Final Exam – Version B.ECON 500 – Summer 2004.1. Consider a consumer with 321)( xxXU . For this individual, 321xMU  and22123 xxMU .a. Are the preferences of this consumer “monotonic”? Explain. (2 points)b. Specify 2,1MRS as a function of 1x and 2x. (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). (6 points)2. “Gaining extra revenue is easy for any firm – all it must do is to sell more output.”Do you agree? If so, explain why this statement must always be true; if not, provide an example to illustrate why this statement might not always be true. (8 points)3. Prove whether the production function LKKLF 23),(  exhibit Increasing, Decreasing, or Constant Returns to Scale. (4 points)4. Richard and Patrick devote each workday to producing either “potatoes” or“chicken.” On any given day Richard can produce either 8 pounds of potatoes or16 pounds of chicken, while Patrick can produce either 5 pounds of potatoes orC pounds of chicken.a. Based upon the provided information, which individual has an absoluteadvantage in the production of potatoes? Explain. (3 points)b. Specify a value of C for which Richard has a comparative advantage inthe production of chicken. Justify your answer. (3 points)c. Specify a value of C for which Patrick has a comparative advantage inthe production of chicken. Justify your answer. (3 points)d. In general, is it ever possible for Richard to simultaneously have acomparative advantage in the production of both potatoes and chicken?Clearly explain. (4 points)5. 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 shirtsPrice Elasticity of Demand -1.65 -1.23Cross-Price Elasticity of Demand .17 .24Income Elasticity of Demand .33 -.09Based upon these values, answer the following questions.a. Under current market conditions, is demand for Burberry golf shirtsElastic, Inelastic, or Unit Elastic? Clearly explain. (3 points)b. Under current market conditions, are Burberry golf shirts and Fidra golfshirts complements to or substitutes for one another? Clearly explain. (3points)c. Under current market conditions, would an increase in consumer income lead to an increase or decrease in demand for Fidra golf shirts? Clearly explain. (3 points)6. For the production function KLKLF ),(: LMPL21 andKMPK21.a. Derive the functional form of KLMRTS,. (2 points)b. Is KLMRTS, “Diminishing”? Clearly explain. (2 points)7. Consider the market for coffee beans. Suppose that between 2001 and 2004 bothsupply and demand increase. Clearly explain how the equilibrium price andquantity in 2004 compare to the corresponding values in 2001. (6 points)8. Michael the Salmon Fisherman faces inverse demand of 10100)(qqPD, where q is the number of pounds of salmon he supplies to the market. This inverse demand curve is illustrated below. It follows that marginal revenue is5100)(qqMR . Michael’s Total Costs of production are FcqqTC )(, with 1000  c and 0F. It follows that Marginal Costs of production arecqMC )(. Your answers to parts (a), (b), and (c) should appear in the graph below.a. Draw the corresponding Marginal Revenue and Marginal Cost curves, identifying all intercepts. (4 points)b. Graphically identify the profit maximizing level of output and the corresponding profit maximizing price. (4 points)c. Graphically illustrate the resulting “Consumers’ Surplus” and “Deadweight Loss” in this market. (4 points)d. With only the provided information, can you determine if Michael is able to earn a positive profit? Clearly explain. (4 points)pq)(qPD100100009. Consider a competitive (“price taking”) firm with Short Run costs of production given by FqqqCSR2412)(. For this firm qqMCSR212)( .a. Decompose Total Costs of production into Variable Costs and Fixed Costs of production. (2 points)b. Derive the Average Variable Costs function. (2 points)c. For what range of prices will this firm choose to “shutdown” in the short run? Clearly explain. (4 points)d. Determine the profit maximizing level of output for this firm if 12p. (4 points)e. Continuing to assume 12p, clearly determine the unique value of F for which the maximum profit of the firm is exactly equal to zero. (4 points)10. Consider a firm with the production function LKLKF 3),( . This firm iscurrently operating in the short run with 4K units of capital.a. Suppose the firm wishes to produce an arbitrary level of output 0q. Graphically illustrate the solution to the short run cost minimization problem for this firm. (4 points)b. Determine the short run cost minimizing level of labor. (4 points)11. Consider a market in which demand is given by the function ppD100)( .a. Is the “Law of Demand” satisfied in this market? Clearly explain. (2 points)b. Graphically illustrate the change in Consumers’ Surplus if price were to decrease from $25 to $16. (4 points)(blank