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.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.3P

See similar textbooks

Similar questions

Consider the following production function for shirts: q = v6 L3/4K/4, where L is worker-hours, and K is sewing machine-hours. a. Compute the marginal products of labor and capital, the average product of labor, and the marginal rate of technical substitution of labor for capital (i.e. how many units of capital are needed to make up for the loss of one unit of labor)? b. Are there diminishing returns to labor (that is, does the marginal product of labor decrease when labor L increases)? What about to capital? Is there diminishing marginal rate of technical substitution (MRTS)? с.
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?
Consider the following production function that depends only on labor:Q = 4L + 12L² - 6L³ 1. Compute the APL (average product of labor). 2. Compute the MPL (marginal product of labor). 3. What is the value of L* at which APL is the highest? 4. For L > L*, which one is bigger, APL or MPL? How about when L < L* and L = L*? 5. Draw APL and MPL on the y-axis as a function of L on the x-axis. Label the point of the intersection of APL and MPL.
Consider the following production function: q = 32LK + 10L2 - Assume capital is fixed at K= 25. At what level of employment does the marginal product of labor equal zero? The marginal product of labor equals zero when (Enter a numeric response using an integer.) Beyond a labor input of 40, the marginal product of labor is 20 étv MacBook Air DI DD F3 F5 F6 F7 FB F10 FW 2# $ & 3 4 5 8 9 E R Y P D F G н J K C V B N M command V
Consider the following production function: Q = (6L + 3K)¹/2 1. What is the Marginal Product of Labor (MPL)? What is the Marginal Product of Capital (MPK)? Are they diminishing? 2. What is the Average Product of Labor (APL)? What is the Average Product of Capital (MPK)? 3. What is the TRSL,K? Is the absolute value of TRSLK diminishing in L or K? 4. Are there constant, decreasing, or increasing returns to scale?
Can you draw( i need a graphs) labor supply function : U(c,l)=log(c)+log(l) where, c-represents the consumption level of the individual and l-represents the leisure, while the market wage is 10 and available time is 20. Find and Draw the labor supply function! Graph
Suppose the production function for widgets is given by q=KL+6L²-0.1L³ where q represents the annual quantity of widgets produced, K represents annual capital input and L represents annual labor input. A) Suppose K=10. At what level of labor input does average product of labor reach a maxiumum? How many widgets are produced at that point? B) Again assuming that K=10, at what level of labor input does MPL=0? C)Determine and show whether the production process exhibits law of diminishing returns.
A farmer uses a certain technology that produces electricity. His production function is given as: q = f (k, l) = 1000k¹⁰/20 – 201³ Where q is the no. of megawatts of electricity his company is producing. Suppose that their electrical generators, k=20, calculate for the following: 1. Marginal product of labor 2. Average product of labor if k=20 3. If k decreases from 20 to 17, calculate the new MP of labor and the average product. Explain intuitively what happens to the MP and the average product.
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?
What is the marginal physical productivity (MPP) of the inputs given the function Q=18x21+2x1x2+2x22 ? Select one: а. МPPx1336х1+2x1MPPx2-2x1+4х1 b. МPPX1336x1+2x1MPPx2-2x2+4х2 С. MPPX1=36+2x2+2MPP×2=2x1+4x2 d. MPPX1=36x1+2×2MPPX2=2x1+4x2
Production Function and Input Demand Consider the production function Q = K + √L. Derive the inputdemand curves for L and K, as a function of the output Q, inputprices w (price of labor services) and r (price of capitalservices). Does the production function exhibit IRS, CRS orDRS?
Brian uses wool (K) and labour (L) to produce t-shirts (q). The production function is: q = min{1/3L, 2K}.If he uses 0.5 kg of wool and 3 hours of labour, he can produce 1 t-shirt. 1. The pice of wage per hour is given by w=$10 and the price of each kg of wool is given by r=$4. What is the L(q) and K(q)?