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Unformatted text preview: DO NOT TAKE TIDS EXAM APART Student Name TEST I Prof. Vitaliano Managerial Economics Fall 2009 Answer Four Questions, but only four (25 pts each). Answer every bullet. Show All Work. Circle the number ofthe four questions you answer. I.The Cognitive Science Department has conducted experiments with students and has determined that the typical RPI student has the following weekly utility function for Pizza (Z) and all other goods (X) (U = Utils ofUtility). U = .100nZ + .901nX (In = natural logarithm) Ifthe typical student has a weekly budget of$100 and pizza costs P z each and X costs P x each. derive the utility maximizing demand curve equation for pizza using the Lagrange multiplier method. Use "L" for the Lagrange equation. (Helpful hint: dU/dlnZ liZ). (20) Ifthe budget was increased by a small amount ($1), by how much would utility change? (5) 2. In Lab # 2 you estimated the following per capita demand curves for cigarettes (assume all coefficients are significant): (I) Q = 3681 - 37 Price + 2 Income + SOAds (II) InQ = S.2S -1.lllnPrice + I.OSlnIncome + .OSlnAds Using model (I), compute the price and income elasticity of demand at Price = 110, Income = $1000 and Ads = 2.38. (10) Determine the equation ofmarginal revenue for demand curve (I). (5) Model (II) is the market demand, and Lorillard Tobacco Co's market share is .37. By how much (percentage) should Lorillard markup up the marginal cost of it's own brand of cigarettes to maximize profits? Why doesn't the percentage markup vary when marginal cost varies? (10) 3 . Assume a typical poor household has monthly income of $1 000 and spends forty percent buying food at present ($400) to maximize utility. The price offood is $5 per unit. Show this on a fully labelled indifference curve diagram, including the budget line intercepts, the equilibrium coordinates and the marginal rate of substitution at the equilibrium. Plot income on the vertical axis and food units on the horizontal axis. Empirical studies estimate the income elasticity of demand for Food by poor households as + 0.50. (10) The government now gives this household $200 worth ofFood Stamps per month, free of charge, and all of it must be spent on buying food. Assume this rule is obeyed. Show on your diagram the new equilibrium amount of food units and non-food purchased. Proponents ofFood Stamps claim they are needed to reduce hunger in America and if $200 cash was given instead there is no guarantee it will all be spent as food. Explain the flaw in this argument. (15) 4. The owners of an Iowa com fann employ a manager who is paid a flat salary...
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- Spring '08