrels per year and consumption would fall to 6 billion barrels.
c)       How much is the optimal consumption tax? Is the optimal tariff greater than or less than the optimal consumption tax?  Which is more efficient, the tariff or the consumption tax?

HW#10 -- In part due to pressure from French Farmers, the European Union imposes import restrictions on food imports from the rest of the world, through its Common Agricultural Policy (CAP) and its Common External Tariff (CET). 
  1. Suppose this import restriction takes the form of a tariff. Assume that this tariff has a significant effect on the world price of food, use a supply and demand diagram to show the effects of this tariff on European food markets.  Carefully labeling areas, how much does this change producer surplus, consumer surplus, and the government budget?  Can the tariff improve overall welfare in the EU?  How much does it affect the net welfare of the rest of the world?
  2. Consider the effect of the above tariff on a small economy that joins the EU, and still imports food from the rest of the world (but not from the rest of the EU).
    1. Show the effects of this tariff on the small economy.
    2. Show the effects of an equivalent import quota.  What are the quota rents, and who gets them?  If at first glance the quota is equivalent to the tariff, what are some of the reasons that economists consider quotas to be much less preferable?
    3. Show the effect of a production subsidy that has the same effect on farmers.  How much does this change producer surplus, consumer surplus, and the government budget?  How does the production subsidy compare to the tariff?