25.Consider a one-period closed economy model with government. The aggre-gate production is given byY = 2Nwhere N represents the employment and z is the total factor productivity.The consumer's preferences are given byU (C, 1) = ln (C) + In (1)subject to the following budget constraintwhere denotes profits. The consumer has h units of time to split between laboursupply and leisure. The government spending is denoted by G and lump-sum taxesare denoted by T. The government's budget constraint is G = T.C=w(h-1) +- T(a) Solve the firm's maximization problem and derive the labour demand curve.(b) Graph the labour demand curve and explain its shape.(c) Show that profits are equal to zero, π = 0.(d) Set up the Lagrangian, solve the consumer's optimization problem and derive thelabour supply curve.(e) Graph the labour supply curve and explain its shape using the substitution andincome effect.(f) Solve for the competitive equilibrium and show that the optimal labour is N* =and real wage rate is w* = z.zh22(g) Derive the equilibrium solution for output, Y*, and consumption, C*, in terms ofz, h and G.(h) Suppose that z = 4, h = 24, G = 5. Compute the equilibrium values of N*, w*, Y*, C*, T*.(Hint: You can use the Excel file used in class to verify your answers.)(i) If you use the social planner's problem, would you obtain the same solution?Briefly explain.

Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

(a) Solve the firm's maximization problem and derive the labour demand curve. (b) Graph the labour demand curve and explain its shape. (c) Show that profits are equal to zero, T = 0. (d) Set up the Lagrangian, solve the consumer's optimization problem and derive the labour supply curve. (e) Graph the labour supply curve and explain its shape using the substitution and income effect. (f) Solve for the competitive equilibrium and show that the optimal labour is N* = 2h+G and real wage rate is w* = 2. 2z

(a) Solve the firm's maximization problem and derive the labour demand curve. (b) Graph the labour demand curve and explain its shape. (c) Show that profits are equal to zero, T = 0. (d) Set up the Lagrangian, solve the consumer's optimization problem and derive the labour supply curve. (e) Graph the labour supply curve and explain its shape using the substitution and income effect. (f) Solve for the competitive equilibrium and show that the optimal labour is N* = 2h+G and real wage rate is w* = 2. 2z

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter16: Labor Markets

Section: Chapter Questions

Problem 16.12P

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Please Show Each and Every Working VERY CLEARLY. There are NO multi-questions here, only just multi-PART questions which are CONNECTED to each other, and hence, Please do NOT Leave any, Thank You! marginal propensity