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 functionQ=KL.

1. (a)Suppose the price of capital (r) increases. Using carefully labelled diagrams, illustrate what happens to the optimal choice ofKandLand the demand curve/quantity demanded for labour. for the optimal choice, just illustrate graphically.
2. (b)Now, suppose there was no price increase. Instead, suppose that Big Boss decided to produce a lower quantityQ0. Draw a new version of the two graphs above to illustrate this case, showing the change in optimal choices ofKandLand the change in the demand curve/quantity demanded.
3. (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. Now draw a second Total Cost function (TC2) to illustrate the case where the price of labour decreased.
4. (d)Suppose that you knowK= 4Q/r2andL= 2Q/w2. You also know thatw= 3andr= 1, but Big Boss has not yet told you how much to produce. how to find the expressions forTC(Q),AC(Q)andMC(Q).