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.

... m - (1-p)h)/2. Then, use the budget ... Please note that this problem is solved using particular assumptions ... time period i. Other assumptions are used (please see ...

... You can use the first two FOC to find that . ... While a specific functional form for utility function is used , the steps are detailed enough for a student ...

... variables such that the following objective function is maximized ... one of the sweeteners can be used: x SS ... we just need to modify the utility constraint. ...

... method applied objective function was: to use enough time to ... The parameter values were deﬁned using Problem k ... sub-utility function and were used in different ...

... Thus the proposed model is used to derive new implications ... However the ﬁrm can use the existence of loss aversion ... is a result of the ﬁrm using the eﬀect ...

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... (a) [0.5 pt] A firms production function is given ... 26.67 66.67 93.33 20.00 200 200 Using Solver. ... each country are represented by the following utility functions: ...

... 2. Prove the envelope theorem and use it to derive Hotelling's lemma. ... In fact, if you give me any utility function representing a preference relation ...

... Analytic Hierarchy Process which can be used to find ...Using this procedure, one can select the alternative with ... weights of each objective, we use the following ...