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(c(t), l(t)) = = c(t)¹-0 – 1 - 1-0 (1 — l(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)ª(l(t)L(t))¹–a where we also assume population growth rate is n.
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- 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.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…Suppose that an economy has the following production function: Y = F(K, LE) = K1/2(LE)!/2 Assume that the rate of depreciation is 5 percent per year (d = .05), the rate of population growth is 3 percent per year (n = .03), the rate of labor efficiency growth is 3 percent per year (g=.03) and the saving rate is 60 percent (s = 0.6). Calculate the per effective worker production function, the steady-state levels of capital per effective worker (k*), output per effective worker (y*), consumption per effective worker (c*), and investment per effective worker (i*) %D %3D
- Consider an economy described by the production function Y=F(K, L)=?^0.4?^0.6 A) What is the per-worker production function?B) Assuming no population growth or technological progress, find the steady-state capital stock per worker, output per worker, and consumption per worker as a function of the saving rate and the depreciation rate.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 =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.
- In the neoclassical growth model, the steady-state capital-labor ratio is determined by the equation (A k=y/(n-d) B k= (n+ d)y C) k= s(n + d) D k= (n + d)/sy E)k=sy/(n + d)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.Consider an economy described by the production function Y=F(K,L)=K^(0.5) L^(0.5). 1. Does this production function have constant returns to scale? 2. What is the per-worker production function, y=f(k)? 3. Assuming no population growth or technological progress, the economy saving rate is 30%, capital depreciation rate is 10%, what are the steady state k, y, c? 4. Now we assume population growth at 5%, and still no technological progress, the economy saving rate is 30%, capital depreciation rate is 10%, what are the steady state k, y, c now? 5. Now we consider technological progress in this production function so we have Y=F(K,LE)=K^(0.5) (LE)^(0.5). Technological progress increases at 5% per year, still we assume population growth at 5%, the economy saving rate is 30%, capital depreciation rate is 10%, what are the steady state k, y, c now? 6. Based on the steady state in question 5, at what rates do total output, output per worker, and output per effective worker grow? 7. Based on…
- According to the neoclassical growth model, the production function of an economy can be represented as Y=f(L,K, A). Which of the following is considered as a decline in technology under this framework? A fall in the capital to labour ratio Depreciation of capital stock A fall in labour to capital ratio. An increase in the number of steps a business must take to obtain government approval to sell a new product Reduction in immigration4. 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.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).