Question

2. Suppose the firm has the one variable production function Q=L?. Assume that the wage rate is w= 20 and that the firm has fixed costs of 10. Finally, assume that the firm is a price taker and the market price is 2. a) Show that this production function exhibits increasing returns to scale. Show that the marginal product of labor is increasing. Illustrate the production function. Is it convex, concave or neither? b) Find the variable and total cost curves for the firm. Illustrate both. Are they convex, concave or neither? c) Find the MC and AC curves. What is the optimal size of the firm? For what values of output does the firm have economies of scale? Illustrate both. In general, the firm maximizes profits by setting MR = MC. However, there are instances where doing so does not maximize profits (think of the shut-down decision from class). d) Find the quantity, Q*, such that MR = MC. Illustrate the MR and MC curves in a diagram and indicate Q*. e) If the firm were to produce more than Q* then would firm profits rise or fall? Briefly explain (you may use your diagram in your explanation). Q* is a critical value of your profit function (i.e. it is a max, a min or a saddle value). However, it is not the maximum of the profit function. What critical value is it? Briefly explain or use calculus to demonstrate your answer.

Answer 1

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