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Problem Set 4

Econ 433

Fall 2021

1. (35 points) This problem set asks you to use diagrammatic techniques to evaluate the effects of various changes on the equilibrium in a specific factor (Ricardo-Viner) model. There are two goods, food and clothing. Food is made using land and labor. The quantity of land is fixed. Clothing is made using capital and labor. The quantity of capital is fixed. Increases in the use of any factor raise the marginal product curve of the other factor used in production. Labor is fixed in total, but it can move from one industry to another in a country. The economy is small: That is, it faces given prices at which it can trade. It imports food and exports clothing at these prices.

a. Use a four quadrant diagram to construct the Production Possibility Frontier (PPF) for this economy and the equilibrium under free trade in this diagram.

b. Show the returns to land, labor and capital. What is the effect of a tariff on food on the real return to these three factors?.

c. For given product prices, explain the effects of an increase in temporary workers (whose utility we do not value) in this country. Does labor gain or lose from this change? Do owners of capital and land gain or lose from this change? Does the economy as a whole gain or lose?

d. What is the effect of an increase in capital? Does labor gain or lose from this change? Do owners of existing capital and land gain or lose from this change?

e. Now assume that the country is large so that changes in its relative supply can affect world prices. What do you expect would happen to equilibrium prices in the world under free trade in response to the innovation described above? Hint: For any given prices what happens to the world relative supply of clothing relative to food?

Extra Credit (10 POINTS)

f.Suppose that instead of capital increasing as in part d), an innovation has made capital more productive in this economy/country than before so that effective capital has increased though physical capital has not. Do owners of capital in this country gain or lose due to the innovation at given prices?

2. (30 points) A small open economy has two sectors: food and manufacturing. There are 20 workers in the economy. In manufacturing the value of marginal product of workers is given by

V M P L = 20 − L.

The value of marginal value product of labor in agriculture is constant at 10.

a. How many workers will work in each sector? What is the value of output of each sector? (Hint-add up the MVPL over all units employed)

b. Now suppose there is a union in manufacturing which offers a wage of 12. If there is full employment what happens to the allocation of labor and the wages in the two sectors. Depict the effect of the union on the country’s income.

c. Suppose that workers migrate to manufacturing to get the higher wage. As a result, there is unemployment. If labor demanded in manufacturing is A and there are B > A workers lined up to get a job, assume that only a fraction A/B of them get employed while the remaining are unemployed. Thus, workers must choose between being employed for sure in agriculture or risking unemployment for a higher wage in manufacturing. In this setting what is the effect of the union? Make sure you depict the equilibrium with migration

d. Will there be unemployment? Where will the economy be in terms of its production possibilities? What would a subsidy to labor of $2 in both sectors do to the equilibrium? Can you explain why?

3. (35 points) There are two goods, food and clothing, and two factors, capital and labor, used to make these goods. Both goods are made by this country to begin with. The clothing industry is capital intensive relative to the food industry. Once capital is invested in an industry, it takes a form which makes it useless in the other industry. Thus, in the medium run, the capital in one industry is not usable in the other industry or is industry specific. In the long run, capital can move between industries. Labor is fixed in total, but it can move from one industry to another in a country in the medium and in the long run. The economy is small: That is, it faces given prices at which it can trade. It imports food and exports clothing at these prices.

a. In this economy, what is the effect on the real and nominal returns to labor of a tariff on the import of food in the medium run? Why?

b. Explain how your answer to the previous part can help explain the politics of the Corn Laws of 1815 in England and the triff on manufacturing imports in the US prior to the Civil War..

c. Would you expect labor to favor a tariff on food? Why? Be sure to explain the conditions under which it would favor a tariff on food.