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AMU ECON 201 - Workbook For Chapter 23
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Workbook For Chapter 23 Of Frank and Bernanke’s Principles of Economics. Part 2 Hints for the Review Questions Question 9 Notice that taxes are not expenditures themselves, but they affect people’s expenditures. Step-by-steps for the Problems Fill in your answers to the selected problems here. Do the rest of the assigned problems on a separate piece of paper. Problem 5 Hints: • Equation 26A.2 tells us that: [ ]XNGITcCcY +++−−=1111 If you know calculus, it’s pretty obvious that [ ]PAEcY ∆−=∆111 If the multiplier is 2.5, all you have to do is to multiply 2.5 times the change in planned autonomous expenditure that you are given in the question. • Notice that Taxes are not expenditure, but yet we are asked to analyze the effect of a change in tax collections. Again, if you know calculus, it’s pretty obvious that TccY ∆−−=∆111 The reason is that higher taxes reduce after-tax income, which in turn reduces consumption (which is a part of expenditure) by the proportion c1. It’s clear that the relation between taxes and expenditure is negative: when one goes up, the other goes down. So while a change in G changes expendituredirectly, a change in T only changes expenditure indirectly, through its effect on after-tax income. • Don’t forget to explain why the multiplier is 2.5 (Hint: from the C function, in problem 2, the mpc is 0.6. See Appendix B.). Problem 6 An economy is initially at full employment, but a decrease in planned investment spending (a component of autonomous expenditure) pushes the economy into recession. Assume that the MPC of this economy is 0.75 and the multiplier is 4. a. To find out how large is the recessionary gap after the fall in planned investment, we could follow two strategies. One, find potential output and actual GDP, and subtract one from the other. We don’t have either number. We don’t have any way to calculate them, either. But we do know that the “economy is initially at full employment.” This means that originally, Y = ___. Investment has changed, but we don’t know by what dollar amount. So let’s call the change in investment ∆I (this is read as “delta I”, and it means the change in I. It’s pretty standard notation). Then we can simply say that ∆Y = ____ ∆I. From this information, how large is the recessionary gap (Y* – Y > 0) after the fall in planned investment? ___________________________________________ . b. By how much would the government have to change its purchases to restore the economy to full employment? The easiest way to understand this question, even if it’s a little round-about, is to go through these tables. Suppose an economy originally looks like this: T C= 100+ 0.75(Y-T) IP G NX Y =(1/(1-0.75))* (C-cT +IP+G+NX) 100 200 200 -50 Calculate Y by noticing that C is the autonomous component of C, that is, the part of consumption that doesn’t change with income. Then calculate C,using the value for Y that you just found. Then check that the numbers add up right so that Y = C+IP+G+NX. Suppose that Investment decreases by 100 (∆I = –100). Fill in the table again: T C= 100+ 0.75(Y-T) IP G NX Y =(1/(1-0.75))* (C-cT +IP+G+NX) 100 100 200 -50 Do the same assuming that it was Government Expenditure that had decreased by 100 (∆G = –100): T C= 100+ 0.75(Y-T) IP G NX Y =(1/(1-0.75))* (C-cT +IP+G+NX) 100 200 100 -50 Finally, suppose that it had been Autonomous Consumption that decreased by 100 (∆C = –100): T C= 0+ 0.75(Y-T) IP G NX Y =(1/(1-0.75))* (C-cT +IP+G+NX) 100 200 200 -50 You should find that decreasing any component of autonomous expenditure by 100 has exactly the same effect on output.1 Formally, mpcNXYGYIYCYP−=∆∆=∆∆=∆∆=∆∆11 (All components of PAE have the same effect on Y). Now, going back to the original question: If IP decreased by ∆I, what would be the change in G necessary to reverse its effect on Y? ____________________ . (Hint: would ∆G have to be smaller than, larger than, or equal to ∆I?) c. Alternatively, what happens if the government changes taxes? To answer this, notice that a change in T has a smaller effect. Suppose that T rises 1 The reason this is true is that C-bar, IP, G, and NX all enter into the PAE function additively (in a linear fashion) and their coefficients are all = 1. Mathematically, T has a different effect because its coefficient is |– mpc| < 1. by 100 (∆T = 100).T C= 100+ 0.75(Y-T) IP G NX Y =(1/(1-0.75))* (C-cT +IP+G+NX) 200 200 200 -50 Remember, first use the reduced-form equation to calculate equilibrium Y and then calculate C. You must do it this way because Y determines C. Again, check that you did this right by making sure Y = C+IP+G+NX. The reason for why the effect of T is less than that of IP or G is that an increase in T reduces consumption (which is a component of autonomous expenditure) by less than the increase in T. Looking at the consumption function, )( TYcCC −+=, we can tell that ._______=−=∆∆mpcTC We also know that =−=∆∆mpcCY11________, which is the multiplier. So the effect of T on Y will be the effect of taxes on consumption expenditure, multiplied by the multiplier =−−=∆∆=∆∆∆∆mpcmpcTYTCCY1___________. So if taxes were to rise by an amount ∆T, consumption expenditure would fall by an amount (–mpc) (∆T), and output would fall by an amount (–mpc)/(1–mpc) (∆T) = ______ (∆T). Now, suppose that both taxes and autonomous PAE changed at the same time, but leaving output unchanged. We know that PAEmpcY ∆−=∆11 And we know that TmpcmpcY ∆−−=∆1 So if we change both, but leave output unchanged,mpcPAETTmpcPAETmpcmpcPAEmpcY∆−=∆∆−=∆∆−−=∆−=∆1110 For concreteness, suppose that ∆PAE = –100. Use the above formula to calculate what ∆T would have to be in order to keep Y unchanged. _________ . Now you can answer the question: IP decreased by ∆I, causing a recessionary gap. Using the above formulad. Given that the mpc is 0.75, calculate , by how much would T have to change to close the recessionary gap? ________________________________________________ . mpcGY−=∆∆11= _____ and −−=∆∆mpcmpcTY1= _____. Suppose we want to keep the budget in balance, so ∆G = ∆T = BB. The total change in PAE


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AMU ECON 201 - Workbook For Chapter 23

Course: Econ 201-
Pages: 14
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