http://users.wfu.edu/cottrell/ecn207/cobb-douglas.pdf

3. (15) Consider a Cobb-Douglas production function with three inputs. K is capital (the number machines), L is labor (number of workers) and E is energy from fossil fuels (number of terawat hours). Assume the production function is given by Y = AKO.2 10.5 EO.3 a. Derive an expression for (1) The marginal product of capital (2) The marginal product of labor (3) The marginal product of energy b. Suppose the amount of fossil fuels available shrinks by 5%. (1) What happens to total output produced (in percent)? (2) What happens to the real rental price of capital (in percent)? (3) What happens to the real wage? (in percent) (4) What happens to the real price of fossil fuels (in percent)? (5) What happens to the share of output going to owners of capital, workers, and energy companies (owners of fossil fuels)? Explain