Exam #2. ECON 500 – Spring 2004. 1. Consider a consumer with monotonic preferences. Consider the following three consumption bundles: )8,5(=A , )10,6(=B , and )9,25(=C . Answer the following questions based upon only this information. a. How does this consumer rank bundles )8,5(=A and )10,6(=B ? Clearly explain. (4 points) b. How does this consumer rank bundles )10,6(=B and )9,25(=C ? Clearly explain. (4 points) c. Suppose prices are 41=p and 32=p and the income of the consumer is 60=I . Determine if each bundle above is affordable or not affordable. (6 points) d. At the prices and income considered in part (c), could any of the bundles above be optimal for this consumer? Explain. (6 points)2. Consider a consumer with 221)( xxXU = . For this individual, 221xMU = and 2122 xxMU = . a. Specify 2,1MRS as a function of 1x and 2x . (2 points) b. 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). (8 points) c. Determine the level of utility (as a function of prices and income) that this individual realizes as a result of consuming this optimal bundle. (3 points) d. Based upon your answer to part (c), will this individual be better off or worse off if: income doubles (so that initialnewII 2=) and the price of commodity two triples (so that initialnewpp,2,23=), with the price of commodity one held fixed (so that initialnewpp,1,1=)? (3 points)3. Consider an individual who optimally consumes 21211233),,(ppIIppx+= . a. Is commodity one an ordinary good or a Giffen good? Explain. (3 points) b. Is commodity one a normal good or an inferior good? Explain. (3 points) c. Is commodity one a substitute for or a complement to commodity two? Explain. (3 points) 4. Does the production function LKLKF += 2),( exhibit Increasing, Decreasing, or Constant Returns to Scale? Clearly explain. (10 points)5. Suppose market demand is given by ppx120)( = . a. Will Consumers’ Surplus increase or decrease as price is decreased? Explain. (4 points) b. Graphically identify the change in Consumers’ Surplus as a result of a decrease in price from 16=Hp to 9=Lp . (4 points) c. Noting that “the demand curve becomes flatter as we move to lower price, higher quantity pairs,” place a numerical bound on the change in Consumers’ Surplus as price decreases from 16=Hp to 9=Lp . (5 points) d. Suppose you are told that for a general decrease in price from a high price of Hp to a low price of Lp (that is, for any ∞<<<HLpp0 ), the change in Consumers’ Surplus is ()LHppCS −=∆ 240 . Does this expression seem consistent with your answers to parts (a) and (c) above? Explain. (4 points)6. The Cross Price Elasticity of Demand for Coffee with respect to Tea is (.15). Explain what this means with a numerical example. What does the fact that the number is positive tell you about the relationship between Coffee and Tea consumption? (8 points) 7. “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, explain why this statement might not always be true. (10 points)8. A firm produces output using two inputs, labor and capital. Is it possible for the production process to exhibit Diminishing Marginal Returns with respect to each input, but at the same time exhibit Increasing Returns to Scale? (hint: consider the Cobb-Douglas production function βαLAKLKF =),( with 0>α and 0>β, recalling that for this function 1−=βαβLAKMPL and βααLAKMPK1−= ) (10 points)blank
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