# Exam206 - lump sum payments to the consumers Note that this...

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Lyon Econ 7140 March 2, 2006 Second Exam 1. The individual’s utility function ( ) 4 3 2 1 , , , x x x x U is strictly quasi-concave, where commodities 1 and 2 are food items and 3 and 4 are clothing items. Show how you would go about proving that we can combine commodities 1 and 2 into a composite commodity called food and 3 and 4 can be combined into a composite commodity called clothing. Outline every thing, and prove all that you have time to. 2. We analyze the welfare loss of placing a sales tax on the commodity 1 x . The representative consumer has utility function and transformation function: () 2 1 , x x u 2 C u u strictly quasi-concave () 0 , 2 1 = x x G with G , 2 C G strictly concave, ( ) () 0 , , 2 1 2 2 1 1 < x x G x x G G is identified from the problem: Max: 2 2 1 1 x p x p + Subj to: () 0 , 1 21 11 1 x a a f 2 C f i and strictly concave () 0 , 2 22 12 2 x a a f i f have positive marginal products 0 1 12 11 + a a a 1 a given 0 2 22 21 + a a a 2 a give We place a sales tax on 1 x such that the consumer pays ( ) 2 2 1 1 1 x p x p + + τ but the seller receives only 2 2 1 1 x p x p + . The government then redistributes the tax revenue with random
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Unformatted text preview: lump sum payments to the consumers. Note that this leaves the government with zero tax revenues. Using the information that we developed in class identify the welfare loss of this taxing scheme. Identify the loss in both a production possibility diagram and a supply-demand diagram. Prove all that you have time to. 3. This is a peak load problem. The city of Logan is selling electricity during the afternoons and evenings at 15 cents per kilowatt hour and in the morning at 8 cents. The demand curves are 1 1 250 x p − = and 2 2 175 x p − = , respectively for evenings and mornings. The implicit user cost of capacity is 10 cents per kilowatt hour and the operating cost is 5 cents per kilowatt hour. Is this the efficient set of prices? If not find the efficient set. Is there price discrimination in this set? Explain....
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