Ecos3005: Tutorial 1
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Ecos3005: Tutorial 1
For discussion Week 2
Question 1: Cost Concepts and Optimization
A company called Vivo has crude oil in storage. It has already built a refinery that uses crude as an input to produce diesel. This capital equipment is specialized and has no other use.
1. Give examples of Vivo’s opportunity cost of using its stockpile of crude oil to produce diesel. What is the short-run opportunity cost to Vivo for using its capital (the refinery)? What is the long-run opportunity cost of its capital?
2. The (annualized) opportunity cost of Vivo’s refinery is F = 100. The variable cost, including the opportunity cost of crude, is VC(q) = q2 , where q is the quantity of diesel produced. What is the firm’s long-run total cost as a function of output C(q)? What is its marginal cost and average cost?
3. Sketch the firm’s average and marginal cost curves on a diagram. Mark the cost and quantity at the minimum of average cost. (Hint: you can use the fact that the marginal cost curve intersects the average cost at the minimum of AC. We show this relationship in Question 2.)
4. Suppose that the price of diesel is p, and the Vivo has no influence over this price. The firm’s long-run profits are T (q) = pq − C(q). Find the first order condition for the profit maximizing q* . Then use this condition to show that the firm will supply where the marginal cost equals the price, p (assuming it supplies a positive volume).
5. Suppose that the price is p = 25. How much diesel would Vivo produce, and what are it’s profits. Can you say that the firm is making economic profits?
6. Suppose that the price is p = 10. What would be its profit-maximizing output, and profits? Would the firm choose to produce anything at this price?
Question 2: Cost Concepts and Optimization
Let the total costs for a firm producing the quantity q be C(q). Then the average cost of producing q is:
C(q)
q
Find the first order condition for the minimum of the average cost function (hint: use the product rule). Then show that the marginal cost curve intersects the average cost curve at the minimum of average cost.
Question 3: Simultaneous move games
An old lady is looking for help crossing the street. Only one person is needed to help; a second person doesn’t make a difference. You and I are the only two people nearby. Each of us will gain satisfaction of 2 if the lady gets the help she needs, regardless of who helps her, and 0 if she does not. But each one who goes to help will incur a cost of 1. We must both make a decision whether to help or not in the same instant.
1. Set this scenario up as a normal-form game by writing down the payoff matrix for You and I.
2. Identify any Nash equilibria to the game. Explain why they are Nash equilibria.
2022-09-26