Question

Determine the optimal quantities of both x_{1} and
x_{2} for each utility function. The price of good 1
(p_{1}) is $2. The price of good 2 (p_{2}) is $1.
Income (m) is $10.

a.) U(x_{1},x_{2}) =
*min*{2x_{1}, 7x_{2}}

b.) U(x_{1},x_{2}) =
9x_{1}+4x_{2}

c.) U(x_{1},x_{2}) =
2x_{1}^{1/2} x_{2}^{1/3}

Please show all your work.

Answer #1

**x1 = 4.375, x2 = 1.25****x1 = 5, x2 = 0****x1 = 3, x2 = 4**

Suppose x1 and x2 are perfect substitutes
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2x1 + 6x2. If p1 = 1,
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Alice’s preferences over two goods are described by the utility
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Qin has the utility function U(x1, x2) = x1 + x1x2, where x1 is
her consumption of good 1 and x2 is her consumption of good 2. The
price of good 1 is p1, the price of good 2 is p2, and her income is
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Setting the marginal rate of substitution equal to the price
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a. Show that the above utility function corresponds to (hint:use
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1. The perfect substitute utility function at p=1
2. The Cobb-Douglas utility function as p -->0
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