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- Consider the economic model: Yt = C +i Ct myt-1 act-1 where is GDP, c is consumption, i is investment, m and a are multipliers. (i) Write down a difference equation for y (ii) Find the condition under which the steady state exists, and find the steady state solutionConsider the two-sector macroeconomic model of a fictitious country: dy dt C = 0.5 Y + 540 I = 425 Where C = consumption; I = investment and Y = national income. = 0.034(C+I - 0.6 Y) Determine the following: (a) If Y(0) = 14,000, find an expression for Y (t) by solving the differential equation. (b) Find the time taken for income to fall to 13,000. (c) Is the system stable or unstable? Explain your answer.1- Equilibrium-defining equations in an IS-LM model are presented as follows: Y=C+I+G, C = C₁ + f(Y) = g(r), I = 1o — h(r), G = Go, and Mo = 3Y - i(r) where Co, Io, Go, Mo> 0 are exogenous variables, and f, g, h, i are continuously differentiable wwwwww and strictly increasing functions satisfying: Y = C₁ + f(Y) = g(r*) + Io − h(r) + Go Mo 3Yi(*). = for the unique equilibrium (rª,Y*). You should also assume that f' (Y) = (0, 1) (Why?). Find dr*/d Mo and dy* /d Go, and interpret your results.
- 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?. 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 ? = 255.10.14 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.)
- A closed economy which is shown below, endogenous variables are Y, I, C, i and exogenous variables are Go and Mo and parameters are a,b,t,d,e, k. Y= C+l+G C= a+ b(1-t)Y |= d-ei G= Go Md= Ms Ma= ky-li Ms=Mo Calculate the equlibrium level of I by using inverse matrix rule.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,…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?
- 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.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