Suppose you have the utility function of u(x1, x2) = x1x2 and a budget constraint of p1x1 + p2x2 m. Use this information to answer the following questions: (a) What is the Lagrangian for this constrained optimization problem? (b) In the last homework you found that the optimal amount of x *1 was m/2p1 and the optimal amount of x* 2 was m/2p2. How would you find this using the Lagrangian method? Show your work. (c) What do you notice about these two demand functions as their respective prices increase?
Suppose you have the utility function of u(x1, x2) = x1x2 and a budget constraint of p1x1 + p2x2 m. Use this information to answer the following questions: (a) What is the Lagrangian for this constrained optimization problem? (b) In the last homework you found that the optimal amount of x *1 was m/2p1 and the optimal amount of x* 2 was m/2p2. How would you find this using the Lagrangian method? Show your work. (c) What do you notice about these two demand functions as their respective prices increase?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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