]31=JConsider a Solow model in discrete time. The following system of equations fullydescribes the model economy:Ct + It = YtKt+1 = (18)Kt + ItIt = SYtY₁ = AK¤(Z₁N₁){¹-a}Where Ct is consumption in period t, It is investment in period t, Y is output in period t, Ktis capital in period t, N₁ is labour force at time t, Zt is labour augmenting technology attime t, & is the depreciation rate, s is the saving rate; A is total factor productivity in periodt. Assume that Nt+1 (1 + n)Nt and Zt+1 (1+z)Zt, where 0 < n < 1 and 0 < z < 1.Denote kt = Kt/ZtNt the level of capital per efficient labour.A) Derive the expression of the growth rate of capital y = (kt+1 − kt)/kt.B) How does a one-off permanent increase in the saving rate s affect output andconsumption in the steady-state? Explain.C) Derive and explain the intuition behind the steady-state level of capital per efficientworkers in terms of the model parameters. How the level of capital per efficientworker would change following an increase in population growth rate?

Solow growth model is an exogenous growth model. It is a long run model which explains the path of…

Answered: B) How does a one-off permanent…

B) How does a one-off permanent increase in the saving rate s affect output and consumption in the steady-state? Explain.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter5: Business And Economic Forecasting

Section: Chapter Questions

Problem 1.6CE: Estimate the double-log (log linear) time trend model for log cruise ship arrivals against log time....

See similar textbooks

Similar questions

. Consider the macroeconomic model of a two-sector economy (i.e. no government or trade) using standard notation. Assume that the consumption function is linear, i.e. of the form: C = a +bY . It is known that when ? = 110, the value of consumption, C , is equal to 160.8, and that when ? = 170, the value of C is 207.6. (a) Determine the consumption function and derive the savings ( S ) function for the model. What is the marginal propensity to consume? (b) Determine the equilibrium level of national income when planned investment ? = 255.
1
Exercise 3: Population growth and technological progress Consider a version of Solow's Model: Y₁ = AKL₁¹-a sYt = Kt+1 — Kt +6Kt Lt = Lo(1 + n)t 1 a) Rewrite the production function and the equation of capital accummulation using variables normalized by the units of labor, i.e. k = K/L; y = Y/L b) What are the values of k and y in a steady state? What are the growth rates of aggregate output and aggregate consumption? Consider this different version of Solow's Model: 1-a Y₁ = AKtº (E₁L₁) ¹-ª sYt Kt+1 - Kt + 8Kt Lt = Lo(1 + n)t Et = Eo(1+x)t c) Rewrite the production function and the equation of capital accummulation using variables normalized by the units of effective labor, i.e. k = K/(EL); y = Y/(EL). d) What are the values of k and y along a balanced growth path? What is the growth rate of aggregate output and aggregate consumption along this BGP?
10.14 Total economic output in three years. The n - vector xt denotes the economic output of a country in n different sectors, in yeart. An economist models the economic output using a linear dynamical system model xt+1 = Axt, where A is an n \times n matrix. Assuming her model is correct, find an expression for the total economic output in yeart + 3, in terms of xt and A. (The total economic output is the sum of the economic output in the n sectors.)
In 1928, Charles Cobb and Paul Douglas published a study in which they modeled the growth of the US economy during the period 1899 to 1922. The function used to model production was of the form: (1) P(L, K) = 6LªK!-a where P is total production (monetary value of goods produced in the year); L, the amount of work (total number of person-hours worked in a year); and K, the amount of capital invested (monetary value of machinery, equipment and buildings). In these terms, the hypotheses made by Cobb and Douglas can be stated as follows: (i) If either labor or capital cancel each other out, so does production. (ii) The marginal productivity of labor is proportional to the amount of output per unit of work. (iii) The marginal productivity of capital is proportional to the amount of production per unit of сapital. 1. The output per unit of work is (a) Tick the alternative that, for some constant a, describes the hypothesis (ii) = aP·L. = a. P () aL L P = a. (b) If we keep K constant, K = K0,…
Solow model. One economy evolves as in the baseline Solow model. The production function is Cobb-Douglas with a = 0.5. The number of workers is constant at N = 100 million. The saving rate is 22% of income and the stock of capital depreciates a 5% every year. In the current year t, there are Kt = 625 million units of installed capital. Write down the dynamic equation for capital accumulation and find the change in capital per worker from year t to year t + Report the rates of growth of capital per worker, output per worker and consumption per worker from year t to year t + 1. Find the amounts for capital per worker, output per worker, and consumption per worker in steady state. Make a graphical representation of the accumulation of capital per worker in year t and discuss the future evolution to reach the steady state (long-run) Calculate the golden-rule level of capital per worker for this economy and report the gain of consumption per worker obtained relative to the value in…
See Figure 2.2 and examine the model. Unlike other circular flow models, this model is missing another sector/s. what is the missing sector?
The equation S = I + NCO describes the savings market for an entire national economy engaged in foreign trade. Between the variables I and NCO, which represents the amount of national savings utilized in the domestic economy and in foreign markets? How do you know?
Between Foreign Direct Investment (net inflows %) and Real GDP Growth ( %): A. Identify the independent and dependent variable and explain Between Foreign Direct investment (net inflows %) and Real GDP per capita (constant %) a. Identify the independent and dependent variable and explain
Suppose the macroeconomic parameters are as follows in Turkey. Production: Y = A K1/3 L2/3 (A= 7 ) Factor supplies: K, L (K = 3000, and L= 1300) Government: 2200, Taxes: 2000 Consumer behavior C = 1000 + 0.6 (Y-T Investment behavior | = 3000 - 1000г Compute real interest rate in Turkey (Show the percentage value as numerical such as 15 for %15 or 0.15).
Suppose that the economy is summarized by the following: Technology (Production Function): Yt = 10 (Kt)0.3 (Lte)0.7 Consumption function: Ct = 0.8Yt Depreciation rate: 8% (i.e. δ= 0.08) Population growth: 2% (i.e. n = 0.02) Technological growth: 4% (i.e. g = 0.04) 1. Assuming that in 2013 the US economy is in the steady state and L2013 = Le2013 = 8, what is the value of ke2014, ye2014, ce2014 , k2014, y2014, and c2014 ?
where The total fresh vegetables consumed per person per year can be modeled by V(t) = 0.5(t-4)²-3 V(t) is the total fresh vegetables consumed per person in pounds per year t years since 1999. In 2009, what is the total fresh vegetables consumed per person will be? {final answer will be number only}.