! plz solved all parts ...i'll give you multiple votes Question 1: Neoclassical Growth with Endogenous Labor SupplyConsider a neoclassical growth model augmented with labor supply decisions. In particular,total population is normalized to 1, and all households have utilityU =e u(c(t), 1 – 1(t))dt,where 1(t) e (0, 1) is labor supply. In a symmetric equilibrium, employment L(t) is equalto l(t). Assume that the production function is Y (t) = F(K(1), L(t)), which satisfies thestandard properties.(i) Define a competitive equilibrium.(ii) Set up the current-value Hamiltonian that each household solves, taking wages andinterest rates as given, and determine the necessary and sufficient conditions for theallocation of consumption over time and the leisure-labor trade-off.(iii) Set up the current-value Hamiltonian for a planner maximizing the utility of the repre-sentative household, and derive the necessary and sufficient conditions for a solution.(iv) Show that the two problems are equivalent given competitive markets.

Neoclassical growth theory is an economic theory that explains how three driving forces—labor,…

Answered: Question 1: Neoclassical Growth with…

Economics (MindTap Course List)

13th Edition

ISBN:9781337617383

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter8: Aggregate Demand And Aggregate Supply

Section: Chapter Questions

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Consider the production function modelled by the following equation: Y₁ = AK₁-α(BH₂)ªL₹ where Kt is capital, Ht is human capital, Lt is the number of workers, B is a scalar larger than 0, A is the (constant) level of technology, 0 < a <1 and 0 <ɛ<1. a) Does this production function satisfy all the neoclassical properties? Discuss the meaning of each property intuitively and mathematically. t Imagine that parents invest in the human capital of their children up to the point where the marginal product of physical capital, Kt, is equal to the marginal product of human capital, Ht. b) What is the relation between Kt and Ht? Use this relation to write down total output as a function of Kt only. Q3(b) in order to make output a function of K alone, after establishing that H and K are proportional, should we also establish H=h*L to remove L from the equation? Or are we treating L and H as independent variables like we did for the previous PSET and question 3(a) above.
Consider the following production function: Y; = AKEH?-"L || where Kris capital, Ht is human capital, Leis the amount of workers and A is the (constant) level of technology. (i) Does this production function satisfy all the neoclassical properties. Discuss the meaning of each property INTUITIVELY.
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?
Consider the simple (one period) production model. The production function is Cobb Douglas, exhibits constant returns to scale, and the exponent on capital equal to 0.25.
b) have a Cobb-Douglas production function where a = 0.2, L = 400, and labor income + capital income = $2,000, what is the price of the output given the neoclassical theory of distribution holds? Using the model for a closed economy, if the nominal wage is $40 and we %3D
Assume that digital revolution popularizes the use of artificial intelligence (computers) in the workplace. The production function becomes: Y = 0.25 K(2/5)(ACN)(3/5) where C stands for the number of computers.: a) Use growth accounting to predict the increase in total output in response to an increase in the number of computers by 10 percent. b) The nominal interest rate on government bonds equals 9 percent and inflation equals percent. The rate of GDP growth is equal to the result obtained in (a). Use the debt dynamics equation and graph to explain whether or not the level of public debt in percent of GDP can be stabilized if the government runs a primary deficit. c) Use the neoclassical investment model (equation and graphs) to assess the impact of a decrease in the number of computers on investment (in traditional physical capital K).
* 5. The labor market model (I): Suppose the following equations characterize supply and demand in the labor market model: labor supply: L³ = 2 × w + 30 labor demand: Lª = 60 – w Equilibrium occurs at an employment level L* and a wage w*, so that the labor market clears. That is, supply is equal to demand: L'= Lª (a) What are the endogenous variables in the labor market model? (b) Solve for the equilibrium values of these endogenous variables.
The production function for an economy can be expressed as Y= F(K,L), where Y is real GDP, K is the quantity of capital in the economy, and L is the quantity of labor in the economy. If Y = K0.5 L0.5, what is real GDP if the quantity of capital is 900 and the quantity of labor is а. 400? b. What is/are the endogenous variable(s) in this model? What is/are the exogenous variable(s) in this model? с.
Consider an economy in which production is characterized by the neoclassical productionfunction:Y = K0.5N0.5Suppose that it has a saving rate (s) of 0.1, a population growth rate (n) of 0.02, and an average depreciationrate (d) of 0.03.a) Write this production function in per capita form, and find the steady-state values of per capitacapital k and per capita output y.b) At the steady-state value of k, is there more or less capital than at the golden-rule level?c) Determine what saving rate would yield the golden-rule level of capital in this model.
Preference Shocks and Production Shocks. Suppose that firms and consumers co-exist in the static (one-period) consumption-leisure model. The representative firm uses only labor to produce its output good, which the representative consumer uses for consumption. Suppose the production function is linear in labor, so that output of the firm is given by A. n, where A is a production function shock (aka, exogenous total factor productivity). Suppose there are no taxes of any kind, and the consumer's utility function is given by u(Bc, I) (the function u satisfies all the usual properties we assume for utility functions), with the exogenous parameter B denoting a preference shifter. Finally, the real wage is given by w = A. A. Briefly explain why the real wage is given by w = A. For each of the following three questions, clearly sketch your diagrams on ONE SINGLE graph with consumption on the vertical axis and leisure on the horizontal axis. B. Suppose currently A= A and B = Bo (that is, A…
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