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.

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

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

Your family is offering you your choice of two alternatives. The first alternative is to give you a money gift of $19,000. The second alternative is to make an investment in your name. This will quickly have the following two possible outcomes:
Outcome Probability
Receive $10,000 0.3
Receive $30,000

Part 1
Entrepreneur Jones has a utility index of 5 for a loss of $1,000, and 12 for a profit of $3,000. He says that he is indifferent between $10 for certain and the following lottery: a 0.4 chance at a $1,000 loss and a 0.6 chance at a $3,000 profit. What is his utility index for $10?
Part 2
Suppose that Smith has a uti

4. Congress is allocating $1 million of research funding. It can fund research in surfboard safety, B, or in snowmobile safety, S. Since research is measured in dollars, the price of each good is $1.
The utility of each Californian is
The utility of all other Americans is
a. To make this decision, Congress uses the soci

The attached table displays George's consumption of soda pop and pretzels. The price of each soda pop is $2.00 and the price of each pretzel is $5.00.
A. Fill in the missing total utility, marginal utility, and marginal utility/price (MU/Price). Place the final answer for each in the correct shaded area within the table.

Consider a utility-maximizing consumer who devotes all of his weekly income, I = $720 to purchases of caviar (available at the market price, px = $10 per serving) and high-end denim jeans (available at the market price py=$120 per pair). Compute this consumer's optimal consumption of caviar (x) and jeans (y) for each of the foll

I need some help in answering the questions about this case study:
U = A(D^1/3 * C^2/3)
Doughnuts are $5
Cookies are $20
Income is $200
a. Assume that A= 1 for Janet's utilityfunction (above). Calculate the marginal utility of doughnuts; the marginal utility of cookies;
b. Calculate the marginal rate of substitution of