Unformatted text preview: Problem 2: A consumer purchases two goods, X and Y. Her utility function is given by: U(X, Y) = X 1/2 Y. The price of X is given as 5, the price of Y is given as 10, and income is given as $4,500. (a) Solve for the optimal (numeric) values of X and Y by using the Lagrangian method. (b) Suppose income increases by $1. What will be the increase in this consumer’s level of utility? (c) Suppose the price of X increases to $10. Solve for the optimal (numeric) values of X and Y, as well as the level of utility attained. (d) Calculate numeric values for the: iv) total effect of the price change v) substitution effect of the price change vi) income effect of the price change In order to find the substitution effect, you can choose to keep either utility or purchasing power constant. 1...
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- Winter '08