Problem Set 3 Solutions

So after plugging in the right values we solve for m

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Unformatted text preview: until you reach the same utility at the new prices). So after plugging in the right values we solve for m in the formula: .3ln(.3m/1.25) + .7ln(.7m/1) = .3ln(30) + .7ln(70) x .3 .7 .3 .7 3.994 ‐>ln[(.3m/1.25) (.7m) ] = 3.994 -> (.3m/1.25) (.7m) = e -> .5077m = 54.27 -> m = 106.89 Now CV = m – 100 because 100 is the original wealth, so CV = 6.89. For EV, we do the same thing, except in the formula .3ln(.3m/p ) + .7ln(.7m/p ) = x y .3ln(X*) + .7ln(Y*), X* and Y* are the optimal values after the price change, and p and p x y are the optimal prices before the price change. Plug in these values and solve for m: .3ln(.3m/1) + .7ln(.7m/1) = .3ln(24) + .7ln(70) .3 .7 .3 .7 3.927 -> ln[(.3m) (.7m) ] = 3.927 -> (.3m) (.7m) = e -> .5429m = 50.75 -> m = 93.49 Now EV = 100 – m, so EV = 6.51. Finally, the CS is just the integral of the demand function X = 30/Px from Px=1 to Px=1.25, which is 30*ln(1.25) - 30*ln(1)...
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This note was uploaded on 02/09/2014 for the course ECON 1130 taught by Professor Baum-snow during the Spring '11 term at Brown.

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