Q1 2 Points A representative household receives utility from consumption c and supplying labor/:u(c.1)=c+1-1 As usual, / is the share of time that the household spends working. The household owns anexogenously determined amount of capital /bar (k), earns the nominal rental rate R on each unit of its capital holdings,earns the nominal wage W on each unit of labor it supplies, and pays the price P per unit of consumption. TheRhousehold's budget constraint is: Pc = WI+ar (k) Solve the household's utility maximization problem and select whichbof the following represents the household's labor supply equation:0/=R1W2 P4 P-p()(bar (k))WP21 W<+4 P2ФW.2R.((bar (k))'P' PW.32+PRRW2 P1-p(bar (k)))WP-p()(bar (k))WPP/=1=1+92W+P

Detailed explanation:Utility Function: The utility function given is u(c,l)=c+φ1−l. This…

Answered: Q1 2 Points A representative household…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider a consumer with the following utility function for consumption and leisure: U (R, C ) = 160 ln N + Y where N is the hours of leisure (“recreation”) consumed per day (24 maximum) and Y is dollars spent on consumption (p = 1). The consumer has an hourly wage w. (a) Assume the consumer derives all income from work at a wage rate w. Derive the labor supply function, LS(w). (b) For what values of w does the consumer work zero hours? (Hint: does a corner solution arise?) (c) Suppose that w = 10. How many hours does this consumer work? If the wage rate increases to w′ = 16, how many hours do they work? What is the total effect on the supply of labor?
Q1 A representative household receives utility from consumption c and supplying labor l: u(c, 1) = √c+y√√1-1 As usual, is the share of time that the household spends working. The household owns an exogenously determined amount of capital, earns the nominal rental rate R on each unit of its capital holdings, earns the nominal wage W on each unit of labor it supplies, and pays the price P per unit of consumption.. The household's budget constraint is: Pc Wl+ Rk Solve the household's utility maximization problem and select which of the following represents the household's labor supply equation: 1-2 (WP)k +4P 1-2-() 1= 01= l= 1-4(wk) 1+4 W-²(WP) Save Answer
Suppose your weekly allowance from your parents is $100 and your part-time job pays $10 per hour. The slope of the line plotting the relationship between the hours worked per week (the horizontal axis) and the income per week (the vertical axis) is $. (Enter your response as an integer.) Suppose you start with 10 hours of part-time work and then decide to increase your time working by 3 hour(s). By how much will your weekly income increase? $. (Enter your response as an integer.) Suppose you start with 10 hours of work and then decide you need additional income of $20 per week. How many additional hours would you have to work? hours. (Enter your response as an integer.)
(Short Answers) 1. Jie works in a university. He can work as many hours as he wishes at a wage rate of w. Let C be the number of dollars he has to spend on consumption and let R be the number of hours of leisure that he chooses. Assume that Jie has the utility function U(C, R) = In(C) + In (R). He carms $4 per hour and has 80 hours per week to devote to labor or leisure, and has no income from sources other than labor. a) How many consumptions does he choose? How many hours of leisure does he choose? b) Suppose that Jie's wage rate will rise to $6 per hour from next year. How many hours of leisure per week will he choose next year? You are required to decompose his change in demand into the substitution effect, ordinary income effect and endowment income effect. c) Suppose that Jie will get $4 per hour for the first 35 hours that he works and $6 per hour for every hour beyond 35 hours a week from next year. How many hours of leisure per week will he choose next year?
H1. Suppose an individual has a utility function U = C+3L, where C is the consumption level and L is the leisure hours. Suppose the individual has 100 hours in total for work and leisure and $10 non-labor income. The wage rate is $3.14. Which feasible consumption level maximizes the individual’s utility? (a) 0 (b) 1.8 (c) 9.42 (d) 10 (e) 31.4 (f) 96.86 (g) 100 (h) 131.4 (i) 314 (j) 324 (k) 414
A worker has 110 hours available in a week that can be used for leisure (L) or work (h). The utility function is U = (1 - α)ln(C) + α ln(L), where C is consumption. a) The price per unit of consumption is 1, the hourly wage is w, and the worker has a non-labor income of V. Show that the labor supply is: h* = (110(1-a)- (av)/w). Also, find the demand for consumption and leisure. b) What is the effect on labor supply of i) an increase in the hourly wage and ii) an increase in non-labor income? c) Set α = ½. What are C, L, and h when w = 200 and V = 10000? What is the reservation wage? d) What is the effect on labor supply of i) a 30% income tax and ii) a 10% wealth tax (on V)? e) What is the labor supply if V increases to 11600? f) An increase in V to 11600 gives the worker the same utility as w = 250 and V = 10000 (you do not need to show it). What are the income, substitution, and total effects on labor supply of an increase in wage from 200 to 250 while V remains at 10000?…
Tatum is a mother of Anny (1 year old). Tatum derives utility from income Y (i.e. a disposable income that she can spend on consumption goods other than childcare) and leisure L according to the utility function U(Y,L)=Y*L . She has non-labour income of $300 per day. Her time endowment is 16 hours per day that can be spent either on Leisure (which mostly consists of caring for Anny) or labour market work. If Tatum works she has to leave Anny in the child care. Tatum’s wage is $30 per hour, while the childcare cost $5 per hour. Tatum only uses childcare when she works. Compute how many hours Tatum will work under these circumstances. Round your answer to the second decimal point.
A. Consider a consumer whose preferences can be represented by Cobb-Douglas utility function u(x₁, x₂) = xx where ₁ and 2 are the quantities of good 1 and good 2 she consumes. Let p₁ and p2 be the prices of good 1 and good 2 and let m denote her income. 1. Derive the consumer's Marshallian demand functions. 2. Derive the consumer's Hicksian demand functions. 3. Derive the consumer's expenditure function. 4. Let m = 20, P₁ = 2, and p2 = 1. Suppose that the price of good 1 drops to p₁ = 1. Find the following (a) Compensating variation (CV) (b) Equivalent variation (EV) (c) Change in consumer surplus (ACS) (d) Compare CV, ACS, and EV. 5. Let m = 120, P₁ = 1, and p2 = 1. Suppose that the price of good 1 increases to P₁ = 2. Find the following (a) Compensating variation (CV) (b) Equivalent variation (EV) (c) Change in consumer surplus (ACS) (d) Compare CV, ACS, and EV.
5. A consumer's utility function over leisure and consumption is given by u(L, Y) = LY. Wage rate is w and the price of the composite consumption good is p = 1. (a) Suppose w = 10. Find the optimal leisure - consumption combination. (b) Suppose the overtime wage law is passed so that the firm must pay 1.5 times the normal wage for hours worked beyond the first 8 hours. Find the effect on the hours worked. Decompose the effect into substitution effect and income effect.
1 The consumption-leisure framework Suppose that the representative consumer has the following utility function over consumption (c) and labour (n): u(c, l) = ln c − A 1 + � n 1+� (1) where, as usual, c denotes consumption and n denotes the number of hours of labour the consumer chooses to work, The constants A and � are outside the control of the individual, but each is strictly positive. Suppose the budget constraint (in real terms) faced by the individual is given by: c = (1 − t) · w · n (2) where t is the labour tax rate, w is the real hourly wage rate, and n is the number of hours the individual works. Remember, as seen in class, n + l = 1 is always true. Using the static consumption-leisure framework, answer the questions that follow. 1. State the utility maximization problem, and state carefully the choice variables in the problem. [2] 2. Write the Lagrangian function for this problem. [2] 3. Using the Lagrangian function from above, derive the first order condition with respect…
Q1) Deborah has 80 hours per week available for work and leisure. Her current rate is $25 per hour. Deborah has $400 of rental income every week. a) Construct a proper diagram to describe Deborah's choice of working 40 hours per week. Calculate Deborah's maximum possible income and optimal income, and show them in the diagram. b) Suppose Deborah recently moved into her boyfriend's place. She shares the household expenses and is "taxed" 50% of her wage income. Draw another diagram to compare Deborah's choice in Part a) and a new labor supply decision of working 50 hours per week due to the "tax". Clearly label out the income effect, substitution effect and total effect in the diagram.
Consider an individual whose utility function is U(C, R) = 2C - (4 - R) 2 where R is the amount of leisure the consumer experiences per day. Suppose that the individual normally sleeps T hours a day, and they can spend the remaining hours between work and leisure. The individual receives an hourly wage of w > 0 and has also an income of Y > 0 a day from non - labour sources. The price of consumption goods is p per unit.

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