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Problem Set 3

EC2202

Problem 1 Alwyn Young wrote a paper published in 2005 in which he studies the macroeconomic consequences of the horrible tragedy of AIDS in sub-Saharan Africa. Answer the following questions, motivated by his research (there is no need to read the paper in order to complete this exercise). 1. In the production function approach we studied in class, we noted that the wage rate is equal to the marginal product of labor. Write the mathematical expression of this statement. That is, write the wage as a function of capital, labor, and the TFP parameter. 2. Young estimates that AIDS may eventually kill 25 percent of the population in some of the poorest countries of the world. Assuming TFP and the amount of capital are unchanged by the epidemic, by how much would the wage rate change as a consequence of AIDS. 3. Discuss your result. Why does the wage rate change? Why is the effect larger or smaller in magnitude than 25 percent? In what sense is there a “gift of the dying,” to use Young’s evocative title? 4. In a paragraph or less, discuss any questions you may have regarding this result.

Problem 2 In 2011 dollars

Relative to the U.S. values (U.S. = 1)

(1)

(2)

(3)

(4)

(5)

(6)

Country

Capital per person

Per capita GDP

Capital per person

Per capita GDP

Predicted y∗

Implied TFP to match data

United States

141,841

51,958

1.000

1.000

1.000

1.000

South Korea

120,472

34,961

Indonesia Mexico

41,044 45,039

9,797 15,521

Ethiopia

3,227

1,505

(from Jones, Chapter 4, Problem 5 and 6) The table below reports per capita GDP and capital per person in the year 2014 for 5 countries. Your task is to fill the missing columns of the table. 1

1. Given the values in columns 1 and 2, fill in columns 3 and 4. That is, compute per capita GDP and capital per person relative to the U.S. values. 2. In column 5, use the production model (with a capital exponent of 1/3) to compute the predicted per capita GDP for each country relative to the United States, assuming there are no TFP differences. 3. In column 6, compute the level of TFP for each country that is needed to match up the model and the data. 4. Comment on the general results that you find. 5. Repeat questions 1-4 for Indonesia and Mexico only, but this time assume the production is given 1 3 by Y = AK 4 L4 . That is, assume the exponent on capital is 34 rather than 13 so that diminishing returns to capital are less. In question 4, compare the results with those obtained with a capital exponent of 13 . Why do you think the results are different? Is it reasonable to assume a capital share of 34 in the model?

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