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380 Problem Set _ 6-expenditure function

# 380 Problem Set _ 6-expenditure function - c How much will...

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Consumer Choice: Expenditure Functions Problem Set 6 Econ. 380 R. Pope Winter 2011 Graphical 1. Why does a Laspeyres price index like the CPI (consumer price index which keeps the market basket fixed) tend to overstate the cost of living when a price increases. Calculus or at least More Technical Problems 2. Mr. A derives utility from the number of martinis he drinks , U(m)=m. However, he only enjoys martinis made in a particular way: two parts gin (g) to one part vermouth (v). Hence is utility function is U(m)=U(g,v)=min(g/2,v). a. Derive the Indirect Utility Function. b. Derive the expenditure function?
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Unformatted text preview: c. How much will expenditure increase if the price of gin doubles? d. What happens to expenditures if both the price of gin and vermouth double? 3. For the general Cobb-Douglas utility function, 1 ( , ) , 0 1 a a U x y x y a-= ≤ ≤ and using , , and for prices and income x y p p I a. Derive the indirect utility function and give its meaning. b. Derive the expenditure function for arbitrary utility level U and give its meaning. b. Give the best intuitive or graphical explanation that you can for why the expenditure function is concave in prices....
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