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) b) d) L(H, N) = 20 x [lo-8N"-2 Beginning at H = 4- and N = 4-9, show that the marginal product of health expenditures and the marginal product of nutrition expenditures are both decreasing. Does the production function 1.01, N) exhibit increasing, decreasing or constant returns to scale? Suppose that a country is suffering a famine and nutritional expenditures are fixed at N = 2. Graph L(H, N) with L on the vertical axis and H on the horizontal axis. [You can use values of H between 1 and 5.] Suppose the country in part (c) received foreign food aid resulting in an increase in nutritional expenditures to N = 4. Add the new graph of L(H, N) to the graph you made in part (c). Suppose the country is operating at N = 4 and H = 2 (this is a point on the graph you made in part (d)). If you ran and N60 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