A production function is given by f(K,L)=K+L. (a) Does this production function exhibit decreasing, constant, or increasing returns to scale? (b) The average product of capital is defined as total output divided by the amount of capital input. The average product of labor is defined as total output divided by the amount of labor input. Suppose that K=1 and L=4. Determine the average and marginal products of capital and labor, respectively. Determine what happens to the average and marginal product of labor and capital if K is increased to K=9. (c) Determine the TRS (assuming K in on the vertical axis and L on the horizontal axis). (d) Determine the firm's profit-maximizing demand for inputs K and L as a function of input prices, r and w, respectively. (e) Now suppose that the production function is given by f(K,L)=(K+L)2. Determine the type of returns to scale. Can we determine the firm's profitmaximizing demand for inputs K and L as a function of input prices, r and w, now? (Answer: Only the ratio of inputs can be determined. Unique solutions for optimal level of inputs cannot be found. Why?) A production function is given by f(K,L)=K+L. (a) Does this production function exhibit decreasing, constant, or increasing returns to scale? (b) The average product of capital is defined as total output divided by the amount of capital input. The average product of labor is defined as total output divided by the amount of labor input. Suppose that K=1 and L=4. Determine the average and marginal products of capital and labor, respectively. Determine what happens to the average and marginal product of labor and capital if K is increased to K=9. (c) Determine the TRS (assuming K in on the vertical axis and L on the horizontal axis). (d) Determine the firm's profit-maximizing demand for inputs K and L as a function of input prices, r and w, respectively. (e) Now suppose that the production function is given by f(K,L)=(K+L)2. Determine the type of returns to scale. Can we determine the firm's profitmaximizing demand for inputs K and L as a function of input prices, r and w, now? (Answer: Only the ratio of inputs can be determined. Unique solutions for optimal level of inputs cannot be found. Why?)