ECON 500 - Fall 2004 Final Examination 1. Nick and Chris devote each workday to producing either “apples” or “bananas.” On any given day Nick can produce either 8 pounds of apples or 24 pounds of bananas, while Chris can produce either 6 pounds of apples or B pounds of bananas. a. Based upon the provided information, which individual has an absolute advantage in the production of apples? Explain. (2 points) b. Based upon the provided information, which individual has an absolute advantage in the production of bananas? Explain. (2 points) c. Specify a value of B for which Chris has a comparative advantage in the production of apples. Justify your answer. (4 points) d. In general, is it ever possible for one individual to simultaneously have a comparative advantage in the production of both apples and bananas? Clearly explain. (4 points)2. Consider a market in which Supply and Demand are respectively given by the functions ppS 3)( = and ppD 240)(−=. a. Determine the functional form of inverse demand, )(qPD. (2 points) b. Determine the price for which consumers would be willing and able to purchase exactly 10 units of this commodity. (2 points) c. At a price of 10=p is there “excess demand,” “excess supply,” or neither? Clearly explain. (2 points) d. Suppose “Supply Changes” so that the new supply function is ppSnew6)( = . Will this change in Supply lead to an increase or decrease in Consumers’ Surplus? Clearly explain. (4 points)3. J.R. and Diana like to consume 1x =(hotdogs) and 2x =(slices of pizza). Diana’s utility is given by the function 2142)( xxXU += ; J.R. has “monotonic preferences” (you know nothing else about his preferences). Consider the following three consumption bundles: )4,0(),(21==AAxxA ; )1,1(),(21==BBxxB ; and )1,9(),(21==CCxxC . a) Can you determine which of these three bundles Diana likes the most? If so, identify her most preferred bundle and explain why she finds it to be the most desirable of the three; if not, explain why it is not possible to identify which bundle is her most preferred. (4 points) b) Can you determine which of these three bundles J.R. likes the most? If so, identify his most preferred bundle and explain why he finds it to be the most desirable of the three; if not, explain why it is not possible to identify which bundle is his most preferred. (4 points)4. Consider a firm with the production function KLKLF 82),( += . For this firm 2=LMP and KMPK4= . a) Determine the functional form of KLMRTS, (the “Marginal Rate of Substitution of Labor for Capital”). (2 points) b) Does KLMRTS, appear to be “diminishing”? Clearly explain. (2 points) c) Clearly sketch the isoquant associated with 16=Q units of production (clearly labeling each intercept). (3 points) d) Does this production technology appear to exhibit Increasing, Decreasing, or Constant Returns to Scale? Clearly explain. (3 points)5. Clearly answer each of the following: a) What is the difference between a positive statement and a normative statement? (4 points) b) Does the following statement appear to be a positive statement or a normative statement: “In auctions on eBay many bidders engage in ‘sniping.’ That is, they do not submit their bids until seconds before the end of the auction.”? Explain. (4 points) c) Does the following statement appear to be a positive statement or a normative statement: “In order to be fair to all bidders, eBay should change their rules so that an auction cannot end until at least 10 minutes after any bid has been submitted.”? Explain. (4 points)6. Ernie wears Fidra golf shirts; Adam wears Burberry golf shirts. They notice the following elasticities for these two products under current market conditions: Elasticity Burberry shirts Fidra shirts Price Elasticity of Demand -1.12 -.94 Cross-Price Elasticity of Demand .31 .43 Income Elasticity of Demand .17 -.26 Clearly answer the following questions. Within each explanation, be sure to specify which value (or values) above your answer is based upon. a. Would an increase in the price of Fidra golf shirts result in an increase or decrease in total expenditure on the product? (4 points) b. Under the current market conditions, are Burberry golf shirts and Fidra golf shirts complements to or substitutes for each other? (4 points) c. Would an increase in the income of consumers in this market lead to an increase or decrease in demand for Burberry golf shirts? (4 points)7. Consider a firm operating in the long run with the production function {}KLKLF ,min),(31= . a. Suppose the firm wishes to produce an arbitrary level of output 0>q . Graphically illustrate the solution to the long run cost minimization problem for this firm. (3 points) b. Suppose the firm wishes to produce an arbitrary level of output 0>q . Determine the long run cost minimizing levels of labor and capital. (4 points) c. Determine the long run cost function of this firm. (2 points) d. Suppose the wage rate for each unit of labor were to decrease. Clearly explain how this change would this alter the long run cost minimizing level of labor, the long run cost minimizing level of capital, as well as the long run costs of producing 0>q units of output. (3 points)8. Consider a firm with Total Revenue (denoted )(qR ) and Total Costs (denoted )(qC ) as illustrated in the graph below: a) For what range of output is this firm able to earn a positive profit? Clearly explain. (4 points) b) For what range of output is the demand for the output of this firm elastic? Clearly explain. (4 points) c) What level of output appears to maximize profit? Clearly explain. (4 points) $ q )(qC)(qR00AqBqCqDqEq9. Consider a consumer with 212)( xxXU=. For this individual, 212xMU = and 122xMU = . a) Specify 2,1MRS as a function of 1x and 2x . (2 points) b) Based upon your answer to part (a), are the preferences of this consumer “convex”? Clearly explain. (2 points) c) Determine the utility maximizing consumption bundle for this consumer (that is, the optimal levels of 1x and 2x , each as a function of prices and income). (4 points)d) Determine the level of utility (as a function of prices and