1. Consider a static labour supply model for an individual. Assume that the personworks a positive number of hours. Assume that the utility function is of the followingform: U=x0.5 +8(T-h)(0.5) where x is consumption and his hours of work, and 8 is aparameter of the utility function. The person is paid a wage of w for each hourworked. The person has no other source of income other than employment earnings.Assume that the price of x equals 1.a) Specify the utility maximization problem, write down the Lagrange function, andsolve for the first order conditions.b) Solve for the MRS condition between consumption and hours of work.c) Assume that 8=2 if the person has a child living at home, and 8=1 otherwise.Explain (and either show mathematically or graphically) how this will affect theoptimal number of hours of work of the person.

The Marginal Rate of Substitution (MRS) is an economic concept that represents the rate at which a…

1. Consider a static labour supply model for an individual. Assume that the person works a positive number of hours. Assume that the utility function is of the following form: U=x0.5 +8(T-h)(0.5) where x is consumption and his hours of work, and 8 is a parameter of the utility function. The person is paid a wage of w for each hour worked. The person has no other source of income other than employment earnings.

1. Consider a static labour supply model for an individual. Assume that the person works a positive number of hours. Assume that the utility function is of the following form: U=x0.5 +8(T-h)(0.5) where x is consumption and his hours of work, and 8 is a parameter of the utility function. The person is paid a wage of w for each hour worked. The person has no other source of income other than employment earnings.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

QUESTION 1 For the production function Q = K0.5L0.3 and the budget 143 = 6K + 5L find the optimal employment of L. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).
Suppose life expectancy in years (L) is a function of two inputs, health expenditures (H) and nutrition expenditures (N) in hundreds of dollars per year. The production function is L = CH0.60 NO.40 Beginning with a health input of $500 per year (H = 5) and a nutrition input of $300 per year (N = 3), show that the marginal product of health expenditures and the marginal product of nutrition expenditures are both decreasing. The change in the marginal product of health expenditures (MPH) is AMPH ΔΗΓ and the change in the marginal product of nutrition expenditures (MPN) is AMPN AN = Life expectancy (L) Health expenditures (H) Q Q 2
(Based on Chapter 2, Problem 1 of Benjamin et al., 2031) Amit has $2000 of annual non-labour income. He has 80 hours per week that he can allocate between labour and leisure, for 80 x 52 = 4160 hours per year. His current wage rate is $20 per hour and he chooses to work 2200 hours a year. (a) Draw a leisure - labour diagram, clearly indicating Amit's current labour supply decision. (Your diagram should be clearly labeled and include Amit's budget line and an indifferent curve showing his leisure and consumption of goods and services at his optimal choice. Use the figures provided to find the y-intercept and his consumption if he doesn't work.) (b) Amit's wage rate increases to $25 per hour. In response, he increases his labour supply to 2300 hours. If he were "compensated" accordingly, at this new wage rate he would be just indifferent to working 2200 hours at his original wage rate and working 2400 hours at the new wage. Illustrate Amit's new optimal choice. Use the information…
Capital (K) 60 60 45 T A T' Q = 1,000 0 60 Labor (L) 240 What is the Marginal Rate of Technical Substitution (MRTS) (slope of the isoquant Q=1000) at point A? Line TT'is tangent to the isoquant Q-1000 at point A. Please show your calculations.
Suppose that the price of labor (the wage rate) is $100 a day and that the rental price of capital is $50 a day. Currently the Jedie Weapons Corporation is using ten units of capital and five units of labor to produce 500 lightsabers a day. Each lightsaber sells for $2. At the current input use levels, the marginal product of capital is 40 lightsabers per day and the marginal product of labor is 60 lightsabers a day. Is the firm making an economic profit at its current levels of operation? 2. Could the firm increase its profits at the current level of output by adjusting its use of labor and capital? If so, how should input use be adjusted?
Edie chooses to work 90 hours per week when the wage rate is $16 per hour. If she is offered time-and-a-half ($24 per hour) for “overtime work” (i.e., hours in excess of 90 per week), will she choose to work longer hours? Support your results with a diagram.
If the marginal product of labor is 25 and the marginal product of capital 10, what is the marginal rate of technical substitution of labor for capital?
During the 1920s, Charles Cobb and Paul Dougkas modeled totalproduction output P (of a firm, company or entire economy) as a function of labourhours involved x and capital invested y (each includes the monetary worth of allbuildings and equipment). The Cobb-Douglas production function isP(x, y) = k x^α y^(1−α),where k ad α are constants representative of a particular firm or economy.(1) Show that doubling of both labor and capital results in doubling productionP.(2) Suppose a particular firm has the production function for k = 120 andα =3/4. Assume each unit of labor costs $250 and each unit of capital costs$400, and that the total expense for all costs cannot exceed $100,000. Findthe maximum production level for the firm.(3) Compute the production level at x = 64 and y = 81. If the capital isdecreased by 3 units, by how many units the labor should be adjusted toso that there is not change in production level.
thankyou
Consider the following Labour-Leisure Choice model. Utility function over consumption (C) and leisure (L) 1 3 U(CL) = cL4 Total hours H = 20 Labour hours: N = H-L Non-labour income: 1 = 20 Lump-sum tax T= 10 Hourly wage w = 3 Suppose that the hourly wage increases to 5 What is the substitution effect of this wage change on labour supply(N)? A. -1.10 B. -2.10 O C. +1.10 OD. +2. 10 O E. None of the above
Q2. The production function is y = LaK¹- and (p = $10,w = $20, r = $15). (1) Show whether the production exhibits DRS or CRS or IR.S. (ii) Obtain the Marginal Rate of Technical Substitution (MRTS). (iii) Find (Lº, Kº) to minimize the cost in producing given output, y=100.
Suppose a production function is given by the equation Q = LVK. 1. Graph the isoquants corresponding to Q = 10, and Q = 20. 2. MP = √K and MP = 0.5(L/VK). Find the Marginal Rate of Technical Substitution LK (MRTSLK). Do these isoquants exhibit diminishing marginal rates of technical substitution? (Does the slope get flatter as L increases?) 3. The cost of labor is w = $5 per labor hour and the cost of capital is r = $15 per machine hour. What is the equation of the $1500 iso-cost curve?