a) In the long run, both labor, L, and capital, K, are variable costs. Show in a graph, where you have the quantity of L on the X-axis, and the quantity of K on the Y-axis, how one can indicate combinations of L and K that cost the same to produce. What is this type of lines called?

b) Then show how one can indicate combinations of L and K that produce the same quantity of the good. What is this type of lines called?

c) The firm always wants to minimize its cost of production. Choose a certain quantity in your graph, and show how the firm would minimize its cost of producing that quantity.

d) What is the mathematical criterion for a cost-minimizing choice of L and K? What does that correspond to in the graph?

e) Show, in your graph, how to derive the long-run expansion path.

f) Show how to derive the short-run expansion path.

g) Use the information in your graph to derive the long-run cost curve. First, choose levels for the cost and the production in the graph you have constructed. Then, draw a new graph, with the quantity produced, q, on the X-axis, and the cost, C, on the Y-axis.