# ECON 400 A consumers utility is defined by the function

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## ECON 400 A consumers utility is defined by the function

1. A consumers utility is defined by the function

U(x1,x2) = x11/2 x21/2

Assume the prices of x1 and x2 are respectively defined by \$5 and \$10, and the consumer has 20 dollars in income.

1. a.) Find the consumer’s Marshallian demand for both goods, x(p, w). Use the short cut method and compare your results using the Lagrangian method.
2. b.) How in words would this result (in a) differ from the Hicksian demand curve. Show how (no calculations need) you derive the expenditure function and then get to the Hicksian demand curve. (Hicks keeps utility constant while accounting for differences in prices, Marshall
3. c.) Assume the price of x1 increases to \$10, what is the compensating variation needed to keep the person on the same indifference curve.Hint:E = U( P1/a) a(p2/1-a)) 1-a

use your answer in part a to find utility (U).  Then multiply utility by (10/.5).5*(1/.5.5).  Then evaluate this number at price of \$10 and price of \$5 such as CV=E(10) – E(5).