A consumer has preferences over bundles of leisure (L) and consumption (z) respresented bythe utility function u(L, r) = La and has 24 hours in the day to divide between work andlesiure. This consumer has sorme positive amount of nonwork income per day (m > 0) andis able to select how many hours they wish to work at some positive wage per hour (w > 0).Find the consumer's reservation wage as a function of m: this is the lowest wage at which theconsumer will work positive hours. Equivalently, it is the highest wage at which the consumerwill work zero hours. (Hint: this is all about the MRS when working zero hours.)

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Answered: A consumer has preferences over bundles…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Suppose we calculate the MRS at a particular bundle for a consumer whose utility function is U(q1,q2). If we use a positive monotonic transformation, F, to obtain a new utility function, V(q1,q2) = F(U(q1,q2)), then this new utility function contains the same information about the consumer's rankings of bundles. Prove that the MRS is the same as with the original utility function.
solve this all these three subparts early i upvote
Problem 3. Find the total differential for the following utility function U(x1,x2): U(X,X) = xỉ +X - SX,X If The total differential of this function can be written as au au dU = dx, + -dx 3x2 axy Interpret the total differential for utility function
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Consider a worker who consumes one good and has a preference for leisure. She maximizes the utility function u(x, L) = xL, where a represents consumption of the good and L represents leisure. Suppose that this worker can choose any L € [0, 1], and receives income w(1 – L); w represents the wage rate. Let p denote the price of the consumption good. In addition to her wage income, the worker also has a fixed income of y ≥ 0. (a) Write down the utility maximization problem for this consumer. Solution: The problem is max x L s.t. px ≤w(1 L) + y. x>0, LE [0,1] The budget constraint may also be written with equality since preferences are monotone. (b) Find the Marshallian demands for the consumption good and leisure. Solution: Using FOCs will find the maximum since preferences are Cobb-Douglas (and therefore convex). Dividing the FOCs L= Xp and x = Xw gives wL = px. Substituting into the budget constraint and checking the restriction L = [0, 1], we get and x(p, w, y) L(p, w, y) = = = 1 w+y…
Each day, Luke must decide his leisure hours, L, and his consumption, C. His utility function is given by the following equation U(L, C) = (C – 30)(L – 12). Luke receives $50 welfare payment per day. Show all the steps, with definition of every new notation used in the steps. a) Suppose that Luke's hourly wage is $5. Find Luke's daily budget constraint equation and graph it. b) If Luke's wage is $5 per hour worked, what is Luke's optimal consumption, (L*, C*)? · c) Assume that the wage is an unknown variable, w. What is Luke's leisure demand L(w)?- d) What is Luke's reservation wage, the lowest wage Luke is willing to work for? -
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just subparts g and h
Consider a representative consumer with preferences over consumption e and leisure I given by u(e,l) = 1/4 * ln(c) + 3/4 * ln(l) Assume that the price of consumption is normalized to p = 1 and the consumer has h = 24 hours of total time available to divide between work and leisure. The consumer's wage per hour of work is w = 24 The consumer also receives dividend (profit) income of pi = 39 and pays lump-sum taxes of T = 7 (a) Write out the consumer's budget equation, and draw a graph of the budget constraint. (b) Solve for the optimal decisions e and 1. How many hours per day is the consumer working? (c) Suppose the consumer's wage decreases to w = 16 Solve for the new optimal choices of c and I". Relative to the solution in part (b), do consumption, leisure, and hours worked increase, decrease, or stay the same? Give an intuitive explanation for why these changes occur. (d) When the wage changes in part e, determine whether the consumer experiences an income effect, a substitution…
Consider a worker who consumes one good and has a preference for leisure. She maximizes the utility function u(x, L) = xL, where a represents consumption of the good and L represents leisure. Suppose that this worker can choose any L = [0, 1], and receives income w(1 L); w represents the wage rate. Let p denote the price of the consumption good. In addition to her wage income, the worker also has a fixed income of y ≥ 0. (a) Write down the utility maximization problem for this consumer. (b) Find the Marshallian demands for the consumption good and leisure. (c) Find the indirect utility as a function of p, w, and y.
On average, people sleep 8 hours per day meaning that each individual has 16 hours per day to allocate between labour and leisure. Assuming that the wage rate is $15 per hour and there are non-labor income is zero. The utility function of an individual is given by U(Y, L) = YL and for simplicity, the price index for real income is 1. a. Determine the budget constraint. b. Determine the marginal rate of substitution. c. What are the optimal labor and leisure hours? d. At the optimal relationship, what is the utility level for the individual?

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