Answer these questions about a firm’s production decisions:

a. A firm’s production function requires that it use at least one unit of labour and one unit of capital, i.e. L ≥ 1 and K ≥ 1. Initially the production function is Q = √KL . Over time, the production function changes to Q = L√K . Does this change represent technological progress? Show if this change is labour saving or capital saving. Carefully explain your answers.

b. A firm produces solar panels and use labour (L) and materials (M) in the production process where the production function is Q = 50√ML + M + L. Are the returns to scale increasing, constant, or decreasing for this production function? Prove your answer. Is the marginal product of labour ever diminishing for this production function? If so, when? Is it ever negative, and if so, when? Explain.