# ps1 - u x 1,x 2,x 3,x 4 = x 1 x 2 4 min 2 x 3,x 4(a Derive...

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Problem Set 1 Due Thursday, Sept. 10th, by 10pm 1. Suppose Joe’s utility function was given by u ( x 1 ,x 2 ) = x 1 / 2 1 + 2 x 1 / 2 2 . (a) Show whether or not Joe’s tastes are homothetic. (b) Calculate Joe’s elasticity of substitution. (c) Suppose the p 1 = 1, p 2 = 4, and Joe’s income is \$120. How much of x 1 and x 2 does Joe consume? (d) Now suppose that p 2 falls to \$2. Calculate Joe’s demands for x 1 and x 2 . Is the demand for x 1 higher or lower than in part (c)? 2. Sarah’s utility function is given by
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Unformatted text preview: u ( x 1 ,x 2 ,x 3 ,x 4 ) = x 1 x 2 + 4 min { 2 x 3 ,x 4 } . (a) Derive Sarah’s demands for x 1 ,x 2 ,x 3 and x 4 as a function of the prices of the four goods and her income. (b) Show whether or not any of the goods could be inferior. (c) Calculate Sarah’s demands when p 1 = 3, p 2 = 1, p 3 = 2, p 4 = 2, and I = 24. (d) Suppose Sarah quits her job and her income falls to \$12. Recalculate Sarah’s demands. 1...
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