Consider a firm that is making a cost-minimizing choice in the long-run for a given quantity of output, Q₁ . Suppose this firm has a cobb douglas production function Q = K L .

(a) Suppose the price of capital (r) increases. Using carefully labelled diagrams, illustrate what happens to the optimal choice of K and L and the demand curve/quantity demanded for labour.

(b) Suppose there was no price increase. Instead, suppose that Big Boss decided to produce a lower quantity Q₀ . Draw a new version of the two graphs above to illustrate this case, showing the change in optimal choices of K and L and the change in the demand curve/quantity demanded.

(c) Plot the total cost function (TC₁) for the firm on a graph with Total Cost on the vertical axis and quantity on the horizontal axis. Draw a second Total Cost function (TC₂) to illustrate the case where the price of labour decreased.

(d) Suppose that K = 4Q/r² and L = 2Q/w² . Also, w = 3 and r = 1, but Big Boss has not yet told you how much to produce. Find the expressions for TC(Q), AC(Q) and MC(Q) .