(1)A utility maximizing consumer purchases two commodities. The utility function is U= Q1 Q2 + 3Q1 + Q2. The prices of both commodities are $8 and $12, respectively. The consumer has an income of $212 to spend on the two goods and wants a combination of both goods that will maximize the utility function. (a)Set up the Lagrange function that could be used to determine the optimum combination of both goods required to optimize the utility function. (b)Use the framework of the Lagrange function to find the optimum combination of Q1 and Q2. (c)lf the consumer is willing to spend one additional dollar on these commodities, determine the marginal utility derivable from this extra expenditure.

(1)A utility maximizing consumer purchases two commodities. The utility function is U= Q1 Q2 + 3Q1 + Q2. The prices of both commodities are $8 and $12, respectively. The consumer has an income of $212 to spend on the two goods and wants a combination of both goods that will maximize the utility function. (a)Set up the Lagrange function that could be used to determine the optimum combination of both goods required to optimize the utility function. (b)Use the framework of the Lagrange function to find the optimum combination of Q1 and Q2. (c)lf the consumer is willing to spend one additional dollar on these commodities, determine the marginal utility derivable from this extra expenditure.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.12P

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