The rate at which the consumer is just willing to substitute leisure for consumption goods is.Choose the correct one.● MRSI.C = 4○ MRS₁₁c = //○ MRS₁,c =○ MRS₁,c= 41 This problem considers the decisions of a consumer whose preferences are givenbyu(C,1)=C+4 lnl,in which C' is the quantity of consumption and I is the quantity of leisure. The consumer faces twoconstraints. The time constraint is given by 1 + N³ = 1 with NS as the time spent working (or thelabor supply). The main advantage of working is the wages consumers receive.Consumers take wages as given (outside of their control) and obtain wage income equal to wN³.The budget constraint is C wNsT, with π as real dividend income and T as the real=lump-sum taxes paid to government.

By calculating the partial derivative of the utility function u(C, l) with regard to leisure (l) and…

Answered: The rate at which the consumer is just…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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This problem considers the decisions of a consumer whose preferences are given by u(C, 1) = C + y log 1, in which is the quantity of consumption and I is the quantity of leisure. The consumer faces two constraints. The time constraint is given by 1 + N = 1 with N³ as the time spent working (or the labor supply). Assume that 0 < x < 1. The main advantage of working is the wages consumers receive. Consumers take wages as given (outside of their control) and obtain wage income equal to w Nº. The budget constraint is C = wN+T-T, with as real dividend income and T as the real lump-sum taxes paid to government. Assume that an interior solution always exists in the optimal consumption-leisure choice.
Consider a consumer who could earn $400 per week and has 50 weeks available each year to allocate between work (H) and nonmarket time (L). They have no non-labour income. Their utility function is U = C2L , where C is the value of consumption goods. What is their optimal choice for the number of weeks in nonmarket time and consumption? Show this in a diagram. Suppose the government introduces a policy that (i) offers no benefits to people who do not work, (ii) offers a wage subsidy on earnings at a rate of 25%, with a maximum benefit of $5000, and (iii) the benefit is subject to reduction at a rate of 25% for every dollar earned above $20,000 in the year. Show the person’s new budget constraint in a new diagram, and discuss how the person’s optimal choice might change (you do not have to calculate this, but point to where it is likely on the new budget constraint). Discuss how income and substitution effects play a role.
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An individual values both consumption and leisure. Suppose the individual has 1600 hours per week they can allocate between leisure and work. IF the individual works, they make a wage of $25 per hour. The individual's utility function is given as a function of leisure time, L and consumption, c: U(L, c) = L^(1/2)c ^ (1/2) a) Draw the individual's budget constraint for leisure and consumption. b) How much leisure time will the individual have when utility maximizing? c) Consider a Universal Basic Income policy like the one proposed by Andrew Yang that would give all individuals a lump -sum, unconditional cash transfer of $1,000 each month. How much leisure time will the individual have when utility maximizing with the cash transfer? d) Now suppose, instead of a cash transfer, a minimum wage of $40 per hour is implemented. How much leisure time will the individual have when utility maximizing with the cash transfer? e) What change in leisure time can be attributed to the substitution…
Question You are the manager of a firm and you are required to optimize the Cobb Douglas function given the following parameters. The maximum amount of money available is$1600 where the price of K = 12 and the price of L=6. That is PK=12 and PL=6. The function is given as q=K0.4+L0.6. What is the constraint equation? a. none of the above b. 12K - 6L = 1600 c. 12K/6L = 1600 d. 12K+6L=1600
This problem considers the decisions of a consumer whose preferences are given by u(C,1)=C+4 lnl, in which C' is the quantity of consumption and I is the quantity of leisure. The consumer faces two constraints. The time constraint is given by 1 + N³ = 1 with NS as the time spent working (or the labor supply). The main advantage of working is the wages consumers receive. Consumers take wages as given (outside of their control) and obtain wage income equal to wN³. The budget constraint is C wNsT, with π as real dividend income and T as the real = lump-sum taxes paid to government.
In a standard consumer optimization problem in microeconomics, a consumer purchases any pair of goods untilU1U2=p1p2(?), at an interior solution, where Ux is the marginal utility of good x for the consumer and px is the price of good x, where x={1,2}. What is the corresponding optimality condition for a worker-consumer in his labour-leisure optimization problem and why is it just a variation on the standard optimality condition (?)?
A) Ana decides every day how many hours to work and how much beef to consume. She spends all income earned from work each day on consumption of beef. Her utility function for free time (t, 24 hours minus hours worked) and consumption (y) is: U(t, y) = 2t + y The price per unit of beef consumed is 4 and her hourly wage is 1. • Using a diagram and appropriate algebra, explain what Ana's optimal number of hours work and units of beef consumed are each day. Ana reads a book about the impact of beef consumption on climate change and realises that there is a cost to society of her beef consumption. She takes account of this impact on society in her own decisions, incorporating a disutility of -0.03y per unit of beef consumed. She still only consumes beef and spends all income earned each day on this consumption. • Explain, using a diagram and appropriate algebra, how recognition of the impact of her consumption choice on climate change impacts on Ana's daily free time and beef consumption…
Task 4: leisure or work? The consumer choice is not restricted to the choice of consumption goods. In fact, it can apply to all our decisions that involve trade-offs. Suppose Mary has a wage per hour of 10 euros. With her earned income she consumes. That is, C = wH per day. She also decides how many hours to work of take leisure time each day. H = 24 – N, where H is work and N is leisure. Her utility is given by C1-o U(C, N) + B log(N) 1- o (a) Solve for the optimal decision of labor/leisure. Plot the budget constraint and the indif- ferent curve. What is the labor supply function? (b) If o > 1, what is the shape of the labor supply? How does it relate with the income and
Ana decides every day how many hours to work and how much beef to consume. She spends all income earned from work each day on consumption of beef. Her utility function for free time (t, 24 hours minus hours worked) and consumption (y) is: U(t,y)=2t^1/2 + y The price per unit of beef consumed is 4 and her hourly wage is 1. Using a diagram and appropriate algebra, explain what Ana’s optimal number of hours work and units of beef consumed are each day. Ana reads a book about the impact of beef consumption on climate change and realises that there is a cost to society of her beef consumption. She takes account of this impact on society in her own decisions, incorporating a disutility of -0.03y per unit of beef consumed. She still only consumes beef and spends all income earned each day on this consumption. Explain, using a diagram and appropriate algebra, how recognition of the impact of her consumption choice on climate change impacts on Ana’s daily free time and beef…
Sharon spends her time (16h) between leisure (L) and work and he consume Y product from his working income (P=1). Assume that she gets W$ per hour of working (W>0) and has the following utility function: U (L, Y) =LY 4Y. a.Calculate the demand function for L. and show it on a graph (L. vs W). b. Calculate the labor supply (H) and show it on a graph (H vs W). c.What will happen to L. Y and H if the wage per hour (W) will decrease?
A consumer has preferences over bundles of leisure (L) and consumption (z) respresented by the utility function u(L, r) = La and has 24 hours in the day to divide between work and lesiure. This consumer has sorme positive amount of nonwork income per day (m > 0) and is 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 the consumer will work positive hours. Equivalently, it is the highest wage at which the consumer will work zero hours. (Hint: this is all about the MRS when working zero hours.)

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