2. Please go as much as you can to characterize the balanced growth path for the followingeconomy: We introduce leisure into an otherwise standard neoclassical growth framework.Utility function becomes:u(e(t), (1)) = 0)!- –1,(1-((1))1-0where 1-1(t) denotes leisure time and (t) is the time devoted to production. Productionfunction for output is:Y(1) = AK(1)" ((1)L(1))!-awhere we also assume population growth rate is n.

A balanced growth path is a steady state in which all economic variables grow at the same constant…

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: c(t)1--1 1-0 u(c(t), l(t)) = ¹(1-((t)) where 1-1(t) denotes leisure time and ((t) is the time devoted to production. Production function for output is: Y(t) = AK(t)" (((t) L(t))¹-a where we also assume population growth rate is n.

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: c(t)1--1 1-0 u(c(t), l(t)) = ¹(1-((t)) where 1-1(t) denotes leisure time and ((t) is the time devoted to production. Production function for output is: Y(t) = AK(t)" (((t) L(t))¹-a where we also assume population growth rate is n.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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: c(t)!-0 1– 0 1 (1 – l(t)) u(c(t), 1(t)) = where 1-1(t) denotes leisure time and l(t) is the time devoted to production. Production function for output is: Y (t) = AK(t)"(e(t)L(t))'-a where we also assume population growth rate is n.
Consider an economy with a Cobb-Douglas production function with α = 1/3 that begins in steady state with a growth rate of technological progress of g of 2 percent. Consider what happens when g increases to 3 percent. (a) What is the growth rate of output per worker before the change? What happens to this growth rate in the long run? (b) Perform a growth accounting exercise for the economy, decomposing the growth rate in output per capita into components contributed by capital per capita growth and technology growth. What is the contribution of the change in g to output per capita growth according to this formula? (c) In what sense is the growth accounting result in part b producing a misleading picture of this experiment? Explain why this is the case.
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.
1. Consider a Cobb-Douglas production function that features capital-augmenting technology: Y(t) = [A(t) K(t)]aL(t)¹-a. Assume that technology A(t) grows at rate u: A(t) = μA(t). Show that the economy converges to a balanced growth path, and find the growth rates of Y and K on the balanced growth path. 2. Let the production function be Y(t) = J(t)aL(t)1-a, where J(t) is the effective capital stock. The dynamics of J(t) are given by j (t) = sA(t)Y (t) — 8(t). The presence of the A(t) term in this expression means that the productivity of investment at t depends on the technology at t. Show that the economy converges to a balanced growth path. What are the growth rates of Y and J on the balanced growth path? dy* S as y* 3. Find the elasticity of output on the balanced growth path with respect to s: Consider a Solow economy that is on its balanced growth path. Assume for simplicity that there is no technological progress. Now suppose that the rate of population growth falls. 1. What…
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.
7. 1. Consider a neoclassical growth economy described by the following.•Yt = K0.3t ·L0.7t (aggregate production function)•s = 0.35 (saving rate)•δ = 0.10 (depreciation rate)•n = 0.01 (population growth rate)•L1 = 120 (initial population)•K1 = 160 (initial capital stock)•g = 0 (technological growth rate)Compute K, Y , k, y, and c for the first three periods. Please report numerical answersto two decimal points. (a) K1 = ; Y1 = ; k1 = ; y1 = ; c1 =(b) K2 = ; Y2 = ; k2 = ; y2 = ; c2 =(c) K3 = ; Y3 = ; k3 = ; y3 = ; c3 =
A CES production function with physical and human capital Consider the CES production function in terms of physical capital, K, and human capital, H: where 0 a. Set up the Hamiltonian and find the first-order conditions. b. What is the optimal relation between K and H? Substitute this relation into the given production function to get a relation between Y and K. What does this “reduced-form” production function look like? c. What is the steady-state value of the ratio of physical to human capital, (K/H)∗? d. Describe the behavior of the economy over time if the initial condition is such that K(0)/H(0)? e. Suppose that the inequality restrictions IK ≥ 0 and IH ≥ 0 apply. How do these constraints affect the dynamics if the economy begins with K(0)/H(0)∗?
Assume the production function takes the general form: Y=Z*F (K,L,A)where all marginal products are positive.Which 3 of the following statements are correct?a. If A is fixed, then population growth acts as a drag on growth of output per person.b. If A is fixed, then population growth acts as a drag on growth, and so Malthus was correct that populationgrowth will always reverse the impact of technological improvements.c. Both rises in z and rises in K/L (capital intensity) will boost output per worker.d. Growth in output per worker can occur due to rises in z (technology) or rises in K/L (capital intensity), orboth.
4. Given the utility function U(C₁, dt+1) = Inc, + Blndt+1 and the production function F(K,L) = K*L¹-* where c, is the consumption of the young and dt+1 is the consumption of the old. The growth rate of population is given as Nt+1 = (1 + n)N₁ The constraints are given as follows: Ct + St = Wt dt+1 = Rt+1. St Find the steady-state values of per capita physical capital, saving and consumption.
4. Consider the following endogenous growth model: a representative household's life-time utility function is given as: pe C(t)!-o – 1 -dt. 1- 0 The production function is: Y (t) = AK(t)ª Hp(t)'-a where Hp(t) denotes human capital used in production. Human capital accumulation equation is: Н() — ВНE() — 6H(), where HE(t) is human capital devoted to education. In total we have HE(t) + Hp(t) H(t). Denote the fraction of human capital allocated to production by ø(t). Please go as far as you can to characterize the balanced growth path of the economy.
Suppose that the production function for an economy is given by Y = K1/4L3/4. The depreciation rate is 4%, the saving rate is 12%, Suppose that now there is labor augmenting technology, the rate of labor-augmenting technological is 2 percent. At what rate does total output, output per worker, and output per effective worker grow?
Suppose the per-worker production function is: y = A(1-ga) Where ga is the fraction of all workers that produce technologies. Further, suppose the growth of technology is given by the following equation growth of A = (ga/m)(L) Suppose L = 1 and m = 7, and that initially ga = 0.7. If g, fell to 0.8 the level of output per worker would: Impossible to say fall stay the same O rise