Suppose life expectancy in years (L) is a function of two inputs: health expenditures (H) and nutrition expenditures (N) both measured in hundreds of dollars per year. The production function or longevity is: (, ) = ^.^.

a) Beginning at = and = , show that the marginal product of health expenditures and the marginal product of nutrition expenditures are both decreasing.

b) Does the production function (, ) exhibit increasing, decreasing or constant returns to scale? c) Suppose that a country is suffering a famine and nutritional expenditures are fixed at = . Graph (, ) with on the vertical axis and on the horizontal axis. [You can use values of H between 1 and 5.]

d) Suppose the country in part (c) received foreign food aid resulting in an increase in nutritional expenditures to = . Add the new graph of (, ) to the graph you made in part (c).

e) Suppose the country is operating at = and = (this is a point on the graph you made in part (d)). If you ran a Non-Government Organization (NGO) with the ability to increase nutritional expenditures to that country by 1 or health expenditures in that country by 1, which would you choose in order to maximize the effect on life expectancy of that additional expenditure?