PS 2 with Answers - 1/10 METU Department of Economics Econ...

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Unformatted text preview: 1/10 METU Department of Economics Econ 202 Macroeconomic Theory Spring 2010 Problem Set 2 with Answers Q.1 You are given the following information about the economy of Dollarland. When income is zero, consumption expenditure is $100 billion. The marginal propensity to consume out of income is 0.75. Investment is $500 billion; government purchases of goods and services are $750 billion; a) If taxes are a constant $1000 billion and do not vary as income varies. So T = 1000 i) Write down the consumption function out of disposable income (ܻ ௗ ) and income (Y). C = 100 + 0.75 Y C = 100 + 0.75 ( ࢅ ࢊ + 1000) = 850 + 0.75 ࢅ ࢊ . ii) Write down the saving function out of disposable income (ܻ ௗ ) and income (Y). ࢅ ࢊ = ࡯ + ࡿ => S = – 850 + 0.25Y d S = – 850 + 0.25 (Y – 1000) = – 1100 + 0.25Y iii) Does MPC out of (ܻ ௗ ) and MPS out of (ܻ ௗ ) sum up to 1? Why or why not? Does the same result hold for the MPC and MPS out of Y? Yes, it always has to hold since; disposable income is either consumed or saved. Yes in this case because all taxes are lump-sum. iv) Calculate total autonomous expenditure. A = 100 + 500 + 750 = 1350. v) What would be the autonomous expenditure if 0.75 was MPC out of ܻ ௗ ? A = 100 + 500 + 750 – 0.75*1000 = 600 vi) Calculate the multiplier. 1 / (1 – 0.75) = 1 / 0.25 = 4 vii) Write down the equation that describes the demand for goods (Z). Z = C + I + G = 1350 + 0.75Y viii) Calculate the equilibrium output algebraically and show it graphically. ࢅ ࢋࢗ = 1350 / 0.25 = 5400 b) If, in addition to an autonomous amount of $1000 billion, taxes were to increase by $10 billion when income increased by $100 billion, how would your answers to parts a.i to a.viii change? So T = 1000 + 0.1Y i) C = 100 + 0.75Y (same as in (a.i)) ࢅ ࢊ = ࢅ − ࢀ = ࢅ − ࢀ ૙ + ࢚ࢅ = (૚ − ࢚)ࢅ − ࢀ ૙ => ࢅ = ሾ૚/(૚ − ࢚)ሿሾࢅ ࢊ + ࢀ ૙ ሿ 2/10 ࡯ = ૚૙૙ + ૙. ૠ૞ ൤ ૚ ૚ − ૙. ૚ (ࢅ ࢊ + ૚૙૙૙)൨ = ૢ૜૜ + ૙.ૡ૜ࢅ ࢊ ii) S = – 933 + 0.17Y d S = – 933 + 0.17 ((1 – 0.1) Y – 1000) = – 1103 + 0.153Y. iii) Again MPC (out of ࢅ ࢊ ) + MPS (out of ࢅ ࢊ ) = 1. But since here we also have induced taxes MPC (out of Y) + MPS (out of Y) ≠ 1, but MPC (out of Y) + MPS (out of Y) + marginal tax rate = 1 (income is either consumed, or saved, or taxed). Answers given to (a.iv) – (a. viii) do not change here because, neither the C function (out of Y) nor G, nor I have changed. Q.2 Suppose in a hypothetical economy with no government, the consumption function is given by ܥ = 250 + 0.6 ܻ ௗ , while investment is given by I = 150. a) What is the equilibrium level of income in this case?...
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This note was uploaded on 03/22/2012 for the course ECON 202 taught by Professor Tunc during the Spring '10 term at Middle East Technical University.

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PS 2 with Answers - 1/10 METU Department of Economics Econ...

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