1. Consider the following static model. The consumer has preferences such that he always sets his consumption equal to è, where è is exogenously fixed. The consumer has h units of time that he can allocate between working hours (NS) and leisure (1). The wage per hour is w. The representative firm has a technology for producing consumption goods, given by y=zNd where z is the total factor productivity and Nd is the labor input. Denote the profit of the firm as 7. The firm belongs to the representative consumer. The government imposes proportional tax 7 (set exogenously) on the labor income of the representative consumer. The government spends the tax revenue to give lump-sum subsidy B to the representative consumer. 1). Write down the consumer's budget constraint. 2). Solve consumer's optimization problem. 3). Write down the firm's optimization problem and find î and w.

1. Consider the following static model. The consumer has preferences such that he always sets his consumption equal to è, where è is exogenously fixed. The consumer has h units of time that he can allocate between working hours (NS) and leisure (1). The wage per hour is w. The representative firm has a technology for producing consumption goods, given by y=zNd where z is the total factor productivity and Nd is the labor input. Denote the profit of the firm as 7. The firm belongs to the representative consumer. The government imposes proportional tax 7 (set exogenously) on the labor income of the representative consumer. The government spends the tax revenue to give lump-sum subsidy B to the representative consumer. 1). Write down the consumer's budget constraint. 2). Solve consumer's optimization problem. 3). Write down the firm's optimization problem and find î and w.

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

show all working.
A Firm's Optimization with CES Production Function The Constant Elasticity of Substitution (CES) production function is a flexible way to describe how a firm combines capital and labor to produce output, allowing for different levels of substitutability between the two inputs. The elasticity of substitution, denoted by σ, measures how easily the firm can substitute capital for labor (or vice versa) while maintaining the same output level. The parameter p is related to the elasticity of substitution by the formula σ = 1/(1 - p). Now, let's consider a firm that operates for two periods (t and t + 1) and produces output according to the CES production function: F(Kt, Nt) = [aK{ + (1 − a)N]¹º 0
Consider the Diamond model with logarithmic utility and Cobb Douglas production.Describe how each of the following affects K t+1 as a function of K t(a) A rise in n.(b) A downward shift of the production function (that is, f (k) takes the form Bk α , and B falls).(c) A rise in α.
Assume a firm is trying to maximize output subject to a budget and is currently in the long run equilibrium shown below. Make changes to the graph to show the impact of a decrease in the wage. Make sure that the graph shows the new output-maximizing combination as well as the new levels labor and capital.
Please get correct, means a lot. Super important.
Suppose we have one consumer with a Cobb Douglas utility function for consumption, x, and leisure, R : u(x, R) = a ln a+(1-a) In R. The consumer is endowed with one unit of labor/leisure and there is one firm with a constant-returns to scale technology: a = aL. Determine r(p, w) and R(p, w).
sitier the production model studied in Chapter 4. Final output in the economy is pro- duced using capital K and labor L. The production function is: Y = ĀK'/³L^/5 Assume that the supply of all inputs are exogenous and equal to L and K. Perfectly compet- itive firms are price-takers and choose how much capital and labor to demand by maximizing profits. Let w and r denote the wage and rental rate of one unit of labor and capital respec- tively. (a) What are the 5 endogenous variables in this model? Also list the exogenous variables and the parameters and provide a brief explanation of each. (b) Show the first order conditions for labor and capital. Explain the intuition for why these conditions are optimal for a firm. Are there diminishing returns to these inputs in this model? ( (c) Show that the solution for output per capita can be written as y = Ak/5. Observed GDP per capita is 3 in this economy. Capital per person is 32. If Ā = 1, what does this model predict for GDP per person?…
Please answer C and D
Production. Assume a production with two variable inputs (L, K). Show graphically the following and explain: (a) fixed-proportions production function (b) inputs are perfect substitutes
5. Suppose the economy consists of a representative agent with the following utility function: P U = Cα ( M )1−α. Labor is supplied exogenously at level L¯. Output is sup- plied by a perfectly competitive representative firm, which has production function Y = Lη . Any profits are remitted to the representative agent. There is a government, which purchases amount G of goods and services. This amount is financed by a lump-sum tax, of level T and seigniorage. Money is the only asset in the economy; initial money holdings are given by M l. Money is supplied exogenously by the government. Assume both prices and wages are flexible. (a) Write down the consumer’s and the firm’s intertemporal maximiza- tion problems. (b) Solve for expressions for aggregate demand and supply (that is, out- put as a function of the price…