Suppose life expectancy in years(L) is a function of twoinputs, health expenditures(H) and nutrition expenditures(N) in hundreds of dollars per year. The production function is L=cH^0.80 N^0.20.

Beginning with a health input of $500 per year (H=5) and a nutrition input of $300 per year (N=3), show that the marginal product of health expenditures and the marginal product of nutrition expenditures are both decreasing.

The change in the marginal product of health expenditures (MPH) is

MPH = ???

H

and the change in the marginal product of nutrition expenditures (MPN) is

MPN = ???

N