Exam106 - 4. Using Silberbergs primal-dual optimization...

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Lyon Econ 7140 February 2, 2006 First Exam 1. a. Show that if y 1 /L = y 0 then the change in income is equal to Slutsky’s compensating variation of price, where y i is an individual’s income in year i , and L is the individual’s Laspeyre’s price index. b. Show that if relative prices have changed then real income has increased. 2. 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. 3. 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.
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Unformatted text preview: 4. Using Silberbergs primal-dual optimization problem show that the solution profit function is convex in p and w where p is output price and w is a vector of input prices. 5. In the wheat storage problem one of the necessary conditions is 8 * (1) $ p s 1 where is the current value costate variable, and p s 1 is the price of wheat in storage at time 1 . If the two years are alike, say normal, then we expect the strong inequality to hold. Explain. In your explanation include both the mathematical and intuitive logic. 6. The primary reason economists study duality theory is to play around with the math. T, F, or U. Explain....
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