A household's utility over two consumption goods x and y is U= U(x,y) = xy.

1. Describe the household's indifference curve for U = 1 for values of x and y less than 3 (ie. the curve containing all combinations of x and y such that U(x,y)=1.

Now assume that the household's wealth is w=4 and that the prices of the goods are px = 2 and py = 2.
2. How many units of x can the household consume at most if it does not consume any y?
3. Describe the household's budget line and its relationship to the indifference curve.
4. What is the household's optimal consumption bundle?
5. What is the Marginal Rate of Substitution (MRS) between the two goods?

Note the budget constraint can be written as 2x + 2y = 4

6. Solve this budget constraint for y and substitute it into the utility function to obtain an expression for utility that depends on x only.
7. Maximize this utility to obtain the optimal amount of x. (Take the derivative of this expression with respect to x, set the derivative equal to zero, solve for x)
8, Find the optimal amount of y by using the result for x.
9. How does this optimal consumption bundle compare to the one found graphically.

Solution Preview

1. The curve will be azymptotic to both axes. It will pass through the points (1/3,3), (1/2,2), (1,1), (2,1/2), (3,1/3), etc.

2. 2 units of x

3. It will connect the points (0,2) and (2,0). It will be tangent to the ...

Solution Summary

This solution shows how to find a household's optimal consumption bundle algebraically and graphically.

Given the following information, DESCRIBE the budgetline for the consumer: Be sure to state what the axes are and provide numbers for the vertical and horizontal intercepts. Also what is the slope of the line? Explain what the budgetline represents.
Income =$1000/ month
Price of 1 pound of steak = $4.00
Price of 1 pound

Two consumers, Mamoon and Kader, consume only two goods, good 1 and good 2, with the quantities of each consumed denoted by x1 and x2 respectively. The price of x1 is $6/unit, and the price of x2 is $5/unit. The consumer has a fixed income of $64.
Mamoon has a utility function: U(x1,x2 )=2x1^3 x2^5?
Kader's utility function

1. Using Indifference Curve and BudgetLine analysis, graphically demonstrate the equilibrium of a consumer who is maximizing utility. Briefly explain.
2. Using Indifference Curve and BudgetLine analysis, graphically demonstrate how you can derive a demand curve. Briefly explain.
Note: In the above questions, assume a bun

Budget Constraints
What is a budget constraint? How does a budget constraint explain consumer choices when used in conjunction with indifference curves? Explain what happens if a household looses half of their income, using a budget constraint and indifference curves in your discussion.

Suppose that the typical consumer has the following utility function:
U(N, Y) = N×Y,
where Y = income or expenditures on goods, and N = leisure (non-work) hours. The wage rate is given by w = $10. The consumer is initially taxed at the proportional rate of t1 = .4. The consumer has no unearned income (Y* = 0). The time const

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Attached are 2 utility functions that I'm having trouble with.
Problem 3
For each of the following utility functions, draw indifference curves for utility level 12 and 16. Indicate three bundles on each of these indifference curves by specifying the coordinates of each bundle. Shade the weakly preferred set of bundles you

Summary
If George spends $5 (total) a week on good X and good Y, and if the price of each good is $1 per unit, then how many units of each good does he purchase to maximize utility?
To maximize the utility, George has to spend all his money buying one type of good. Either he buys 5 units of good X or 5 units of good Y.
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