ECON 310 – Fall 2005 Name: ______________________ Exam 1 - Version B (Answer Key) Multiple Choice: (circle the letter of the best response; 4 points each) 1. Which of the following is NOT one of the “three basic analytical tools” (or “three key analytical tools”) upon which nearly all microeconomic analysis relies? c. Opportunity Cost. 2. Normative Analysis e. All of the above answers are correct. 3. Consider the market for “Los Angeles Angels of Anaheim baseball hats.” Between 2002 and 2005 equilibrium price and equilibrium quantity in this market both increased. Which of the following are possible explanations of this observed change in equilibrium? e. Exactly two (and only two) of the above answers are correct. 4. Consider a market in which Demand is given by ppD 8240)(−= (for 300 ≤≤ p ) and Supply is given by 102)(−=ppS (for 5≥p ). In this market b. Equilibrium quantity is 40*=q. 5. Consider the market for “Mighty Ducks of Anaheim hockey jerseys.” Suppose there is a simultaneous increase in Supply and decrease in Demand in this market. Which of the following best describes the resulting change in equilibrium price and quantity? d. “Equilibrium price must decrease; equilibrium quantity could increase, decrease, or remain the same.” 6. The Cross-Price Elasticity of Demand for Coke with respect to the Price of Pepsi is (.52). This value implies that: e. A decrease in the price of Pepsi will lead to a decrease in demand for Coke. 7. Suppose that a 5% increase in the price of cars reduces quantity of cars demanded by 10%. This suggests that: b. Price Elasticity of Demand for cars is 2%5%10−=−. 8. Suppose that demand for paper is given by the inverse function qqPD5120)(−= . It follows that demand is unit elastic b. only at a price of 10)20(21==p.9. Wayne’s preferences are summarized by the utility function 21212),( xxxxU += . As a result, his marginal utility functions are 111xMU = and 12=MU . It follows that d. All of the above answers are correct. 10. Jason spends his entire income on =1x (t-shirts) and =2x (12 packs of Mountain Dew). At per unit prices of 151=p and 42=p he can afford the bundle )10,2(=A but cannot afford the bundle )1,5(=B . From here we can infer that: e. All of the above answers are correct. 11. Consider a market in which both the Law of Demand and Law of Supply hold, and further 40)8(=D and 20)8(=S . It must be that: b. there is “excess demand” at a price of 5=p. 12. James likes both =1x (peanut butter) and =2x (grape jelly). He always gets the same additional satisfaction from “2 more ounces of peanut butter” as he does from “one more ounce of grape jelly.” Which of the following utility functions is consistent with these preferences? d. ()21212, xxxxU += For questions 13 through 15, consider the following scenario. Qihong has income of $I which he uses to purchase =1x (Playstation 2 games) and =2x (Pizzas). Each unit of 1x costs $1p ; each unit of 2x costs $2p . 13. If 150=I , 401=p , and 102=p , e. More than one of the above answers is correct. 14. Suppose Qihong is spending all of his income on “Playstation 2 games” and “Pizzas.” In order to increase his consumption of “Playstation 2 Games” by one unit, he must decrease his consumption of “Pizzas” by d. 21pp units. 15. Focusing on Qihong’s budget line for these two goods, if his income increases from 250=I to 325=I (with prices constant), then d. the vertical intercept and horizontal intercept of his budget line will both increase.“Short Answer” Questions: 1. Abby is a chicken farmer in Salida, CA. She wants to build a rectangular fence as a pen for her chickens. The only supplier in town, “Gary’s Fencing and Wire Supplies,” charges a price of $p for each foot of fence (a price over which Abby has no control). With F feet of fence, the maximum area of a rectangular pen is 16)(2FFA= . Abby must choose how many feet of fence to purchase. She wants to make her chicken pen as large as possible, while spending no more than $600. i. When solving this problem, should Abby treat p as an exogenous or endogenous variable? Explain. (3 points) Since p is “beyond her control,” she should treat it as exogenous. ii. When solving this problem, should Abby treat F as an exogenous or endogenous variable? Explain. (3 points) Since she gets to “choose the value of F ,” she should treat it as endogenous. iii. State Abby’s objective function. (3 points) Since she wants to make the area of her pen as large as possible, her objective function is simply 16)(2FFA= . iv. State the constraint that Abby faces. (3 points) Her choice of F is restricted by 600≤pF . v. Formally state the optimization problem that Abby wants to solve. (4 points) Her optimization problem can be stated as: 16max2}{FF subject to 600≤pF .2. Consider an individual with preferences that can be described by the utility function 214)( xxXu = . For this person 1212xxMU = and 2122xxMU = . i. Are the preferences of this person “monotonic”? Explain. (4 points) Yes, these preferences are “monotonic.” “More is better,” since each marginal utility is always positive. ii. Identify 2 consumption bundles that give this individual “40 units of happiness” (that is, 2 consumption bundles for which 40)(=Xu ). (6 points) 40)( =Xu so long as 40421=xx , or equivalently 12100xx =. For example, the following bundles all lead to the desired level of utility: ()100,1 , ()50,2 , ()25,4 , ()20,5 , ()10,10 , and ()4,25 . iii. Graphically illustrate the indifference curve passing through the 2 consumption bundles that you identified in part (ii). (5 points) iv. Determine the functional form of 2,1MRS . (5 points) 12212,1xxMUMUMRS ==. v. Are the preferences of this person “convex”? Explain. (4 points) Yes, these preferences are “convex.” From the expression for 2,1MRS determined above, there is clearly a “diminishing marginal rate of substitution” in that decreasing 2x and increasing 1x (while keeping the level of utility constant) will decrease the value of 2,1MRS . 2x1x0040Extra Credit! Noel and his brother Liam enjoy going to the pub and consuming 1x =(cigarettes) and 2x =(alcohol). Noel’s utility is given by 2110)( xxXUN=, while Liam’s