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Making a cost-minimizing choice in the long-run

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Reference no: EM132484431

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 = KaLB.

  1. (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. You do not need to solve mathematically 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 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.
  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 know K∗ = 4Q/r2 and L∗ = 2Q/w2. You also know that 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).

Reference no: EM132484431

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