Econ 441 Alan Deardorff Problem Set 2 - Answers Gains and Ricardian Page 1 of 11 Problem Set 2 - Answers Gains from Trade and the Ricardian Model 1. Use community indifference curves as your indicator of national welfare in order to evaluate the following claim: “An improvement in the terms of trade increases welfare only if the country increases its quantity of exports in response. If a country is unwilling or unable to increase exports when their price rises, then the price increase does it no good.” This is false, which we can illustrate as follows: In the figure, the relative price of X rises from p1 to p2, causing production to move to the right, from P1 to P2. With the indifference curves shown, consumption also moves to the right, from C1 to C2, although this is not a necessary result. Indeed, as drawn, the consumption of good X rises by more than the production of X, so that exports of X fall. Nonetheless, the country moves to a higher indifference curve, indicating an improvement in welfare. The reason this is possible without an increase in exports is that, when the price of the exported good rises, the country can buy and enjoy a larger quantity of imports in exchange for its exports, even if it keeps the quantity of exports fixed or even reduces that quantity somewhat. (Here’s a question for you: Is it possible for the quantity of imports to fall in response to such an improvement of the terms of trade? And if so, does welfare still increase? I’ll leave that for you to ponder on your own.)Econ 441 Alan Deardorff Problem Set 2 - Answers Gains and Ricardian Page 2 of 11 2. Consider an economy that does not produce goods, but is simply endowed with certain amounts of them, and in which the population consists of two groups: farmers who own only wheat and weavers who own only cloth. (Never mind that these people don’t actually farm and weave – the names are just for convenience.) There are equal numbers of people in both groups, and they all share identical homothetic preferences for consuming wheat and cloth. a. Draw the production possibility frontier for this economy, and illustrate the autarky equilibrium. It is not really production, of course, but the maximum quantities of the two goods available to the country, and , are now fixed. Since the country can consume these amounts or less, the PPF may be thought of as a rectangle with corner at . The autarky equilibrium is then at that corner, and the autarky prices appear as the price line tangent to a community indifference curve at that point: b. Is it possible to say who is better off in autarky, the farmers or the weavers? On what does that depend? It is not possible to say who is better off in general, since it depends on the quantities of their endowments and the community’s preferences for the goods. But for given endowments and preferences, as in the diagram above, we can use the autarky price line to find the budget lines for the farmers and weavers as groups, and since we’ve assumed equal numbers of both, we can conclude that in the case drawn, the farmers are better off. The farmers’ aggregate budget line is BF and the weavers’ budget line is BW.Econ 441 Alan Deardorff Problem Set 2 - Answers Gains and Ricardian Page 3 of 11 c. Suppose now that the country opens up to free trade at a relative price of wheat that is higher than its autarky price. Show the new equilibrium. d. Construct the utility possibility frontiers for autarky and free trade, and indicate how the actual equilibria along these frontiers will compare. Who gains and who loses from trade? In what sense, if any, are there gains from trade in this case? Since preferences are identical and there are the same numbers of farmers as weavers, the UPFs are downward sloping 45o lines. Since the utility attainable with the income of the country as a whole rises with trade from Ua to Uf, as shown above, the UPF for free trade, UPFf lies further from the origin that the UPF for autarky, UPFa. Thus there are gains from trade in the sense that, if income were somehow redistributed between the groups, it would be possible with trade to make everybody better off.Econ 441 Alan Deardorff Problem Set 2 - Answers Gains and Ricardian Page 4 of 11 To see who gains and loses without such redistribution, rotate the group budget lines in part (b) to reflect the change in prices from autarky to free trade: From this it is clear that the farmers gain and the weavers lose. So the movement in the UPF diagram is as follows:Econ 441 Alan Deardorff Problem Set 2 - Answers Gains and Ricardian Page 5 of 9 3. Which of the following characterize the Ricardian Model? a. Perfect mobility of factors across industries Yes b. Perfect mobility of factors across countries No c. Constant returns to scale Yes (Almost trivially, since, with only one factor, a proportional increase in all factors is just an increase in labor. Since output is proportional to the labor input, this satisfies the definition of constant returns to scale: that a proportional increase in all inputs leads to an equal proportional increase in output.) d. The law of diminishing returns No (Or one could say that it does not apply. That is, an increase in one factor input does not lead to a fall in its marginal product, as the law of diminishing returns would predict. But in this case there is no other factor input to be held fixed, as required for that law to apply.) e. Identical technologies across industries No f. Identical technologies across countries No g. Cournot competition No h. Perfect competition Yes 4. Suppose that a small open economy has 200 workers and that its technology requires 1 worker-hour per unit of food (thus 1 unit of food per worker-hour) and 3 worker-hours per unit of cloth (thus output per worker-hour = 1/3). In autarky, it employs 100 workers in each of the two industries. With free trade, it faces world prices of $10 per unit of food and $20 per unit of cloth. a. Suppose that in autarky, workers in both industries are paid $8 per hour. What are the autarky prices of food and cloth? Prices of the goods are just their costs of production: pF = 8×1 = $8 per unit of Food; pC = 8×3 = $24 per unit of Cloth. b. When the country opens to free trade, under the normal assumptions of the Ricardian model, what will it produce, import, and export? From