ECON 8010 (Spring 2012) Exam 3

Transcription

1 ECON 8010 (Spring 2012) Exam 3 Name _A. Key Multiple Choice Questions: (4 points each) 1. Which of the following is NOT one of the three basic elements of a game? D. None of the above answers is correct (since each choice is one of the three basic elements of a game ). 2. John von-neumann D. More than one (perhaps all) of the above answers is correct. 3. Suppose you have the following observations on the value of a variable Z : 14, 16, 7, 3, 12, 8, 5, 15, 9, 11, and 21. For these observations, D. More than one (perhaps all) of the above answers is correct. 4. A Dummy Variable C. indicates whether an observation is characterized by a particular attribute. 5. Consider a Linear Programming problem in which a decision-maker wants to maximize the function 10x1 40x2 30x3. Suppose the feasible set is defined by the five corner points, ( x 1, x2, x3) : X A (9,0,0), X B (0,8,0), X C (0,0,6), X D (7,3,4), and X E (0,0,0). It follows that the unique solution to this problem is B. X (0,8,0). B 6. Nash s Existence Theorem states that B. 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 ). 7. Which of the following values would appear to be a reasonable value for the Correlation Coefficient between X and Y? B Roger ran a linear regression to estimate the parameters of the equation y b0 b1 x. Which of the following equations would seem like it could reasonably be the output of this exercise? C. y x. 9. Consider a seller of two goods that are substitutes for each other. When maximizing profit, she should price in a way so that A. for each good price/cost markup as a percentage of price is greater than the absolute value of the inverse of own price elasticity of demand.

2 10. Consider a monopolist selling a good for which inverse demand is given by 1 P D ( q) q and cost of production are C ( q) 12q 142. If this seller is able to engage in Perfect Price Discrimination, then A. Consumers Surplus will be equal to zero. 11. The difference between the actual value of y i and the estimated value of y i is called the B. residual. 12. Which of the following statements about this game is correct? D. Neither Player 1 nor Player 2 has a dominant strategy. 13. Which of the following strategy pairs is a Nash Equilibrium? B. Player 1 plays Top with probability 1 3 and Bottom with probability 2 3, while Player 2 plays Left with probability 3 5 and Right with probability refers to a problem of distorted regression results arising from specifying a model which leaves out one or more important independent variables. C. Omitted Variable Bias 15. Hector manages a Chinese buffet in downtown Chattanooga. In an attempt to attract more student diners from UT-Chattanooga, he decides to offer a 15% discount to anyone that shows a valid student ID. This pricing scheme is an example of D. Third Degree Price Discrimination (or Segmented Pricing). 16. Cherry Kool-Aid and Grape Kool-Aid are examples of goods that are C. horizontally differentiated. 17. Which of the coefficient estimates is/are statistically significant at a 5% error level? D. ˆb 0, ˆb 1, and ˆb Based upon his estimated coefficient values, the expected selling price of a 2,200 square foot house on a.40 acre lot is approximately D. $203, Consider a two player game between Player 1 and Player 2. Player 1 has two available strategies: Strategy A and Strategy B. Player 2 has two available strategies: Strategy c and Strategy d. If Strategy A of Player 1 is a Best Reply to a choice of Strategy c by Player 2, then B. Strategy B cannot be a dominant strategy for Player 1.

3 20. Lyle ran a regression to determine the factors that influence salaries at a local law firm. As part of his analysis he stated the following hypothesis: Other factors fixed, there is no relation between height and salary paid to lawyers. This statement is in fact true, but he incorrectly rejected it (i.e., claimed, based upon his analysis, that it is false). In doing so, Lyle committed a B. Type I Error 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, B, and C ) as summarized in the table below: Feed Nutrient A Nutrient B Nutrient C x 5 units 8 units 2 units y 5 units 2 unit 6 units Each pound of x costs px 20 ;and each pound of y costs p y 10. Each day each cow must be feed at least 250 units of Nutrient A, 160 units of Nutrient B, and 180 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) x (the amount of feed x ) and y (the amount of feed y ). 1B. What is Charles Objective Function? (1 point) His objective function is v (. 2) x (.1) y, which he aims to minimize. 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. (4 points) The three constraints which he faces are Constraint A: 5x 5y 250 Constraint B: 8x 2 y 160 Constraint C: 2x 6 y 180

4 These constraint result in a feasible set as illustrated below: 80 y D. Determine the solution to his Linear Programming problem. Determine the total daily expenditures on cattle feed per cow at this optimal choice. (4 points) Recognize that: the slope of the green line (which corresponds to Constraint A ) is 1 ; the slope of the blue line (which corresponds to Constraint B ) is 4 ; and the slope of the red line (which corresponds to Constraint C ) is The slope of the Objective Function is 2. Since the Objective.1 Function is flatter than the blue line but steeper than the green line, the solution occurs at the intersection of the blue line and green line. That is, x * 10 and y * 40. This choice results in V * (.2)(10) (.1)(40) E. A new study has been released which states that cows really only need 150 units of Nutrient C per day. How does the solution to this linear programming problem change in light of this new information? Explain. (2 points) As a result of this change, Constraint C becomes less restrictive. However, Constraint C is not binding at the initial solution. Thus, this change in no way alters the solution to the problem. 90 x

5 2. Angela is in charge of ticket pricing for the Omega Classic Park Amphitheater. This 3,000 seat venue has scheduled two concerts this summer, one featuring the band Night Ranger and the other featuring the band Everclear. The potential market of ticket buyers consists of three different types of consumers, with reservation prices of: Consumer Type Reservation Price for Night Ranger concert Reservation Price for Everclear concert Type A Type B Type C There are exactly 1,000 consumers of each type. The venue has open seating, so the only option is to sell general admission tickets for each show. The combined Fixed Costs of the two concerts is $70,000. Marginal Costs (and therefore Variable Costs) are equal to zero. Recognize that this cost structure implies that maximizing profit is equivalent to maximizing revenue. 2A. First suppose that the seller only considers Simple Monopoly Pricing (i.e., choosing p NR and p E, in order to sell tickets to each show separately). Determine the profit maximizing price for each show and the resulting profit of the venue. (3 points) The best price for Night Ranger tickets is either $130, $60, or $0. These choices would result in: Price Buyers Revenue $130 C $130,000 $60 B and C $120,000 $0 A, B, and C $0 Of these, the best choice is a price of $130. Similarly, the best price for Everclear tickets is either $100, $70, or $10. These choices would result in: Price Buyers Revenue $100 A $100,000 $70 A and B $140,000 $10 A, B, and C $30,000 Of these, the best choice is a price of $70. Charging $130 for Night Ranger tickets and $70 for Everclear tickets gives the venue a profit of: $270,000 $70,000 = $200,000.

6 2B. Recognizing that potential concertgoers appear to have valuations for the two shows that are negatively correlated, Angela suggests that they may want to consider bundling tickets to the two shows. Next suppose that the venue decides to engage in Pure Bundling (i.e., selling tickets to the two shows together, for a price of p b ). Determine the profit maximizing value of p b and the resulting profit of the venue. (3 points) The best bundle price is either $140, $130, or $100. These choices would result in: Price Buyers Revenue $140 C $140,000 $130 B and C $260,000 $100 A, B, and C $300,000 Of these, the best choice is a price of $100. Charging $100 for the bundle gives the venue a profit of: $300,000 $70,000 = $230,000. 2C. Finally suppose that the venue decides to engage in Mixed Bundling (i.e., setting a price of p b for purchasing tickets to the two shows as a package, in addition to prices of p NR and p E for purchasing the tickets separately). Consider p E 95, p NR 125, and p b 130. Determine the resulting profit of the venue from setting these prices. Based upon your answers, which type of pricing Simple Monopoly Pricing, Pure Bundling, or Mixed Bundling is most profitable? (2 points) Under the given mixed bundle prices, buyers of Type A will buy a ticket to the Everclear concert, whereas buyers of Type B and Type C will buy the bundle. This gives the venue revenue of: ($95)(1,000) + ($130)(2,000) = $95,000 + $260,000 = $355,000. and a profit of: $355,000 $70,000 = $285,000. Thus, it follows that Mixed Bundling is the most profitable of the three different types of pricing.