# EC508: Microeconomic Theory Midterm 3

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1 EC508: Microeconomic Theory Midterm 3 Instructions: Neatly write your name on the top right hand side of the exam. There are 25 points possible. Your exam solution is due Tuesday Nov 24, 2015 at 5pm. You may either give it to me in class or scan and it to me. ed exams that arrive with a time stamp after 5pm will not be accepted. 1 Multiple Choice (1 Point Each) 1. If a production process can be represented with a Cobb-Douglas production function Q = L 1 2 K 1 2, then the marginal rate of technical substitution equals (a) K L. (b) L K (c) ln Q2 (d) the marginal rate of technical substitution is not well defined for Cobb-Douglas production functions. 2. Suppose a firm tripled the amount of labor and capital used in the production process and that this change lead to less than a tripling of output. We would say that this firm s production process satisfies: (a) invariant returns to scale. (b) increasing returns to scale. (c) decreasing returns to scale. (d) constant returns to scale. (e) the Law of Diminishing Returns. 3. A competitive firm faces a market price p for each unit of its output. What is this firm s revenue if he produces 10 units of output? (a) R = 16 (b) R = 10 (c) R = 10p (d) R = 10p 2 1

2 4. Which of the following statements is not true about a profit maximizing perfectly competitive firm: (a) Always chooses their output so that price equals marginal cost. (b) Always chooses their output so that marginal revenue equals to marginal cost. (c) Always sets their marginal profit equal to zero. (d) Their supply function is equal to their average total cost. (e) Earns a profit of (P AT C)Q. 5. In the short run, a perfectly competitive firm can earn a positive economic profit. In the long run, we expect (a) the high barriers to entry to keep new firms from entering the market enabling existing firms to maintain positive economic profits. (b) the low barriers to entry to allow new firms to enter the market, pushing down the market price, lowering economic profits to zero. (c) these firms to become oligopolists. (d) profit to be equal to the ratio P MC P. 6. If the firm s revenue function is given by π(q) = 15Q Q 2. What is the marginal revenue? (a) 15Q 2 2Q 3 (b) 15 2Q (c) 15Q + 10 Q (d) A goat herd has the cost function c(q) = 1 4 Q2, where Q is the number of tubs of goat cheese the herd can make in 1 month. If the owner faces a competitive market for goat cheese, with a price of \$5 a tub. How many Q will the owner produce? (a) 9 (b) 10 (c) 11 (d) 12 (e) e iπ 2

3 8. The following matrix game is being played between two firms deciding whether to collude or not. Collude Don t Collude 100,100 5, 190 Don t 190, 5 60,60 Which of the following statements is correct? (a) The profile (Collude, Collude) is a Nash equilibrium. The firms are clearly achieving the best outcome possible as a group. (b) The profile (Don t, Collude) is a Nash equilibrium. Firm 2 is clearly achieving the best outcome possible he can and therefore has no incetive to deviate. (c) The profile (Collude, Don t) is a Nash equilibrium. Firm 1 is clearly achieving the best outcome possible he can and therefore has no incetive to deviate. (d) The profile (Don t, Don t) is a Nash equilibrium. Neither firm can profit from deviating from the profile given what the other firm is choosing. 9. Suppose the production function has constant returns to scale. Then the long run minimum cost (a) has constant marginal cost with respect to output. (b) has increasing marginal cost with respect to output. (c) has decreasing marginal cost with respect to output. (d) has zero marginal cost with respect to output since the derivative of a constant is zero. 3

4 10. Which of the following is not a feature of the Cournot model? (a) In a Cournot equilibrium, neither firm can change its production and make more profit. (b) As the number of firms in the market increases the Cournot equilibrium price approaches the perfectly competive price. (c) If the number of the firms in the market decreases to one, the Cournot equilibrium price is just monopoly price. (d) In a Cournot equilibrium the firms are working together to make the most profit possible. 11. A monopolist faces the inverse demand function described by p = 50 4q, where q is output. The monopolist has no fixed cost and his marginal cost is \$5 at all levels of output. Which of the following expresses the monopolist s profits as a function of his output? (a) 50 4q 5 (b) 50 8q (c) (50 4q)q 5q (d) 50q 4q 2 5 4

5 2 Problems 1. (6 Points) Suppose a firm s production function is f(l, K) = L 2 5 K 2 5. (a) (1 Point) Does this production function exhibit constant, decreasing, or increasing returns to scale? (b) (1 point) Derive the conditional factor demands for labor and capital. 5

6 (c) (1 Point) What is the long run minimum cost function? (d) (1 Points) Suppose capital is fixed at K = K, what is the short run conditional factor demand for labor i.e., how much labor does the firm need to produce Q given that capital is fixed at K = K. (e) (1 Point) What is the short run minimum cost function? In your answer please indicate which portion of the short run cost is the variable cost and which portion is the fixed cost. 6

7 (f) (1 Point) Derive the firm s short run supply function. 7

8 2. Consider the following duopoly problem. Firm A produces a product with C A (Q A ) = Q A. Firm B produces the same product with the same total cost as A i.e., C B (Q B ) = Q B. The market demand is given by the equation P (Q A + Q B ) = 151 (Q A + Q B ). (a) (2 Points) What is Firm A s Profit Function. (b) (2 Points) Solve for each firm s reaction curve. 8

9 (c) (2 Points) Plot these reaction curves on the same graph. Circle the Cournot-Nash equilibrium. (d) (2 Points) Solve for the Cournot-Nash equilibrium. 9

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