4. Consider the Cobb-Douglas production function Q=f(L,K)= 13/4 K1/4 The wage rate is w, the rental rate of capital is r. Note that k and I are inputs, and f is output. Please find: a. Marginal product of each input. b. Average product of inputs. c. Whether the function exhibits constant/increasing/decreasing returns to scale. d. Slope of the isoquant. e. Conditional input demand functions L(w,r,q) and K(w,r,q). f. Effect of change in output for the inputs (Hint: normal or inferior inputs). g. Total cost function C(w,r,q). h. Average cost and marginal cost functions. i. Profit maximizing output of the price-taking firm in the short-run (Hint: capital is fixed in the short-run) 1. Short-term supply curve of the firm Q(p,w,r.K) and comment on its shape