3. Suppose that the production function of an economy is given by Y = √N. The (representative) firm hires workers (N) at a wage rate w. Assume that the firm maximizes profits by choosing how much to produce and how many workers (hours) to hire. (Remember that the profit function is Y - WN.) The representative consumer has preferences given by the utility function U(-) = log (c) + log (1), with a marginal rate of substitution given by c/l, where c is consumption and / is the leisure time. The endowment of time of an individual is 24, which has to be allocated between labor and leisure. (Recall that N + 1 = 24.) a. Derive an expression for the labor demand function.

3. Suppose that the production function of an economy is given by Y = √N. The (representative) firm hires workers (N) at a wage rate w. Assume that the firm maximizes profits by choosing how much to produce and how many workers (hours) to hire. (Remember that the profit function is Y - WN.) The representative consumer has preferences given by the utility function U(-) = log (c) + log (1), with a marginal rate of substitution given by c/l, where c is consumption and / is the leisure time. The endowment of time of an individual is 24, which has to be allocated between labor and leisure. (Recall that N + 1 = 24.) a. Derive an expression for the labor demand function.

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

Suppose you have the following indirect utility function: V(Pa, Py, I) = In PxPy What are marshallian demands for x and y? I (a) (9x9y) = (22) (b) (9,9y) = (In, In 2) (c) (9, 9y) = (exp(2p/py), exp(2ppy)) I (d) (9x, gy) = (2pr+py' px+2py) What is the expenditure function for the associated expenditure minimization problem? (a) E(pa, Py, U) = (P + Py) ln(U) (b) E(pa, Py, U) = √exp(U)Papy (c) E(pa, Py, U)= (p²+p²) In(U) (d) E(pa, Py, U) = exp(U)²papy What are the individual's Hicksian demands for goods x and y? (a) (h₂, hy) = ((BU)¹/², (PU) ¹/²) (b) (ha, hy) = (RU, DU) (c) (ha, hy) = ((2 exp(U))¹/², (exp(U))¹/²) -1/2 (d) (hx, hy) = ((P₂PzU)−¹/², (P₂PzU)-¹/2) Are x and y complements or substitutes?
= 5. Consider an economy with a single (representative) agent with utility function u(x, lc) = x¹/514/5 and an endowment of 0 units of x and 10 units of time, which the agent can use as leisure (c) or labor (L) (i.e., L + lc = 10). The agent owns a firm that produces good x using L as an input, with technology of production given by x(L) = 3√L. Let the price of x be p = 1 and let w denote the price of time (i.e., the price of leisure and the wage). Find the competitive price of time w and the competitive allocation.
Clarice has a utility function: U(Y) = 1000 - (100/Y), where Y is her income. clarice has just graduated from college and has a career choice for her first job of either working as a teacher and earning $40,000 or trying to become a theatre lighting director and earning $70,000 (if there is growth in the demand for theatre) or $20,000 (if there isn't growth in the demand for theatre). there is a 50% probability of growth. a consulting firm guarantees Clarice that it already knows whether there will be growth in the demand for theatre next year. what is the maximum amount Clarice should be willing to pay for this information?
Consider an economy with 2 consumption goods and N consumers, all with the same utility function: 1-a u(x1, x2) = xĩxa, where and E (0, 1) . The goods prices are pi income y1 and the rest have income y2. 2 and p2. Among the consumers, half of them each have (a) Each firm has the cost function c(q) = Bq². Solve for the equilibrium price P2. ' There are n firms operating in the competitive market for good 2.
Suppose the supply function for product X is given by Qxs = −30 + 2Px − 4Pz. How much of product X is produced when Px = $600 and Pz = $60? How much of product X is produced when Px = $80 and Pz = $60? Suppose Pz = $60. Determine the supply function and inverse supply function for good X. Graph the inverse supply function.
Imagine the market for Good X has a demand function of Qdx = 200 – 2Px – Py + .1M and a supply function of Qsx = 2Px – 2Pw, where Px is the price of Good X, Py is the price of Good Y, and M is the average consumer income. Pw is the price of Good W, which is an input to the production of Good X. If Py = 10, Pw = 50, M = $2700, what's the price of X in equilibrium?
John works in a shoe factory. He can work as many hours per day as he wishes at a wage rate w. Let C be the amount of dollars he spends on consumer goods and R. be the number of hours of leisure that he chooses. John's preferences are represented by U(C, R) = CR utility function Question 2 Part a John earns $8 an hour and has 18 hours per day to devote to labor or leisure, and he has $16 of nonlabor income per day. Draw John's indifference curves, budget constraints and solve for his optimal consumption and leisure choices.
For the demand function d(x) and supply function s(x), complete the following. d(x) = 300 - 0.09x², s(x) = 0.03x² (a) Find the market demand (the positive value of x at which the demand function intersects the supply function). X = (b) Find the consumers' surplus at the market demand found in part (a). (c) Find the producers' surplus at the market demand found in part (a). $
5. Consider a two-consumer one-firm economy with a single input good and a single output good. Consumers' utility functions are u4(x4) Suppose that the input good is divisible and that wA = wB = 1/2. Suppose that the output good is indivisible (i.e., that xg, q = 0, 1, 2, ...), and that the firm's production technology is such that it requires 1 unit of input to produce one unit of output. rA + 3r and uB(xB) 4x? + x. (a) Derive the Pareto set of this economy. (b) For all Pareto-efficient allocations from (a), derive a competitive equilibrium for this economy that generates these allocations.
Q1: Suppose Labor and Capital are substitutes and the price of capital falls. All else equal, we should expect the labor select (supply, demand) Curve shift select ( up to the right, down to the left ) and for equilibrium wages to select (rise, fall) Q2: An individual has a utility function over Leisure and Income such that ?=?1/2?1/2 This individual has a budget constraint ?=?⋅(24−?)+? The best possible wage this individual can earn in the labor market is $2 per hour. This individual is $30 in debt (they have negative non-labor income). If this individual is earning a utility level of 4, which of the following are true? Group of answer choices The worker could be supplying 1 unit of Labor The worker could be earning $10 The worker could be supplying 8 units of labor The worker is maximizing their utility given their budget The worker's Marginal Rate of Substitution at the point where the budget constraint intersects the indifference curve is equal to -2
Part A . Consider an economy with the following features. • There are 100 identical consumers that derive utility from consuming three different goods: software, computers, and good m. • Each consumer decision utility function is given by U (c, 8) = 4c¹/48¹/4+m, where e denotes the amount of computers that she consumes, s denotes the amount of software that she consumes, and m denotes the amount of good m that she consumes. cand s must be non-negative, but m can take any real value. • Computers are produced by 20 identical competitive firms with a total cost function given by 10c². • Software is produced by 40 identical competitive firms with a total cost function given by 20s². . QUESTION 1: What are the equilibrium prices for software and comput- ers in equilibrium? Part B • Suppose that there is a positive technology shock in the software industry so that that the new cost function of the software firms becomes 10s². Let C and S denote, respectively, the aggregate level of…
Mia is a registered nurse. She has 18 hours per day to devote to labor or leisure, and has $20 nonlabor income per day. She is paid $10 per hour for the first 8 hours of work and $15 per hour for overtime (for hours worked over 8 hours). Mia's preferences are represented by U(C, R) = CR utility function, where Cis the amount of dollars she spends on consumer goods and R be the number of hours of leisure that she chooses. Question 1 Part a Assuming she can work as many hours per day as she wishes, draw Mia's indif- ference curves, budget constraints and solve for her optimal consumption and leisure choices. Question 1 Part b Suppose that Mia's wage rate rises to $11 an hour for the first 8 hours. She is still paid $15 per hour for overtime. Again, find her optimal choice. Decompose the total change in demand due to a price change into a substitution effect, ordinary income effect and endowment income effect and graphically demonstrate each effect.