ECON 8010 (Spring 2013) Exam 3

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1 ECON 8010 (Spring 2013) Exam 3 Name Multiple Choice Questions: (4 points each) 1. Nash s Existence Theorem states that A. an equilibrium exists in any game of incomplete information, but never exists in any game of complete information.. the only way that a game can ever have an equilibrium is if every player has a dominant strategy. C. every game with a finite number of players, each with a finite number of available pure strategies, has at least one Nash Equilibrium (potentially in Mixed Strategies ). D. None of the above answers is correct. 2. Consider a Linear Programming problem with the three constraints of x 10x 95, x 2 20x3 190, and 10x 1 5x2 20x Which of the following combinations of x, x, ) are feasible? [Note: be careful when looking at the subscripts.] A. ( 3,8,5 ). ( 5,6,4) C. ( 6,9,2) ( 1 2 x3 D. More than one of the above combinations of x, x, ) is feasible. ( 1 2 x3 3. Henrietta ran a regression to estimate qx b0 b1 ln( px ) b2 ln( py ) b3 ln( Inc), where q x denotes quantity of good x, p x denotes price of good x, p y denotes price of good y, and Inc denotes per capita Income in the market for good x. Her estimated coefficient values are b ˆ , b ˆ , b ˆ , and b ˆ These results would suggest that A. good x is a normal good.. demand for good x is unit elastic. C. good x is a complement to good y. D. More than one (perhaps all) of the above answers is correct. 4. refers to a problem of distorted regression results arising from specifying a model which leaves out one or more important independent variables. A. A Dummy Variable. Omitted Variable ias C. Nash s Existence Theorem D. Independence of Irrelevant Alternatives

2 5. enny frequently has lunch at Mary s urger Shack. enny s reservation prices for a cheeseburger, fries, and a drink are R C 4, R F 2, and R D 1 respectively. (Assume this his total value for any combination of the three items is simply equal to the sum of reservation prices for the items which he consumes.) Mary s urger Shack charges p C 2.75 for a cheeseburger, p F for fries, and p D for a drink. Additionally, consumers have the option of getting a combo meal (which consists of a burger, fries, and a drink) for p Given these options, enny should purchase A. Only a cheeseburger.. Only fries. C. A cheeseburger and fries (but no drink). D. The combo meal. 6. In the Cournot Model of competition firms compete by, whereas in the ertrand Model of competition firms complete by. A. sequentially choosing quantities of output; simultaneously choosing quantities of output.. sequentially choosing prices; simultaneously choosing prices. C. simultaneously choosing quantities of output; simultaneously choosing prices. D. simultaneously choosing prices; simultaneously choosing quantities of output. 7. For any Linear Programming problem, imposing an additional redundant constraint would A. not alter the solution to the problem whatsoever.. alter the solution to the problem in such a way so that the value of the objective function at the solution will be smaller. C. alter the solution to the problem in such a way so that the value of the objective function at the solution will be larger. D. alter the solution to the problem in such a way so that the value of the objective function at the solution will be: smaller if the aim is to maximize the objective function, but larger if the aim is to minimize the objective function. 8. Suppose you have the following observations on the value of variable X3 : 9.27, 10.56, 22.38, 15.44, 12.09, 8.76, 7.35, 24.89, 19.31, 9.96, 14.82, 12.39, and ased upon these observations, A. X3 is clearly a dummy variable.. the sample minimum for X3 is C. the sample maximum for X3 is D. More than one (perhaps all) of the above answers is correct. 9. A fried chicken sandwich, a hamburger, a veggie burger, and a hotdog are goods that are A. vertically differentiated from each other.. diagonally differentiated from each other. C. horizontally differentiated from each other. D. undifferentiated.

3 10. John von-neumann A. co-authored the book Economic Applications of Linear Regression Analysis (first published in 1971), in which the concept of a dummy variable was first developed.. was one of the three individuals (along with George Dantzig and Leonid Kantorovich) who essentially developed the subfield of Linear Programming. C. was one of two individuals (along with Oskar Morgenstern) who essentially developed the subfield of Game Theory. D. More than one (perhaps all) of the above answers is correct. 11. Axl manages a Chinese buffet in Athens, GA. In an attempt to attract more student diners from UGA, he decides to offer a 15% discount to anyone that shows a valid student ID. This pricing scheme is an example of A. First Degree Price Discrimination (or Perfect Price Discrimination).. Second Degree Price Discrimination (or Menu Pricing) C. Third Degree Price Discrimination (or Segmented Pricing). D. Fourth Degree Price Discrimination (or Search and Seizure Pricing). 12. A Dummy Variable A. indicates whether an observation is characterized by a particular attribute.. is typically defined in such a way that it can only take on a value of either (0) or (1). C. can only ever be included in a regression as the Y variable (and never as one of the X variables ). D. More than one (perhaps all) of the above answers is correct. For Questions 13 and 14, consider the two player simultaneous move game illustrated below: Player 1 Player 2 Left Right Top 5, 8 4, 1 ottom 2, 0 9, Which of the following statements about this game is correct? A. Player 1 has a dominant strategy, but Player 2 does not.. Player 2 has a dominant strategy, but Player 1 does not. C. Neither Player 1 nor Player 2 has a dominant strategy. D. oth Player 1 and Player 2 have a dominant strategy. 14. Which of the following strategy pairs is a Nash Equilibrium? A. Player 1 plays Top, while Player 2 plays Left.. Player 1 plays Top, while Player 2 plays Right. C. 3 Player 1 plays Top with probability 10 and ottom with probability 7 10, while Player 2 plays Left with probability 8 5 and Right with probability 8 3. D. More than one (perhaps all) of the above strategy pairs is a Nash Equilibrium.

4 15. Consider a market in which Firm A and Firm compete by simultaneously choosing prices ( p and p respectively). The est Reply Function for Firm A is A R 3 R 4 p A ( p ) 13 4 p, and the est Reply Function for Firm is p ( p A ) 12 5 p A. It follows that at the Nash Equilibrium, Firm A will charge a price of and Firm will charge a price of. A. 13; 12.. approximately 17.33; 15. C. 20; 20. D. 55; Which of the following statements is correct? A. For a constraint in a Linear Programming problem, if the value of slack is positive, then the value of shadow price must be equal to zero.. At the solution to any Linear Programming problem, all of the constraints must be binding. C. A constrained optimization problem can be solved using the techniques of Linear Programming so long as all of the constraints can be expressed as linear functions of the choice variables (even if the objective function cannot be expressed as a linear function of the choice variables). D. More than one (perhaps all) of the above answers is correct. For Questions 17 and 18, consider a market in which two firms compete by simultaneously 1 choosing quantities of output. Market demand is given by ( Q) 16 Q, where P D 600 Q q A q. Firm A has costs of C A( q A) 2qA 1, 500; Firm has costs of C ( q ) 3q 1,800. Recall, for the function F( x, y) a by cx x, it follows that F( x, y) x a by 2cx. 17. If Firm A were to produce q A 3, 800 units of output, then Firm would want to produce A. zero units of output.. q 2, 000 units of output. C. q 2, 300 units of output. D. q 5, 800 units of output. 18. At the unique Nash Equilibrium of this simultaneous move game, Firm A will produce units of output and Firm will produce units of output. A. 1,500; 1, ,700; 2,700. C. 3,000; 2,400. D. 4,200; 3,900.

5 For Questions 19 and 20, 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) (v) (vi) (vii) 9,000 22,500 Demand quantity This firm has Fixed Costs of production equal to $19,500. Finally, the seven regions identified above have areas equal to: Area (i) Area (ii) Area (iii) Area (iv) Area (v) Area (vi) Area (vii) $33,000 $29,250 $36,000 $18,000 $20,750 $30,500 $50, When this firm maximizes profit (by way of engaging in Perfect Price Discrimination), it will sell units of output. A. 0. 9,000 C. more than 9,000 but less than 22,500 D. 22, When this firm maximizes profit (by way of engaging in Perfect Price Discrimination), it is able to earn a profit of. A. $78,750. $130,000 C. $149,500 D. $198,500

6 Problem Solving/Short Answer Questions: 1. Charles owns and operates the Goodnight Cattle Ranch in north Texas. He must choose levels of two different types of cattle feed (denoted x and y ) in order to satisfy multiple minimal nutritional standards, while minimizing the costs of purchasing cattle feed. Each pound of each type of feed contains levels of three different nutrients ( A,, and C ) as summarized in the table below: Feed Nutrient A Nutrient Nutrient C x 6 units 10 units 2 units y 6 units 2 unit 8 units Each pound of x costs px 15 ;and each pound of y costs p y 30. Each day each cow must be feed at least 360 units of Nutrient A, 200 units of Nutrient, and 192 units of Nutrient C. Analyze his daily decision of how much to feed each cow. 1A. What are the decision variables for Charles? (1 point) 1. What is Charles Objective Function? (1 point) 1C. State inequalities which summarize the restrictions on Charles choice of the decision variables. Graphically illustrate the feasible set, clearly labeling all relevant intercepts and points of intersection. (3 points)

7 1D. Determine the solution to his Linear Programming problem. Determine the total daily expenditures on cattle feed per cow at this optimal choice. (3 points) 1E. A new study has been released which states that cows really only need 180 units of Nutrient per day. How does the solution to this linear programming problem change in light of this new information? Explain. (2 points)

8 2. The legendary band Pistols N Tulips was recently inducted into the Rock and Roll Hall of Fame (in Cleveland, Ohio), sparking a renewed interest in their music. Their record label has decided to seize this opportunity to release a CD of Greatest Hits and a CD of previously unreleased Rare Songs. The potential market for these CDs consists of four different types of consumers, with reservation prices of: Consumer Type Reservation Price for Greatest Hits CD Reservation Price for Rare Songs CD Type A $5 $17 Type $16 $4 Type C $12 $7 Type D $8 $6 For each consumer, the value of having both CDs is simply equal to the sum of his reservation prices for the two CDs individually. There are exactly 100,000 consumers of each type. The marginal cost of producing each CD is $1 (and fixed costs of production are equal to zero). 2A. First suppose that the record label only considers Simple Monopoly Pricing (i.e., choosing p GH and p RS, in order to sell each CD separately). Determine the profit maximizing price for each CD and the resulting profit of the record label. (3 points)

9 2. Recognizing that potential buyers appear to have valuations for the two CDs that are negatively correlated, the record label contemplates Pure undling (i.e., selling the two CDs together for a price of p b ). Note that the marginal cost of producing a bundle containing one copy of each CD is $2. Determine the profit maximizing value of p and the resulting profit of the record label. (3 points) b 2C. If the record label has the choice to use either Simple Monopoly Pricing or Pure undling, which will they choose? Are consumers better off or worse off when the seller uses the chosen pricing strategy instead of the alternative pricing strategy? Clearly and fully explain. (4 points)

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