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 constraintC=w(h-1) +- Twhere 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.(d) Set up the Lagrangian, solve the consumer's optimization problem and derive thelabour supply curve.

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

5. Consider a one-period closed economy model with government. The aggre- gate production is given by Y = 2N where N represents the employment and z is the total factor productivity. The consumer's preferences are given by U (C, 1) = ln (C) + In (1) subject to the following budget constraint C=w(hl) +-T where 7 denotes profits. The consumer has h units of time to split between labour supply and leisure. The government spending is denoted by G and lump-sum taxes are denoted by T. The government's budget constraint is G = T. (d) Set up the Lagrangian, solve the consumer's optimization problem and derive the labour supply curve.

5. Consider a one-period closed economy model with government. The aggre- gate production is given by Y = 2N where N represents the employment and z is the total factor productivity. The consumer's preferences are given by U (C, 1) = ln (C) + In (1) subject to the following budget constraint C=w(hl) +-T where 7 denotes profits. The consumer has h units of time to split between labour supply and leisure. The government spending is denoted by G and lump-sum taxes are denoted by T. The government's budget constraint is G = T. (d) Set up the Lagrangian, solve the consumer's optimization problem and derive the labour supply curve.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter17: Capital And Time

Section: Chapter Questions

Problem 17.2P

See similar textbooks

Similar questions

Consider the following model of a competitive labour market where both firms and workers have perfect foresight and symmetric information about the price level (that is, no misperceptions). Firms' technology is given by the production function y = a N ½ (production function) where a is a positive constant representing total productivity, N is employment and the elasticity of production to employed labour is 1/2. The government requires firms to pay pension contributions to the fiscal authority: the contribution is a small fraction x of the wage paid to each employed worker. Therefore, firms profits equal P y - W N - x W N and they are maximized taking the price level P, the nominal wage W, and the pension contribution rate x as given. Labour supply is given by: W = P b N where b is a positive constant. Answer all the following questions. a) Derive the labour demand schedule by solving the profit maximization problem of firms.
State the assumptions of the 4th generation Keynesian model and explain how its endogenous variables are determined graphically Graphically demonstrate how to construct an IS(LM) curve. State the product market equilibrium condition, define an IS curve and explain why it is downward sloping.
Using the one factor Ricardian model concept and the unit labor requirements information in the table below, determine a) What is the opportunity cost of domestic and foreign Cheese production?b) What is the opportunity cost of domestic and foreign wine production?c) In which commodity production, domestic has a comparative advantage.Explain.d) In what commodity production, foreign has a comparative advantage.Explain.e) Which country has an absolute advantage. Explainf) If PC is the price of Cheese and PW is the price of Wine, and PC = PW, thenWhat commodities will domestic specialize in?g) If PC is the price of Cheese and PW is the price of Wine, and PC = PW, thenwhat commodities will foreign specialize in?h) Using the comparative advantage information above, determine the commodity thatexported and imported by domestic and foreign respectively?i) If PC = PW or PC/PW = 1, what is the gain from trade obtaineddomestic and foreign if each country specializes inwhich production has a…
Consider a competitive, closed economy with a Cobb-Douglas production function with parameter α = 0.25. The parameter A is equal to 60. Assume also that capital is 100, labor is 100. Assume that in this economy consumption (C) is given by the equation C = 600 + 0.6(Y – T). Investment (I) is given by the equation I = 2,000 – 100r, where r is the real rate of interest in percent. Taxes (T) are 500 and government spending (G) is also 500. (Hint: use the GDP obtained in part a). What are the equilibrium values of C, I, and r? What are the values of private saving, public saving, and national saving?
Consider again the canonical OLG model with log preferences and a Cobb-Douglas production function, but assume that individuals now work in both periods of their lives. (a) Define a competitive equilibrium and the steady-state equilibrium. (b) Characterize the steady-state equilibrium and the transitional dynamics in this economy. (c) Can this economy generate overaccumulation?
The assumption of the Baumol model implies that production in the public sector exhibits constant returns to scale. True or false, and explain
(Production function) A technological breakthrough raises a country’s A ̄ by 10%, but capital and labor are all unchanged. Assuming the country’s production function is given by Y = A ̄K1/2L1/2.(a) Figure out what impact this breakthrough will have on the MPK and MPL in that country. (b) Draw a picture Y of against K holding L fixed. 1 (c) Redraw the picture with A ̄ increased to 1.1A ̄ but L fixed at same level as before. (Production function) For the production function Y = K1/3L2/3 (a) find the function for output per capita (b) What is the growth rate of per capita for this function in terms of the growth rate of K, gK, and the growth rate of L, n.
Given a closed economy where there is no public sector. Production in the economy can be described with the following production function: Y = F (K, AL) = Kα(AL)1−α where Y is the productive capacity of the economy, K is the capital stock, L is the labor force, and A is knowledge. Think of AL as a single factor of production where knowledge and the amount of labor are multiplied together. Let's call the multiplier (ie AL) the efficiency of labor. Given that A = 1.5 and saving is a fixed rate of the production, or s = 33%. The capital stock shrinks by 3% per year, while the population grows is nobody Finally, α = 0.4. Answer the following questions based on the above criteria. (a) Show mathematically that the marginal productivity of labor and capital is positive but diminishing. Explain in words and with a picture what the term positive but diminishing marginal productivity means. (b) Show mathematically that saving and investment are equivalent in a closed economy (c) Show…
The primary goal of effective macroeconomic policies is to reduce uncertainty and risk in economic decision-making and maintain healthy levels of economic growth and minimize price changes. What would be the response by the government for the following events and why? b) The labour market is expected to remain pressured in the near term on the back of surging COVID-19 cases and the reimposition of nationwide Movement Control Order (MCO 3.0).
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
Assume that an economy's production function is Y=1,000L1/2,so that when the marginal product of capital is equated to the real wage the labor demand curve is L = 250,000(P/W)2. The labor supply curve is L = 31,250(W/P). The real wage that solves these equations is W/P = 2. Assume that the expected price level is 10, so that a nominal wage contract setting the wage at 20 is agreed to, making the expected real wage 2. If the price level turns out to be 10, 62,500 workers will be hired and output will be 250,000. If the actual price level turns out to be 20, what will the actual real wage be?b. According to the labor demand curve, how much labor will be demanded if the actual real wage is at the level given in part a?c. According to the production function, if the amount of labor given in part b is actually hired, how much will production be?
– Consider the following one-period model. Assume that the consumption good is produced by a linear technology: Y = zN D where Y is the output of the consumption good, z is the exogenous total factor productivity, N D is the labour hours. Government has to finance its expenditures, G, using a tax on the representative firm. The government collects t units of consumption goods from the firm for each unit of labor it employs (0 < t < 1). There is no other tax in the economy. The firm is owned by the representative consumer who is endowed with h hours of time she can allocate between work, NS and leisure, l. Preferences of the representative consumer are: U(c, l) = ln c + ln l (1) ) Solve for the leisure, l, the consumption, c, employment, N, wage rate, w, tax rate, τ , and output, Y in equilibrium.