3 1. A consumer has the utility function U(x,y) = 2x y where x and y represent the quantity consumed of goods X and Y. a) Find the consumer's marginal rate of substitution of X for Y. For parts (b) and (c) assume that the consumer has $100 to spend on goods X and Y which have fixed prices of px=1 and py=3. Use the Lagrangian method to solve the consumer's optimization problem: b) What are the first order conditions of the Lagrangian. Assume the solution to the consumer's optimization problem is interior. Solve for the consumer's optimal consumption bundle for any prices and income.

3 1. A consumer has the utility function U(x,y) = 2x y where x and y represent the quantity consumed of goods X and Y. a) Find the consumer's marginal rate of substitution of X for Y. For parts (b) and (c) assume that the consumer has $100 to spend on goods X and Y which have fixed prices of px=1 and py=3. Use the Lagrangian method to solve the consumer's optimization problem: b) What are the first order conditions of the Lagrangian. Assume the solution to the consumer's optimization problem is interior. Solve for the consumer's optimal consumption bundle for any prices and income.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

1.
A consumer has the utility function U(x,y) = 2x y' where x and y
represent the quantity consumed of goods X and Y.
a)
Find the consumer's marginal rate of substitution of X for Y.
For parts (b) and (c) assume that the consumer has $100 to spend on goods X and Y
which have fixed prices of px=1 and py=3. Use the Lagrangian method to solve the
consumer's optimization problem:
b)
What are the first order conditions of the Lagrangian.
Assume the solution to the consumer's optimization problem is
c)
interior. Solve for the consumer's optimal consumption bundle for any
prices and income.

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3) The utility function of a consumer who consumes quantities x and y of two goods is defined by the expression U(x, y)=√xy subject to the constraint 7x+3y=84 where $84 is the consumer's overall budget. Assuming marginal utilities U,,U>0, maximize the utility function of the consumer. What are the optimal values of x, y and U(x,y) ?
6. Consider a consumer with the utility function u(x,, x2) = In(x,) + x2 and the budget constraint p, x, + PP2X2 = m. Derive the consumer's demand functions for x, and x2.