2. Consider a Keynesian IS-LM model for national income: Y=C(Y-T) + I (r) + G L(r,Y)= M³ IS: LM: where we consider Y and r as the endogenous variables and G, M³, and T as the exogenous variables. (b) Find the effect of a lump-sum tax, T, change on r, i.e., dr/T, using the implicit function theorem.
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- Consider the Aggregate expenditure model. Where:AD = C + I + G + NX (1)where I, G, and NX are all autonomous.C = C + c∗(Y + T R − T A)(2)where T A = tY with t ∈ [0, 1] is the proportional tax rate and c∗ ∈ (0, 1) is themarginal propensity to consume.a. Using the information above, solve for AD. Combineall the autonomous terms into one term, A. b. In an (x, y) plane, where Y is on the horizontal axis and AD is on thevertical axis, illustrate the AD curve you derived above along with the 450line.Make sure to explain how you got the Y-intercept and solve for the slope c. Provide an economic interpretation for the slope of the AD function. d. Solve for the equilibrium level of output and show what happens to outputwhen G increases by 1 unit. That is, what is ∆Y ? Show your result graphicallyand explain how the AD curves shifts and by how much. Briefly explain.The chart below gives the data necessary to make a Keynesian cross diagram. Assume that the tax rate is 0.4 of national income, the MPC out of after-tax income is 0.9, investment is 58, government spending is 60, exports are 40, and imports are 0.1 of after-tax income. Alt Text: This chart contains the following columns: National Income, After-tax income, Consumption, I+G+X, Minus Imports, and Aggregate Expenditures. The National Income Column contains the following values for each of the following rows: 100, 200, 300, 400, 500, and 600. The only other value provided is the consumption, 104, for national income, 100. What is the equilibrium level of national income for this economy? A) Y=200 B) Y=400 C) Y=300 D) Y=500The chart below gives the data necessary to make a Keynesian cross diagram. Assume that the tax rate is 0.4 of national income, the MPC out of after-tax income is 0.9, investment is 58, government spending is 60, exports are 40, and imports are 0.1 of after-tax income. Alt Text: This chart contains the following columns: National Income, After-tax income, Consumption, I+G+X, Minus Imports, and Aggregate Expenditures. The National Income Column contains the following values for each of the following rows: 100, 200, 300, 400, 500, and 600. The only other value provided is the consumption, 104, for national income, 100. What does consumption equal when income equals 600? Group of answer choices a. 324 b. 374 c. 540 d. 104
- 10 . In the “complete Keynesian model”, the investment functions was I = I0 - f(i). An analyst now proposes the following investment function: I = I0 - f(i) + qY, where “q” is a parameter and Y is national income = GDP. Provide two different arguments, i.e. explanations as to why this investment function makes sense. The focus is on the new term, qY (q times Y), in the function.Course: Macroeconomic - IS-LM Model PROVE MATHEMATICALLY the following: Given an increase in the proportional tax on income(t), what happens to the level of output and to the tax? Hint: remember Consumption Function (C = A + c Yd), where Yd = Y - tY + TR (t is proportional income tax in %)You are provided with the following information about an imaginary economy called Keynesia: Government expenditure 400 Exports 250 Autonomous imports 50 Autonomous consumption 150 Investment expenditure 300 Full- employment output 1900 Marginal propensity to consume 0.75 Marginal propensity to import 0.15 Tax rate 0.25 Required (I) Derive the IS equation (ii) Derive the savings function (iii) Calculate the equilibrium level of income using the aggregate expenditure approach. (iv) What would the value of income be if the trade balance is zero? (v) What would the value of income be if autonomous consumption increases by 50
- 1. Consider the following simple Keynesian model, (i) Rewrite the model into matrix form with Y, C and I as endogenous variables and Go and i as exogenous variables. (The coefficient matrix must be a 3 by 3 matrix.) Y=C+I+Go C = 200+ 0.8Y I= 1000-2000 (ii) Compute the equilibria Y*, C* and I* as functions of Go and i using Cramer's rule. 8Y* (iii) Find and di ƏY* ƏGo (iv) Give an economic interpretation of national income? ƏY* " ƏGo what should the government do if it wants to raise) Given the following simple Keynesian Model: Y = C + I + G + X-M, where Consumption schedule is given as C= 100 +0.75Y Investment (I) = 50 Government (G) = 100 and Net Export (X-M) = 20 i. Calculate the Equlibrium Level of Income ii. Calculate the size of Consumption at the Equilibrium Level iii. Calculate the value of the Government Multiplier iv. Assume Investment (I) changes by 50; calculate the new equilibrium level of IncomeThe Simple Keynesian Model (i.e., the income-expenditure model). Assume: C = 150 + 0.9 DI I = 50 DI = C + I in equilibrium for a 2-sector model (Note: DI = C in a 1-sector model) Define the term, consumption. What is the value of “autonomous” consumption (also called “a” or the vertical intercept)? What is the value of the slope (also referred to as “b”) of the consumption function? There’s another name for the slope of the consumption function. What is it? What is the value of DI when the model is in equilibrium? What is the value of the “oversimplified” expenditure multiplier? If full-employment means that DI = $5000, then how much should autonomous consumption (or autonomous investment) increase to achieve full-employment? (Hint: Use the multiplier process formula.) Draw a graph of this 2-sector model. Indicate equilibrium DI, full-employment DI, as well as…
- Question 1Explain fully how the equilibrium output, income, and employment are determined in the Keynesian model. Illustrate with an appropriate graph. Suppose that the equilibrium GDP is $500 billion and the full employment GDP is $600 billion. If the slope of the AE curve is 0.8, how much would the government have to change its expenditure to get the economy to full employment equilibrium? Illustrate your answer with an appropriate graph, and show the numerical values in your graph. Explain your understanding of the multiplier process used in answering part B.The simple (fixed r, fixed P, fixed W) Keynesian model C=300+0.75 YD I=310 =300+0.75(Y-T) G=160 T=200 C: consumption function YD: disposable income I: investment. G: government spending T: Taxes. What is equilibrium income ($output),Ye? a) 1,227 b) 9,200 c) 2,080 d) 3,680 e) none of the aboveSuppose a closed economy with no government spending which in equilibrium is producing an output and income of 2250. Suppose also that the marginal propensity to consume is 0.80, and that, if at full employment, the economy would produce an output and income of 3850 By how much would the government need to cut taxes (T) to bring the economy to full employment? (round your answer to the nearest whole value)