In the real intertemporal model with investment, the government increases spending on roads and bridges expected to be completed in the future. Firms expect that the new roads and bridges will have a permanent impact on total factor productivity. () llustrate the effect(s) in the current period using relevant diagrams from the macroeconomics course. (i) Explain in detail (by making any necessary assumptions), the effects on NS, NO, yS and yD.
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- 3) In the macroeconomic model below, Y is aggregate output, C is aggregate consump- tion, Io is aggregate investment, Go is government spending, T is the total amount of taxes collected by the government, and t is income tax rate. The variables Y, C, and I are endogenous, Go, Io, and t are exogenous, and a, b, and k are parameters. Y=C+ Io + Go C=a+b(Y-T) T=k+tY (a > 0,6€ (0,1)) (k>0, t€ (0,1)) Calculate the determinant of the coefficient matrix A associated with this system of equations. The determinant of the coefficient matrix A is: 1-b.+ bt a) A b) A-1-b-bt + a c) |A|=b+t d) A1+a+b-t e) |A| =Go+b+t f) A-Io-b+t 8) A = Go + Io +b-t3) In the macroeconomic model below, Y is aggregate output, C is aggregate consump- tion, Io is aggregate investment, Go is government spending, T is the total amount of taxes collected by the government, and t is income tax rate. The variables Y, C, and I are endogenous, Go, Io, and t are exogenous, and a, b, and k are parameters. Y = C + Io + Go C = a + b(YT) T=k+tY (a > 0, b = (0, 1)) (k > 0, t = (0, 1)) Calculate the determinant of the coefficient matrix A associated with this system of equations. The determinant of the coefficient matrix A is: a) |A| = 1-b+ bt b) |A| = 1-b-bt + a c) |A| = b + t d) |A| = 1+ a + b - t e) |A| = Go +b+t f) A = Iob+t g) A = Go + Io +b-ta. 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 a dynamic (two-period) macroeconomic model with a representative household, a representative firm, and a government. The representative household makes consumption- saving and labor supply decisions. The representative firm makes labor demand and invest- ment decisions. (a) Clearly write down the representative consumer's problem and the necessary assump- tions. (b) Clearly write down the representative firm's problem and the necessary assumptions. (c) Clearly definite the competitive equilibrium for this economy. (d) Derive (graphically) the output demand curve. State the necessary assumption(s).(ii) What is the relation between Kt and Ht? Use this relation to write down total output as a function of Ktonly. Imagine that the number of people in this economy, Nt, is different from the number of workers because some people do not work. Lt Let lt - be the number of workers per capita (the fraction of the population that works). Let y Nt Yt be output per capita and Nt Kt kt be capital per capita. Finally, let n be the rate of population growth and y, be the growth rate of labor. Nt (iii) Using the "effective production function" you derived in (b), write down output per capita, yt, as a function of capital per capita, kt, labor per capita, lt, the level of population Nt, and the level of technology, A. Following Solow and Swan, assume there is no government and no net exports, that the depreciation rate of capital is the constant 8 > 0 and the savings rate is constant 0 < s < 1. (iv) DERIVE the fundamental equation of Solow-Swan. How does the growth rate of capital depend on…Identify five (5) areas of the economy where the influence of the 4IR was eitherpositive, negative or both. Clearly outline how the advent of the fourth industrialrevolution influenced the identified areas. Give reasons why you think theinfluence was positive, negative or both.
- Consider the intertemporal model of consumption studied in class, with two possible periods. Consider initially that an individual is a borrower. If the interest rate increases: (a)The individual will never become a saver. (b)The individual will always remain a borrower. (c)The individual will be worse off, provided she remains a borrower. (d)The individual can be better off, but only if she becomes a saver. Both c and d.1) In the IS equation why wasnt G in the calculations. 2)Suppose that with all exogenous variables, including T and M at their original values, households become less confident about the future and reduce their autonomous level of consumption from 200 to 150. Solve for the new values of e, Y and NX. With the help of graphs, explain very carefully the mechanisms by which a new equilibrium is reached. 3)Suppose that with all exogenous variables at their original values, the autonomous part of money demand increases to 70. Solve for the new values of e, Y and NX. With the help of graphs, explain very carefully the mechanisms by which a new equilibrium is reached.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…
- 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 the optimal k* ? Now suppose an…(1)The following macroeconomic model describes the economy of Sunderland. 1. Y= C +I + G + NX 2. C = 220 + 0.63 Y 3. 1 = 1000- 2000R 4. G = Go 5. NX = 525-0.10Y-50OR 6. M (0.1583Y-1000R)P (a)ls it a fair characterization to refer to equation #2 as a "simple" consumption function? Explain. (b)Derive the expression for equilibrium real output, Y, for this economy. Note: In your final expression for Y, restrict coefficient values to three decimal points. (c) Suppose government spending is 1200 , money supply by the Central Bank is 900 and the price level is 1, find the value of GDP (Y) and equilibrium interest rate (R) for Sunderland. Income Identity Consumption function Investment function Government Expenditure Net export function Money market equilibrium (2)The questions in this section are related to the macroeconomic model of Sunderland. (a)The expression you are asked to derive in question #1b can be considered an aggregate demand curve. Do you agree? Explain your answer. (b)Sketch…