Econ 310 Exam #2A Multiple Choice: (circle the correct letter) (4 points each) 1) Consider a market with only two consumers, Consumer A and Consumer B. Consumer A has individual demand given by 22500)( ppDA−= ; Consumer B has individual demand given by ppDB−=100)( . The corresponding market demand, denoted )( pD : a. is a linear function of price. b. is such that 0)50( =D . c. is “downward sloping.” d. is equal to 22600)( pppD −−= for 1000≤≤p . e. cannot be determined from the given information. f. More than one, but not all, of the above are correct. g. None of the above are correct. 2) A normal good: a. has a negative income elasticity. b. has a positively sloped Engel curve. c. is such that the optimal level of consumption decreases as income decreases. d. is such that EVCSCV >∆> for any price decrease. e. Both (b) and (d) are correct. f. Both (b) and (c) are correct. 3) The Price Consumption Curve for commodity one: a. illustrates the optimal level of consumption of commodity one as a function of income. b. illustrates the optimal consumption bundle in ),(21xx -space as income is varied. c. illustrates the optimal consumption bundle in ),(21xx -space as both prices change simultaneously by a common factor. d. must have a strictly positive slope if commodity one is an ordinary good. e. should be drawn in ),(11px -space. f. More than one, but not all, of the above answers are correct. g. None of the above answers are correct.4) Consider a firm for which output is a function of just labor and capital as follows: KLKLF 82),( += . This firm is currently operating in the short run with a level of capital KK= . Suppose the firm wishes to produce KQ 8> units of output as inexpensively as possible. The short run cost minimizing level of labor: a. increases as the wage rate increases. b. decreases as the wage rate increases. c. does not depend upon the wage rate. d. is KQLSR162*−= . e. Both (c) and (d) are correct. 5) Consider a market in which demand is given by ppD−=100)( . As price increases from 40=p to 60=p , Consumer Surplus: a. increases by 400. b. increases by 200. c. decreases by 400. d. decreases by 200. e. increases by some amount less than 200 f. decreases by some amount less than 200. g. None of the above answers are correct. True or False: (circle TRUE or FALSE) (3 points each) 1) TRUE or FALSE: The Engel Curve for any commodity must pass through the origin. 2) TRUE or FALSE: In the long run a firm is not able to vary the amount of at least one input. 3) TRUE or FALSE: By definition, a good is a Giffen good if an increase in price leads to an increase in the level of consumption. 4) TRUE or FALSE: If commodity one is a normal good, then an increase in income will lead to a rightward shift of the demand curve for commodity one. 5) TRUE or FALSE: The production function {}[]28,5min),( KLKLF = exhibits increasing returns to scale. 6) TRUE or FALSE: Compensating Variation in Income answers the question “How much money could we take away from a consumer after a price change, so that the consumer is just as well off as she was before the price change?”Problems and/or short answer questions: 1) A consumer with 21)( xxXu = maximizes utility by consuming 112 pIx = and 222 pIx = . a. Does commodity one appear to be a normal good or inferior good? Explain. (6 points) b. Does commodity one appear to be an ordinary good or Giffen good? Explain. (6 points) c. Determine Indirect Utility as a function of prices and income. (4 points) d. Determine a general expression for the Equivalent Variation in Income associated with a decrease in the price of commodity one from 1p to 1ˆp (for a consumer with an arbitrary level of income I, for which each unit of commodity two costs an arbitrary price 2p ). (10 points)e. Consider such a consumer with 600=I . The price of commodity two is 122=p . Suppose initially 251=p , but then the price of commodity one drastically decreases to 9ˆ1=p . Determine the Equivalent Variation in Income associated with the price change described above. (4 points) f. EXTRA CREDIT (6 points): Prove that in general (that is, for arbitrary 1p , 1ˆp, 2p , and I) for such a consumer the Equivalent Variation in income: does not depend upon 2p and is larger for smaller values of 1ˆp. 2) Give an example of a Cobb-Douglas production function which: a. exhibits decreasing returns to scale. (6 points) b. exhibits increasing returns to scale, and has a diminishing marginal product for each input. (8 points)3) Suppose a firm wishes to produce Q units of output as inexpensively as possible, using two inputs, L and K. Each unit of L costs w ; each unit of K costs r. Suppose LKKLF 6),( = , which implies LKMPL3= and KLMPK3= . a. Determine KLMRTS,. (4 points) b. Determine the cost minimizing level of each input as a function of Q , w , and r. (10 points) c. Determine the minimum costs of producing Q as a function of w and r. (4 points) d. EXTRA CREDIT (4 points): Based upon your answer to part (c), how will the total minimum costs of production change if the firm chooses to double the amount of output produced? Explain.(blank