Alwyn Young, an economist at the London School of Economics, has a paper 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. Assume that the exponent on capital is 1/3 and the exponent on labor is 2/3. Required:
a. In the production function model we examined 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 total factor productivity (TFP) parameter.
b. Young estimates that AIDS may eventually kill 25% 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.
c. Discuss your result. Why does the wage rate change? Why is the effect larger or small in magnitude than 25%? In what sense is there a "gift of the dying," to use Young's title?