Question 1:Consider a representative agent with a utility function:c¹-o1 11-01U (c, l)=01 - 0that he or she maximises subject to a constraint:c=w (hl) -T+™where w, h, l, c, T, and π are wages and hours of time available, leisure, consumption,taxes, and dividend income. Labour supply is Nº = h – l.a) Write the Lagrangian of the representative agent's optimisation problem.

Consumption – Leisure Model: In this model the household determine how he allocate his time between…

Question 1: Consider a representative agent with a utility function: c¹-01 U (c, l) = 1-o that he or she maximises subject to a constraint: c=w (hl) -T+π where W, h, l, c, T, and í are wages and hours of time available, leisure, consumption, taxes, and dividend income. Labour supply is NS = h – l. a) Write the Lagrangian of the representative agent's optimisation problem. 11-01 1-0

Question 1: Consider a representative agent with a utility function: c¹-01 U (c, l) = 1-o that he or she maximises subject to a constraint: c=w (hl) -T+π where W, h, l, c, T, and í are wages and hours of time available, leisure, consumption, taxes, and dividend income. Labour supply is NS = h – l. a) Write the Lagrangian of the representative agent's optimisation problem. 11-01 1-0

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter16: Labor Markets

Section: Chapter Questions

Problem 16.10P

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Consider the following model of labour supply. There is a representative worker with the following utility function: U(C,L) = C + 3L The budget constraint and time constraint are: C = wh + V h = T – L where w = 1,V = 500,T = 100. The notation is the same as question 1. a) Calculate the optimal leisure and consumption. b) Explain why we usually do not use this type of utility function to model the labour supply.
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This question will analyze the impact on a person's labour supply from a shock to their partner's job. Assume leisure is a normal good. Let's assume Vanessa has a wage rate of $20 per hour. Recently her partner, Bill, had to take a wage cut at work, with his wage falling from $45 per hour to $30 per hour, but allowed them to continue working 40 hours per week. Analyze the decision of the household over choice consumption and Vanessa's leisure, taking Bill's hours as given (constant).
√N. The 3. Suppose that the production function of an economy is given by Y = (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 (l), with a marginal rate of substitution given by c/l, where c is consumption and I 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. b. Derive an expression for the labor supply function. c. Compute the equilibrium wage rate and the equilibrium quantity of labor employed. d. Consider a technical improvement of the production process that determines a new production function Y = 2√N. Compute the new equilibrium quantity of labor and wage rate. e. Draw a…
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