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Microeconomics: Utility Maximization

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I need help with the problem below. Please explain in detail. Thank you.

Suppose Bob spends his income (I) solely on goods X and Y. Initially, Bob has $1000/week to spend on consumption and the prices of these goods are Px=$4 and Py=$2. Graph the budget constraint for this problem. Given these prices and income, Bob maximizes utility buy consuming X1 and Y1. On the same graph, indicate this utility maximizing bundle. Suppose that the price of Y fall to $1/unit. Illustrate how this changes Bob's budget constraint. Suppose that after the price change, consumption of Y has increased to Y2 but the consumption of X stays the same at X1.

Graphically illustrate the income and substitution effects for both Y and X generated by the price change.

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This solution provides a detailed, step-by-step explanation of the given economics problem.

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Solving Utility Maximization Problems

Sam enjoys collecting old editions of microeconomic theory books. Unfortunately, he has no income from employment, but he does accept bags of trash to be buried in his yard for a fee. Suppose the price of each old edition microeonomic book is $2, and San charges $1 for each bag of trash. Sam's utility is given by: U = min(2B, 20-T), where B is the number of old edition books, and T is the number of bags of trash collected by Sam. Note: U is the minimum of 2B and 20 - T, and so this is not a differentiable function.

A. With T on the vertical axis and B on the Horizantal axis, graph Sam's indifference curve for U = 4

B. Determine the values of B and T that maximize Sam's utility.

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