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# Exam110 - 2 x 2 is rival and exclusive while good 1 x 1 is...

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Lyon Econ 7140 February 18, 2010 First Exam 1. Let the primal problem be to maximize profits for a price-taker firm. Use the primal-dual problem to show that the solution profit function is convex in w and p . What does this imply about the resource demand functions and the supply function? Explain. 2. An input is inferior if its use decreases as output increases. In addition, an increase in the hire-price of an inferior input will cause marginal cost to decrease. Show that this is so. 3. In this question y i is AGGREGATE income and L is the Consumers’ Price Index. If y 1 /L > y 0 then Hicks would call this an increase in social income. Give Hicks’ reasoning for this conclusion. 4. In this question y i and y f i are INDIVIDUAL i’s money income and full income as defined in class, respectively. Let y 1 > y 2 and y f 1 < y f 2 . Would you rather be individual 1 or 2? Defend you answer. 5. This question is related to Hicks valuation of social income paper. We assume that good
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Unformatted text preview: 2, x 2 , is rival and exclusive while good 1, x 1 , is non-rival and non-exclusive, the government purchases a Pareto optimal level of x 1 , and x 1 is produced by a price-taker industry that exhibits constant returns to scale. a. Using x 2 as the numeraire good derive an expression for social income. b. Explain and defend your measure of social income. 6. Suppose an employer has been paying his workers \$5 an hour for the first 40 hours per week and \$7.50 per hour for voluntary overtime. Average overtime is 10 hours per week. The employer also has to pay \$10 dollars a week social security contribution per employee ( irrespective of hours worked). The workers now suggest abolishing overtime rates and replacing them with a flat rate system paying \$5.50 per hour for each hour from zero upwards. Will the employer agree? Explain everything....
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