Take Home Exam #3.ECON 500 – Summer 2004.1) Suppose that under current market conditions, the price elasticity of demand fororanges is 34.p, while the income elasticity of demand for oranges is58.I.a. Would an increase in the price of oranges lead to an increase or decreasein total consumer expenditures on oranges? Explain. (6 points)b. Would an increase in consumer income lead to an increase or decrease indemand for oranges? Explain. (6 points)2) Consider the production function 210),( LKKLF . For this function,LMPL2 and 10KMP.a. How much output can the firm produce with )20,10(),( KL? (4points)b. Determine the functional form of KLMRTS,. (4 points)c. Is the Marginal Rate of Technical Substitution “Diminishing”? Explain.(6 points)d. Sketch the isoquant associated with 300q units of output. (4 points)3) Suppose the demand for boxes of Franzia wine is given by the functionppD 6)( (for 360 p). As a result, ppD21)(.a. Derive an expression for price elasticity of demand as a function of price.(8 points)b. Is demand elastic, inelastic, or unit elastic if the price of a box of wine is9p? Clearly explain. (4 points)c. What price maximizes total consumer expenditures in this market?Clearly explain. (8 points)4) Consider a firm operating in the long run with the production function KLKLF ,2min),( .a. If the firm wishes to produce 10 units of output as inexpensively as possible, how many units of L and how many units of K should be hired? Clearly explain. (6 points)b. Suppose the firm wishes to produce an arbitrary level of output 0q. Graphically illustrate the solution to the long run cost minimization problem for this firm. (4 points)c. Suppose the firm wishes to produce an arbitrary level of output 0q. Determine the long run cost minimizing levels of labor and capital. (6 points)d. Determine the long run cost function of this firm. (4 points)e. Suppose the wage rate for each unit of labor were to increase. 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 0q units of output. (6 points)5) Determine if each of the following production functions exhibits Increasing, Decreasing, or Constant Returns to Scale:a.LKKLF 2),( . (6 points)b.LKJJKLF 2),,( . (6 points)6) Consider a firm with the production function 5.25.2),( LKLKF . This firm iscurrently operating in the short run with 625K units of capital.a. Suppose the firm wishes to produce an arbitrary level of output 0q. 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)c. Clearly explain how the short run cost minimizing level of labor will change as the wage rate increases. (4
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