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Unformatted text preview: Economics 104A Solution for Problem Set #2 Winter 2009 1. A consumer spends all his money on good 1 and good 2. The consumer’s utility function is: u ( x 1 ,x 2 ) = min { 4 x 1 , 2 x 1 + x 2 } . The price of good 1 is p 1 = 10, the price of good 2 is p 2 = 5, and the consumer’s income is I = 200. (a) Find the consumer’s optimal bundle. Answer: Notice u ( x 1 ,x 2 ) = 4 x 1 when 2 x 1 ≤ x 2 ; u ( x 1 ,x 2 ) = 2 x 1 + x 2 when 2 x 1 ≥ x 2 . It follows that the ICs can be divided into two parts: vertical lines above the ray with slope 2 and straight lines with slope 2 below the ray. (Figure 1 illustrates the IC through bundle (20, 0).) Thus, MRS = 2 at any bundle below the ray. That is, the two goods are perfect substitutes when the quantity of good 2 is less than twice the quantity of good 1. Since p 1 /p 2 = 2, we have MR = p 1 p 2 at any bundle on the budget line below the ray. Consequently, any bundle on that part of the budget line is optimal at given prices. In particular,that part of the budget line is optimal at given prices....
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 Fall '08
 York
 optimal bundle, Charlie

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