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- a. List all the equilibrium conditions of this model and Using the equilibrium conditions listed, write down an expression that describes the evolution of the aggregate capital stock, Kt over time. Briefly explain why this expression is not particularly convenient for our analysis of the model? b.Using your answer to the above question, derive the equation that describes the evo- lution of the the capital stock per effective unit of worker, kt. ' Why is the analysis in terms of the variables per effective unit of worker more useful than the one with the aggregate capital stock? c. Assume that a E (0, 1). Draw a diagram that describes the evolution of kt, and show that there exists a unique steady state, k* > 0. Label properly. Find the expressions for the steady state variables k*, y*, and c* in terms of the parameters of the model. , Now, assume that α = 1. Draw a diagram that describes the evolution of kt, and show that income per worker can grow indefinitely in this case. Label…Consider the following model of an economy operating with fixed wages, prices and interest rates and hasexcess capacity. Adsume all figures are I Zambian kwacha. C=100+0.8yd, T=100+25Y, G=980 and I= 500 Where c is consumption, yd is disposable income, T is taxes net of transformers, G is government spending on goods and services and I is investments. A. Calculate the equilibrium level of national income B. Illustrate your equilibrium in the keyneasian cross diagran C. What is the value of the multiplier D. Is governnent running a surplus or a deficit E. Show the impact of a reduction in government spending by 80 on the equilibrium level of national income F. Illustrate your new equilibrium in the same Keynesian cross diagram as in b.8. Consider the OLG model with capital. Each individual is endowed with y units of the consumption good when young and with nothing when old. Let N be the number of individuals in each generation. Suppose there is one asset available in the economy capital. A unit of capital can be created from a unit of the consumption good in any period t and capital can be created in any amount. One period after it is created, a unit of capital produces X units of the consumption good and then disintegrates. Assume that each initial old can produce Xko units of the consumption good in the first period. Now suppose that an individual's preference is given by U (C₁, C₂) = (C₁) ¹ (C₂) ¹. We focus on stationary allocations. (a) Write down the budget constraints faced by an individual when young and old. Combine the budget constraints to find the lifetime budget constraint for an individual (b) Solve for the optimal allocation of (c, c) for all future generations. What the optimal k* ? Now suppose an…
- 8. Consider the OLG model with capital. Each individual is endowed with y units of the consumption good when young and with nothing when old. Let N be the number of individuals in each generation. Suppose there is one asset available in the economy capital. A unit of capital can be created from a unit of the consumption good in any period t and capital can be created in any amount. One period after it is created, a unit of capital produces X units of the consumption good and then disintegrates. Assume that each initial old can produce Xko units of the consumption good in the first period. Now suppose that an individual's preference is given by U (C₁, C₂) = (C₁) (c₂) } . We focus on stationary allocations. (a) Write down the budget constraints faced by an individual when young and old. Combine the budget constraints to find the lifetime budget constraint for an individual (b) Solve for the optimal allocation of (c₁, c₂) for all future generations. What is the optimal k* ? Now suppose an…8. Consider the OLG model with capital. Each individual is endowed with y units of the consumption good when young and with nothing when old. Let N be the number of individuals in each generation. Suppose there is one asset available in the economy - capital. A unit of capital can be created from a unit of the consumption good in any period t and capital can be created in any amount. One period after it is created, a unit of capital produces X units of the consumption good and then disintegrates. Assume that each initial old can produce Xko units of the consumption good in the first period. Now suppose that an individual's preference is given by U (C₁, C2) = (C₁) 1 (C₂) ¹. We focus on stationary allocations. (a) Write down the budget constraints faced by an individual when young and old. Combine the budget constraints to find the lifetime budget constraint for an individual ) (b) Solve for the optimal allocation of (c, c) for all future generations. What is the optimal k* ? Now suppose…Piketty (2014) argues that a fall in the growth rate of the economy is likely to lead to an increase in the difference between the real interest rate and the growth rate. This problem asks you to investigate this issue in the context of the Ramsey Cass Koopmans model. Specifically, consider a Ramsey Cass Koopmans economy that is on its balanced growth path, and suppose there is a permanent fall in g. (a) How, if at all, does this affect the k = 0 curve? (b) How, if at all, does this affect the c = 0 curve? (c) At the time of the change, does c rise, fall, or stay the same, or is it not possible to tell? (d) At the time of the change, does r - g rise, fall, or stay the same, or is it not possible to tell?
- 2.2 Consider the following functions for a model economy: Consumption: C=C, +c (Y-T) Investment: I-1, +a Y -br Labour Supply: BN - W/P Money Demand: L-L, +kY - hi Production Function: Y AK"N Tax Revenue: T=T, +tY All variables with a subscript 0 denotes the autonomous component, e.g. C, is autonomous consumption. All lower-case letters (except the real interest rate r and the nominal interest rate I) are parameters. Government expenditure (G), the money supply (M), the level of technology (A) and capital stock (K) are all exogenously given. N is the level of labour employed. For this economy, the general price level (P) and the nominal wage rate (W) are fully flexible. The expected inflation is assumed to be zero.16 100% 3 7 4 Consider the economic model: Yt Ct + it Ct myt-1 act-1 where y 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 solution (iii) Find the condition under which the system converges to the steady state (iv) Find the condition under which y will show sinusoidal (cyclical) pattern (This occurs when the roots of the characteristic equation are complex "6²-4ac < 0") ERMT Problem Paper 01 28°C Light rain || || 3 hpAssume a model with no government and no foregin sector If we gave a savings funcyion thatvis defined as s 200+ (0.1)Y and autonomous investment decreases by 50, by how much wikk consumption change?
- able 27-1 Y = C + I + G C = 500 + 0.8(Y − T) I = 300 G = 700 T = 0.25Y Table 27-1 Y = C + I + G C = 500 + 0.8(Y−T) I = 300 G = 700 T = 0.25Y Refer to Table 27-1. What is the level of consumption in this model? a. 2,550 b. 2,950 c. 2,350 d. 2,750 e. 2,150Let's incorporate the labor-leisure trade-off and capital income taxes in the two-period model. Let c₁, c₂ be consumption in two periods, I the number of hours worked, Te, Te the proportional taxes on consumption in 2 periods, s the saving rate, w the wage rate, b pension in the 2nd period, and 7, the tax on savings (capital income tax). The household's maximization problem in this case is: given by maxe₁,e2,8,1-1 log(c₁) + log (1-1)+5log (c₂) such that (1+T₂) C₁+8 = (1-7)wl and (1+T₂)C₂ = [1+r(1-Ts)]s+b, where measures how the household values leisure vis-a-vis consumption. A. Explain in English the meaning of the objective function and the 2 constraints.Let's incorporate the labor-leisure trade-off and capital income taxes in the two-period model. Let c₁, c₂ be consumption in two periods, I the number of hours worked, Te Te the proportional taxes on consumption in 2 periods, s the saving rate, w the wage rate, b pension in the 2nd period, and 7, the tax on savings (capital income tax). The household's maximization problem in this case is: given by maxe₁,e2,8,1-1 log(c₁) + log (1-1)+5log (c₂) such that (1+T₂) C₁+8 = (1-7)wl and (1+T₂)C₂ = [1+r(1-Ts)]s+b, where measures how the household values leisure vis-a-vis consumption.