ECON 4550 (Summer 2014) Exam 3
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1 ECON 4550 (Summer 014) Exam 3 Name Multiple Choice Questions: (4 points each) 1. Bob owns a food truck. He offers senior citizens a 10% discount. This behavior by Bob is an example of A. First Degree Price Discrimination (or Perfect Price Discrimination). B. Second Degree Price Discrimination (or Menu Pricing) C. Third Degree Price Discrimination (or Segmented Pricing). D. None of the above answers are correct.. Which of the following is NOT one of the three general ingredients which must be specified when stating a constrained optimization problem? A. Constraints. B. Decision Variables. C. Slack. D. None of the above answers is correct (since each choice is one of the three general ingredients to a constrained optimization problem). 3. In the Mixed Extension of a game, A. at every possible outcome, the sum total of payoffs across all players is equal to zero. B. the strategy choice of each player is allowed to be a probability distribution over his available pure strategies. C. players are never allowed to play Pure Strategies. D. None of the above answers are correct. 4. Vanilla Coca-Cola, Cherry Coca-Cola, and Coca-Cola with Lime are examples of goods that are A. always sold by way of First Degree (or Perfect) Price Discrimination. B. complements to each other. C. vertically differentiated from one another. D. horizontally differentiated from one another. 5. Consider a market in which Firm A and Firm B compete by simultaneously choosing prices ( p and p respectively). The Best Reply Function for Firm A is BR 3 p A ( p B ) 8 4 BR 1 p B ( p A ) 16 A B p, and the Best Reply Function for Firm B is p B A. It follows that at the Nash Equilibrium, Firm A will charge a price of and Firm B will charge a price of. A. ;. B. 8; 16. C. 56; 44. D. 64; 48.
2 6. Consider a seller of two goods, Good A and Good B, which are substitutes for each other. The marginal cost of producing each unit of Good A is $1.75, and the marginal cost of producing each unit of Good B is $.5. Further, own price elasticity of demand is constant for each good, equal to a, pa = 1.5 for Good A and equal to b, p b = 1.5 for Good B. Which of the following pairs of prices are possibly the optimal, profit maximizing prices for this firm to charge? A. p a =$4.40 and p b =$ B. p a =$4.75 and p b =$ C. p a =$5.5 and p b =$11.5. D. p a =$5.80 and p b =$ Consider a Linear Programming problem with the three constraints of x 4y 36, 3x y 4, and x y 11. Which of the following combinations of (, y) feasible? A. ( 3,8) B. ( 5,7) C. ( 7,4) D. More than one of the above combinations of ( x, y) is feasible. x are 8. refers to the general practice of charging a different price for different units sold of an essentially identical good. A. Versioning B. Price Discrimination C. Bundling D. Linear Programming For Question 9, consider the two player simultaneous move game illustrated below: Player 1 Player D E F G A 17, 0 3, 13, 0 9, 1 B 1, 15, 14 5, 8 5, 18 C 19, 6 9, 10 7, 4 11, This game has a unique Nash Equilibrium in which Player 1 plays and Player plays. A. A; F. B. A; E. C. B; G. D. C; G.
3 10. Firms A and B operate in a market with demand of D( p) 4, p. They compete by simultaneously setting prices. Consumers make no distinction between the output of Firm A and the output of Firm B (and will therefore simply buy from the firm offering the lower price). Firm A has production costs of C A ( q) 0q, and Firm B has production costs of C B ( q) 0q. In equilibrium A. each firm will set a price of $35. B. the efficient quantity of the good will be traded. C. each firm will earn a strictly positive profit. D. More than one (perhaps all) of the above answers is correct. 11. Consider a linear programming problem in which a firm must choose levels of output of two products, x and y, in order to maximize total contribution. One of the restrictions on the choice of the firm is an assembly line constraint, which states that the chosen levels of output must satisfy x y 50. At the solution to the linear programming problem: the Slack for the assembly line constraint is 0; the Shadow Price for assembly line capacity is $5; the Upper Range for the Shadow Price of assembly line capacity is 1; and the value of the Objective Function is $1,50. If the firm instead had 54 units of assembly line capacity (i.e., if this restriction had instead been x y 54 ), then the value of the Objective Function at the solution would be A. $1,150. B. $1,54. C. $1,75. D. $1,350. For Question 1, consider the two player sequential move game illustrated below: Player 1 A B Player Player C D E F This game has a unique Subgame Perfect Nash Equilibrium in which: Player would choose following a choice of A by Player 1; Player would choose following a choice of B Player 1; and Player 1 chooses. A. C; F; A. B. C; F; B. C. D; E; A. D. D; F; B.
4 13. John has reservation prices for good 1 and good of R 1 and R 98. He has the option to buy good 1 at a price of p 1 40, buy good at a price of p 38, or a bundle consisting of both good 1 an good at a price of p b 65. Given these options, John should choose to A. purchase only good 1. B. purchase only good. C. purchase the bundle consisting of both good 1 and good. D. not make any purchase. 14. Consider a Linear Programming problem with the three constraints: (i) x 1 3x 36, (ii) 3x 1 x 66, and (iii) 4x 1 4x 100. Which of the constraints is redundant? A. (i) x 1 3x 36. B. (ii) 3x 1 x 66. C. (iii) 4x 1 4x 100. D. None of the above answers is correct (since none of the constraints is redundant). Suppose that Ty and Logan are playing the game which is partially illustrated by the payoff matrix below. The payoffs of the players are not given in this matrix, but all of the relevant best reply arrows for each player are illustrated. Answer Questions 15 and 16 based upon the information conveyed in this payoff matrix. Ty X Y x Logan y 15. Which of the following strategy pairs is a Nash Equilibrium? A. Ty plays Y and Logan plays x. B. Ty plays X and Logan plays y. C. Neither A nor B are correct (i.e., neither choice A not choice B describe a Nash Equilibrium). D. Both and A and B are correct (i.e., both choice A and choice B describe a Nash Equilibrium). 16. Based upon the different types of games discussed in lecture, this game appears to be A. a Prisoners Dilemma. B. a Cat-and-Mouse Game. C. a Coordination Game. D. an Anti-Coordination Game.
5 17. In the Cournot Model of competition, firms compete by A. sequentially choosing prices. B. simultaneously choosing prices. C. sequentially choosing quantities of output. D. simultaneously choosing quantities of output. For Questions 18 and 19, consider a firm facing demand and with marginal costs as illustrated below. Marginal Costs of production are minimized if the firm produces 9,000 units of output. Suppose throughout that this firm is able to engage in First Degree (i.e., Perfect) Price Discrimination. $ MC(q) (i) (ii) (iii) (iv) 9,000 (v) (vi) (vii),500 Demand quantity This firm has Fixed Costs of production equal to $9,000. Finally, the seven regions identified above have areas equal to: Area (i) Area (ii) Area (iii) Area (iv) Area (v) Area (vi) Area (vii) $66,000 $58,500 $7,000 $36,000 $41,500 $61,000 $101, In this market the efficient level of trade is units. When this firm maximizes profit (by way of engaging in Perfect Price Discrimination), it will sell units of output. A. 9,000; 9,000. B. 9,000;,500. C.,500; 9,000. D.,500;, When this firm maximizes profit (by way of engaging in Perfect Price Discrimination), it is able to earn a profit of. A. $407,000 B. $99,000 C. $70,000 D. $41,000
6 0. Jamie has dial-up Internet service at his home through a provider called Old Skool Web. He has the option of choosing either Plan A or Plan B. Under Plan A he would pay a flat fee of $8 per month which would give him 10 free minutes, after which he would have to pay 0 for any additional minutes. Under Plan B he would pay a flat fee of $0 per month which would give him 300 free minutes, after which he would have to pay 10 for any additional minutes. His monthly bill would be lower under Plan A (than under Plan B ) if and only if he uses the Internet for A. less than 10 minutes. B. less than 180 minutes. C. less than 300 minutes. D. more than 300 minutes. 1. Scott and Brad are playing a repeated Prisoners Dilemma with an uncertain end period. Following each period, they will play the game one more time with probability p. Brad is playing a Grim Trigger Strategy. If Scott chooses to cooperate in every period, 3 he realizes an expected payoff of ( c) p p p... If Scott chooses to defect in every period, he realizes a payoff of 3 ( d) 5 10 p 10 p 10 p.... Scott should choose to cooperate in every i p period if and only if (recall: p ) i 1 1 p A. p B. p C. p D. None of the above answers are correct (since there is no range of values of p for which it is best for Scott to choose to cooperate). For Question, consider the following two player simultaneous move game: Player 1 Player Left Right Top 4, 14 8, 0 Bottom 1, 3 6, 9. The game above has a mixed strategy Nash Equilibrium in which Player 1 plays Top with probability and Player plays Left with probability. A. p ; q B. p ; q C. p ; q D. None of the above answers are correct, since this game does not have a mixed strategy Nash Equilibrium
7 ECON 4550 (Summer 014) Exam #3 Name Score on Multiple Choice Questions: out of 88 points. Score on Short Answer Questions : out of 1 points. Exam #1 Grade: + = out of 100 points.
8 Problem Solving/Short Answer Questions: 1. William manages the Hart Ranch and Museum, which includes a 65 acre animal park featuring a herd of American Bison. To provide nourishment for these animals, William must choose levels of two different types of feed (denoted x and y ). He aims to satisfy a pair of nutritional standards, while minimizing the costs of purchasing feed. Each pound of each type of feed contains levels of two different nutrients ( A and B ) as summarized in the table below: Feed Nutrient A Nutrient B x 10 units 3 units y 5 units 1 units p 15 ;and each pound of y costs p Each pound of x costs x y 10. Each day each bison must be feed at least 90 units of Nutrient A and 360 units of Nutrient B. Analyze William s daily decision of how much to feed each bison. 1A. What are the decision variables for William? ( point) 1B. What is William s Objective Function? ( point) 1C. State inequalities which summarize the restrictions on William s choice of his decision variables. Graphically illustrate the feasible set, clearly labeling all relevant intercepts and points of intersection. (4 points)
9 1D. Determine the solution to his Linear Programming problem. Determine the total daily expenditures on feed per bison at this optimal choice. (4 points)
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