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# ps2 - u x 1,x 2,x 3 = x 1 3 x 2 2 x 3(a Derive Michael’s...

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Problem Set 2 Due Thursday, Sept. 17th, by 10pm 1. Terri likes to consume chocolate ( x 1 ) and movies ( x 2 ). Terri’s utility function was given by u ( x 1 , x 2 ) = ( x 1 - γ ) α ( x 2 ) 1 - α where γ > 0. (a) Find Terri’s demands for x 1 and x 2 . Are Terri’s demands homothetic? (b) Derive Terri’s indirect utility function. (c) Derive Terri’s expenditure fuction. (d) Suppose α = 0 . 5 and γ = 2. Calculate Terri’s demands when I = 16, p 1 = 2 and p 2 = 1. Now suppose the p 2 increased to 2. Recalculate Terri’s demands. How much additional money would Terri need to get back to her original indifference curve? (e) Graph your answers to part (d) with x 1 on the x-axis and x 2 on the y-axis, sketching the relevant indifference curves and being sure to label all key points. 2. Michael likes to consume legos ( x 1 ), Wii games ( x 2 ), and science books ( x 3 ). His utility function is given by
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Unformatted text preview: u ( x 1 ,x 2 ,x 3 ) = x 1 + 3 x 2 + 2 x 3 . (a) Derive Michael’s Hicksian demands. (b) Derive Michael’s expenditure function. (c) Michael’s allowance is set at \$28. How much legos, Wii games, and science books will Michael purchase when p 1 = 1, p 2 = 4, and p 3 = 3? (d) Suppose now that p 2 increases to 5. Michael argues that, with the rise in p 2 , his allowance should be higher. How much do his parents need to increase his allowance to get Michael back to his original indiﬀerence curve? (e) Suppose instead p 1 increased to 2 ( p 2 is then at 4). Now how much do his parents need to increase his allowance to get Michael back to his original indiﬀerence curve? How does his consumption of each of the goods change? 1...
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