Theory of production and cost, Microeconomics

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1.A firm producing Golf sticks has a production function given by

Q=2v(K L)

In the short run, the firm’s amount of capital equipment is fixed at k = 100. The rental rate for k is v = $1, and the wage rate for L is w = $4.

Calculate the firm’s short-run total cost curve (STC). Calculate the short-run average cost curve (SAC).

What is the firm’s short-run marginal cost function (SMC)? What are the STC, SAC, and SMC for the firm if it produces 25 golf sticks? 50 golf sticks? 100 golf sticks? 200 golf sticks?

Graph the SAC and the SMC curves for the firm. Indicate the points found in part (b).

Where does the SMC curve intersect the SAC curve? Explain why the SMC curve will always intersect the SAC curve at its lowest point.

Suppose now that capital used for producing golf sticks is fixed at K ¯ in the short run.

Calculate the firm’s total costs as a function of q, w, v, and K ¯

Given q, w, and v, how should the capital stock be chosen to minimize total cost?

Use your results from part (f ) to calculate the long-run total cost of golf stick production.

For w = $4, v = $1, graph the long-run total cost curve for golf stick production. Show that this is an envelope for the short-run curves computed in part (a) by examining values of K ¯ of 100, 200, and 400

2.Comrades Movie Theater serves two kinds of customers: students and staff. There are 900 students and 100 staff. Each student’s willingness to pay for a movie ticket is $5. Each staff willingness to pay for a movie ticket is $10. Each will buy at most one ticket. The movie theater’s marginal cost per ticket is constant at $3, and there is no fixed cost.

A. Suppose the movie theater cannot price-discriminate and needs to charge both students and staff the same price per ticket. If the movie theater charges $5, who will buy tickets and what will the movie theater’s profit be? How large is consumer surplus?

B. If the movie theater charges $10, who will buy movie tickets and what will the movie theater’s profit be? How large is consumer surplus?

C. Now suppose that, if it chooses to, the movie theater can price-discriminate between students and staff by requiring students to show their student ID. If the movie theater charges students $5 and staff $10, how much profit will the movie theater make? How large is consumer surplus?

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