Q3: Consider the following production function: Q = K^1/3 L^1/3 with rental costs r and labour costs w.

a) Draw the isoquant for Q = 100. b) Does this production function exhibit increasing, constant, or decreasing returns to scale? Show/explain. c) Let K be variable. What is the optimal relationship between K and L: (hint: MRTS = L/K) d) What is the input demand for Labour (as a function of Output) and the input demand for Capital? e) Derive the long-run cost function. (eg C = wL + rK where L and K are optimal choices). f) Plot the cost function given w = $20 and r = $10. g) Calculate the long-run costs for Q = 100. Q = 200. h) Does this cost function exhibit increasing, constant, or decreasing economies of scale?