! 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…

ENGR.ECONOMIC ANALYSIS

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Author:NEWNAN

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Suppose that output is given by the neoclassical production function Y (t) = F (K(t), L(t), A(t)) satisfying Assumptions 1 and 2, and that we observe output, capital, and labor at two dates t and t + T . Suppose that we estimate TFP growth between these two dates using the equation Where g(t, t + T ) denotes output growth between dates t and t + T , and other growth terms are defined similarly, while αK(t) and αL(t) denote the factor shares at the beginning date. Let x(t, t + T ) be the true TFP growth between these two dates. Show that there exist functions F such that x(t, t ˆ + T )/x(t, t + T ) can be arbitrarily large or small. Next show the same result when the TFP estimate is constructed using the end-date factor shares: Explain the importance of differences in factor proportions (capital-labor ratio) between the beginning and end dates in these results.
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) (a) Write down the definition of a competitive equilibrium for the above economy. (b) Show that the Walras’ law holds for this economy. (c) Solve for the leisure, l, the consumption, c, employment, N, wage rate, w, tax rate, τ , and output, Y in equilibrium. (d) Solve for the optimal allocation of leisure,…
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 the following one-period model. Assume that the consumption good is produced by a linear technology: Y = zND where Y is the output of the con- sumption good, z is the exogenous total factor productivity, ND is the labour hours. Government has to finance its expenditures, G, using a lump-sum tax, T, on the rep- resentative consumer. 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) = α ln c + (1 − α) ln l (1) where 0 < α < 1 is a parameter. Answers for part b below: A consumer's choice of optimizing its consumption and labor hours (h - l ) is given by the point where , MRS(c , l) = wage rate Now , MRS (c, l) = MU(c) /MU(l) MU(c) = dU/d c = a/c MU(l) = dU /dl = (1-a )/l MRS = a (l)1−a (c)a (l)1-a (c) Putting this in optimal condition we have : a (l)(1−a) (c)a (l)(1-a) (c) = w --- (i) l = w…
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?
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.
Problem 4 Consider the following production function: Y, = AKÇH!-"L where Kr is capital, H;is human capital, Leis the amount of workers and A is the (constant) level of technology. • (1) Does this production function satisfy all the neoclassical properties. Discuss the meaning of each property INTUITIVELY. Imagine that parents invest in the human capital of their children up to the point where the MARGINAL PRODUCT OF PHYSICAL CAPITAL, K, is equal to the MARGINAL PRODUCT OF HUMAN CAPITAL, H:. 2 • (ii) What is the relation between K:and H:? Use this relation to write down total output as a function of Kronly. Imagine that the number of people in this economy, Nr, is different from the number of workers because some people do not work. Let l =4 be the number of workers per capita (the fraction of the population that works). Let y; ミ be output per capita and be capital per capita. Finally, let n be the rate of population growth and y, be the growth rate of labor. (ii) Using the "effective…
Problem 4 Consider the following production function: Y, = AKÇH!-"L where Kr is capital, H;is human capital, Leis the amount of workers and A is the (constant) level of technology. • (1) Does this production function satisfy all the neoclassical properties. Discuss the meaning of each property INTUITIVELY. Imagine that parents invest in the human capital of their children up to the point where the MARGINAL PRODUCT OF PHYSICAL CAPITAL, K, is equal to the MARGINAL PRODUCT OF HUMAN CAPITAL, H:. 2 • (ii) What is the relation between K:and H:? Use this relation to write down total output as a function of Kronly. Imagine that the number of people in this economy, Nr, is different from the number of workers because some people do not work. Let l =4 be the number of workers per capita (the fraction of the population that works). Let y; be output per capita and Kt be capital per capita. Finally, let n be the rate of population growth and y, be the growth rate of labor. (iii) Using the…
2. Please go as much as you can to characterize the balanced growth path for the following economy: We introduce leisure into an otherwise standard neoclassical growth framework. Utility function becomes: u(e(t), (1)) = 0)!- –1, (1-((1)) 1-0 where 1-1(t) denotes leisure time and (t) is the time devoted to production. Production function for output is: Y(1) = AK(1)" ((1)L(1))!-a where we also assume population growth rate is n.
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.

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