MorePracticeQuestionsMT2

MorePracticeQuestionsMT2 - Problem 2: A consumer purchases...

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University of California, Davis Department of Agricultural and Resource Economics ARE 100A Instructor: Monticha Sompolvorachai Winter 2009 Extra Practice Problems for TE, SE and IE Problem 1 A consumer purchases two goods, food (F) and clothing (C). Her utility function is given by: U(F, C) = 2FC + 5F. The price of F is given as 5, the price of C is given as 10, and income is given as $5,000. (a) Solve for the optimal (numeric) values of F and C by using the Lagrangian method. (b) What is the numeric value for λ? Interpret this result. (c) Suppose the price of F increases to $8. Solve for the optimal (numeric) values of food and clothing. Using the demand function from part a, we can find F* given the new P F (d) Calculate numeric values for the: i) total effect of the price change ii) substitution effect of the price change iii) income effect of the price change
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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 consumers 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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