2&3, thanks!

2. (12 points) Consider the following technologies involving capital and labor: a. f' ( K, L) = K1/21 1/3 b. f- (K, L) = 312/312/3 c. f3(K, L) = K1/2 + L1/2 d. f* (K, L) = 2K + 3L. a) (4 points) Which have decreasing / constant / increasing returns to scale? b) (4 points) Compute the technical rate of substitution for each at (K, L) = (1, 1) c) (4 points) Which exhibit decreasing returns to labor input 3. (12 points) Profit maximization Consider the technology fi(K, L) = K1/21/3. The price of labor is w, the price of capital is r and the firm's sales price is p. a) (4 points) Find its maximum profit in the short run where capital is fixed at K. Simplify as much as possible. b) (4 points) Find its optimal output in the long run where both labor and capital can be chosen. Simplify as much as possible. c) (4 points) If the firm's production function is f?(K, L) = 3K2/3 12/3, its maximum profit in the long run where both labor and capital can be chosen. Simplify as much as possible