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The utility that Meredith receives by consuming? food, F, and? clothing, C, is given byU(F,C)=FC.
Suppose that? Meredith's income in 1990 is? $1200 and that the prices of food?(PF?) and clothing?(PC?)are? $1.00 per unit for each. By? 2000, however, the price of food has increased to ?$2.50and the price of clothing to ?$4.00.
Let 100 represent the? cost-of-living index for 1990. Calculate the ideal and the Laspeyres? cost-of-living indexes for Meredith for 2000.?(?Hint:Meredith will spend equal amounts on food and clothing with these? preferences.)
That? is, the marginal utility of food is
MUF=Cand the marginal utility of clothing is
MUC=?F,so Meredith will maximize utility where
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