Using utility function to solve for optimal choice

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 constraint is given by
24 = N + H,
where H is hours of work.

Solve for the optimal choice. Graph this solution. How many hours of work is the consumer working? What is her income?

Can you show me the steps needed to solve the this problem?

Solution Preview

First, we need to know the marginal rate of substitution (MRS) between leisure and income for this consumer. The MRS describes how much income is worth in terms of leisure. It is the slope of the indifference curve.

We obtain the MRS of substitution by differentiating the utility function. If is U =NY then we differentiate with respect to leisure to get MU(N) = Y and differentiate with respect to income ...

Solution Summary

Given a utility function and time constraint, the ideal work/leisure combination is found.

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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

Let
U(x,y) = x * (y^2)
1. Derive the indirect utilityfunction as a function of px, py and M, where px and py
are respectively the prices of the two goods x and y, and where M is the consumer's
income.
2. Now calculate the level consumption of both goods and the level of utility achieved
by this consumer if prices a

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** Please see the attached file for a PDF formatted copy of the problem description **
Two consumers each have an income of $300, with which they buy good X (costing $5) and good Y (costing $4). If A's preferences are given by U_A = X^2 Y and B's preferences are given by U_B = X(Y+100), what is the optimal amounts of X and Y

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Mamoon has a utilityfunction: U(x1,x2 )=2x1^3 x2^5?
Kader's utilityfunction

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How do I derive the optimal bundle/utility maximizing problem?

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Outcome Probability
Receive $10,000 0.3
Receive $30,000