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?

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Chapter1: Making Economics Decisions
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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?
Transcribed Image Text: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?
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