Suppose life expectancy in years (L) is a function of two inputs, health expenditures (H) and nutrition expenditures (N) in hundreds of dollars per year. The production function is
L = cH0.8N0.2.
a) Beginning with a health input of $400 per year (H = 4) and a nutrition input of $4900 per year (N = 49), show that the marginal product of health expenditures and the marginal product of nutrition expenditures are both decreasing.
b) Does this production function exhibit increasing, decreasing, or constant returns to scale?
c) Suppose that in a country suffering from famine, N is fixed at 2 and that c = 20. Plot the production function for life expectancy as a function of health expenditures, with L on the vertical axis and H on the horizontal axis.
d) Now suppose another nation provides food aid to the country suffering from famine so that N increases to 4. Plot the new production function.
e) Now suppose that N = 4 and H = 2. You run a charity that can provide either food aid or health aid to this country. Which would provide a greater benefit: increasing H by 1 or N by 1?