Consider a firm with the production of the form: Q =AL^bK^(1-b). The marginal products associated with production are MP_L=bAL^b-1K^1-b, MP_K=(1-b)AL^bK^-b. The input price of labour is w and the input price of capital is r.

A) Determine whether the production function exhibits increasing, decreasing, or constant returns to scale. (5 marks)

B) Derive the input demand functions. (10 marks)

C) Suppose that A=10, b=0.5, w=5, r=10 and the targeted level of output is Q=150. Determine the optimal amount of K and L necessary to satisfy the firm's cost minimization problem.

D) Now suppose that the rental rate of capital drops to r=5. How much capital and labour is required? Explain why the amount of capital is higher, lower, or the same as the amount of labour at the optimal input level.

E) Do parts A)-D) characterize a firm in a short-run or long-run scenario? How do you know?