# 1. What is an investment schedule and how does it differ from an investment demand curve? LO1

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1 Chapter 28 The Aggregate Expenditures Model QUESTIONS 1. What is an investment schedule and how does it differ from an investment demand curve? LO1 Answer: An investment schedule shows the level of investment spending for a given level of GDP. An investment demand curve shows how expected rates of profit and real interest rates determine the level of investment spending. In the simple AE model, investment spending is assumed to be independent of the level of real GDP. 2. Why does equilibrium real GDP occur where C + Ig = GDP in a private closed economy? What happens to real GDP when C + Ig exceeds GDP? When C + Ig is less than GDP? What two expenditure components of real GDP are purposely excluded in a private closed economy? LO1 Answer: The reason why equilibrium occurs when real GDP equals C + Ig in a private closed economy is because it is at this level output where production creates total spending just sufficient to purchase that output. So the equilibrium level of GDP is the level at which the total quantity of goods produced (GDP) equals the total quantity of goods purchased (C + I g ). If real GDP (output) exceeds C + I g the economy will accumulate unplanned inventories. If C + I g exceeds real GDP (output) the economy will draw down inventories faster than planned. In a private closed economy net exports (closed) and the government sector (private) are both excluded from the analysis. 3. Why is saving called a leakage? Why is planned investment called an injection? Why must saving equal planned investment at equilibrium GDP in the private closed economy? Are unplanned changes in inventories rising, falling, or constant at equilibrium GDP? Explain. LO2 Answer: Saving is like a leakage from the flow of aggregate consumption expenditures because saving represents income not spent. Planned investment is an injection because it is spending on capital goods that businesses plan to make regardless of their current level of income. If the two are unequal, there will be a discrepancy between spending and production that will result in unplanned inventory changes. Firms, not wanting inventory levels to change, will change production, implying that equilibrium can only occur when the saving leakage equals the injection of investment spending in a private closed economy. At equilibrium GDP there will be no changes in unplanned inventories because expenditures will exactly equal planned output levels which include consumer goods and services and planned investment. Thus there is no unplanned investment including no unplanned inventory changes. 28-1

2 4. Other things equal, what effect will each of the following changes independently have on the equilibrium level of real GDP in the private closed economy? LO3 a. A decline in the real interest rate. b. An overall decrease in the expected rate of return on investment. c. A sizeable, sustained increase in stock prices. Answer: (a) This will increase interest-sensitive consumer purchases and investment, causing GDP to increase. (b) Investment will decrease because of the lower expected rate of return, causing GDP to increase. (c) By increasing consumption (because households will feel or be more wealthy, or because they are hopeful about an expansion) and by increasing investment, the AE schedule will shift upward, causing the GDP to increase. 5. Depict graphically the aggregate expenditures model for a private closed economy. Now show a decrease in the aggregate expenditures schedule and explain why the decline in real GDP in your diagram is greater than the decline in the aggregate expenditures schedule. What is the term used for the ratio of a decline in real GDP to the initial drop in aggregate expenditures? LO3 Answer: Consider the following numerical example. If the slope of the aggregate expenditures schedule were.8, then the MPC =.8 and the MPS =.2. Therefore, the multiplier would be 1/(.2) = 5. The ratio of decline in real GDP to the initial drop of expenditures would be a ratio of 5:1. That is, if expenditures declined by \$4 billion, GDP should decline by billion. On the graph it can be seen that a one-unit decline in (C + I) leads to a five-unit decline in real GDP. 6. Assuming the economy is operating below its potential output, what is the impact of an increase in net exports on real GDP? Why is it difficult, if not impossible, for a country to boost its net exports by increasing its tariffs during a global recession? LO4 28-2

4 The Keynesian perspective, on the other hand, suggests that society s savings will not necessarily all be channeled into investment spending. If this occurs, we have a situation in which aggregate demand is less than potential production. Because producers cannot sell all of the output produced at a full employment level, they will reduce output and employment to meet the aggregate demand (consumption plus investment) and the equilibrium output will be at a point inside the production possibilities curve at less than full employment. PROBLEMS 1. Assuming the level of investment is \$16 billion and independent of the level of total output, complete the accompanying table and determine the equilibrium levels of output and employment in this private closed economy. What are the sizes of the MPC and MPS? LO1 Answer: Saving: \$ -4; 0; 4; 8; 12; 16; 20; 24; 28; equilibrium output = 340; equilibrium employment = 65; MPC = 0.8; MPS = 0.2 Feedback: Consider the following example. Assuming the level of investment is \$16 billion and independent of the level of total output, complete the accompanying table and determine the equilibrium levels of output and employment in this private closed economy. What are the sizes of the MPC and MPS? 28-4

5 The savings column is found by subtracting Consumption from Real Domestic Output (disposable income) for each row. The answers are reported in the savings column below. We can also find aggregate expenditures by adding consumption and investment, which is reported in the last column in the table below. We can find equilibrium two ways. First, we can find the level of output and employment where Investment equals Savings. Second, we can find the level of output and employment where aggregate expenditures equal real output. Either of these approaches give us the equilibrium level of output of \$340 billion and a level of employment 65 million. The marginal propensity to consume can be found by dividing the change in consumption by the change in real domestic output. MPC = Δ Consumption/Δ Real Domestic Output = \$16/ = 0.8 The marginal propensity to save can be found by subtracting the marginal propensity to consume from one. MPS = 1 - MPC = = 0.2 The expenditure multiplier can be found by dividing one by the marginal propensity or by one minus the marginal propensity to consume. Expenditure multiplier = 1/MPS = 1/(1-MPS) = 1/0.2 =

6 Possible levels of employment (millions) Real domestic output (GDP=DI) () Consumption () Saving () Investment () Aggregate Expenditures () \$ \$ \$ \$ \$ Using the consumption and saving data in problem 1 and assuming investment is \$16 billion, what are saving and planned investment at the \$380 billion level of domestic output? What are saving and actual investment at that level? What are saving and planned investment at the 0 billion level of domestic output? What are the levels of saving and actual investment? In which direction and by what amount will unplanned investment change as the economy moves from the \$380 billion level of GDP to the equilibrium level of real GDP? From the 0 billion level of real GDP to the equilibrium level of GDP? LO2 Answer: At \$380 billion level, saving = \$24 billion; planned investment = \$16 billion. Actual saving = \$24 billion; actual investment is \$24 billion At the 0 billion level, saving = \$8 billion; planned investment = \$16 billion. Actual saving = \$8 billion; actual investment is \$8 billion Unplanned inventories fall -8 billion Unplanned inventories rise 8 billion Feedback: Consider the following example (same as problem 1 example). Using the consumption and saving data in problem 1 and assuming investment is \$16 billion, what are saving and planned investment at the \$380 billion level of domestic output? What are saving and actual investment at that level? What are saving and planned investment at the 0 billion level of domestic output? What are the levels of saving and actual investment? In which direction and by what amount will unplanned investment change as the economy moves from the \$380 billion level of GDP to the equilibrium level of real GDP? From the 0 billion level of real GDP to the equilibrium level of GDP? 28-6

7 At the \$380 billion level of GDP, saving = \$24 billion; planned investment = \$16 billion (from the question). This deficiency of \$8 billion of planned investment causes an unplanned \$8 billion increase in inventories. Actual investment is \$24 billion (= \$16 billion of planned investment plus \$8 billion of unplanned inventory investment), matching the \$24 billion of actual saving. At the 0 billion level of GDP, saving = \$8 billion; planned investment = \$16 billion (from the question). This excess of \$8 billion of planned investment causes an unplanned \$8 billion decline in inventories. Actual investment is \$8 billion (= \$16 billion of planned investment minus \$8 billion of unplanned inventory disinvestment) matching the actual of \$8 billion. When unplanned investments in inventories occur, as at the \$380 billion level of GDP, businesses revise their production plans downward and GDP falls. When unplanned disinvestments in inventories occur, as at the 0 billion level of GDP; businesses revise their production plans upward and GDP rises. Equilibrium GDP in this case, \$340 billion occurs where planned investment equals saving. 3. By how much will GDP change if firms increase their investment by \$8 billion and the MPC is.80? If the MPC is.67? LO3 Answer: \$40; \$24.24 Feedback: Consider the following example. By how much will GDP change if firms increase their investment by \$8 billion and the MPC is.80? If the MPC is.67? First, we need to find the expenditure multiplier. The expenditure multiplier can be found by dividing one by one minus the marginal propensity to consume. Expenditure multiplier = 1/(1-MPC) For our first value, we have an expenditure multiplier of 5 (= 1/(1-0.8)). For our second value, we have an expenditure multiplier of (= 1/(1-0.67)). Some students may round this 3. Second, to find the change in GDP we take the expenditure multiplier and multiply this value by the change in investment. For our first MPC value, the change in GDP equals \$40 (= 5 x \$8). 28-7

8 Four our second MPC, the change in GDP equals \$24.24 (= x \$8). Some students may round this answer to \$24 (= 3 x \$8). 4. Suppose that a certain country has an MPC of.9 and a real GDP of \$400 billion. If its investment spending decreases by \$4 billion, what will be its new level of real GDP? LO3 Answer: \$360 Feedback: Consider the following example. Suppose that a certain country has an MPC of.9 and a real GDP of \$400 billion. If its investment spending decreases by \$4 billion, what will be its new level of real GDP? First, we need to find the expenditure multiplier. The expenditure multiplier can be found by dividing one by one minus the marginal propensity to consume. Expenditure multiplier = 1/(1-MPC) For our first value, we have an expenditure multiplier of 10 (= 1/(1-0.9)). Second, to find the change in GDP we take the expenditure multiplier and multiply this value by the change in investment. Change in GDP = 10 x (-\$4) = -\$40 Third, to find the new level of real GDP we add the change to the original level of real GDP (note, when investment decreases the change is negative). New level of real GDP = \$400 +(-\$40) = \$400 - \$40 = \$ The data in columns 1 and 2 in the accompanying table are for a private closed economy: LO4 a. Use columns 1 and 2 to determine the equilibrium GDP for this hypothetical economy. b. Now open up this economy to international trade by including the export and import figures of columns 3 and 4. Fill in columns 5 and 6 and determine the equilibrium GDP for the open economy. What is the change in equilibrium GDP caused by the addition of net exports? c. Given the original billion level of exports, what would be net exports and the equilibrium GDP if imports were \$10 billion greater at each level of GDP? d. What is the multiplier in this example? 28-8

9 Answer: (a) 400 (b) Column 5: ; ; ; ; ; ; ; ; Column 6: \$ 230; \$ 270; \$ 310; \$ 350; \$ 390; \$ 430; \$ 470; \$ 510; Equilibrium GDP = 350; Change in equilibrium GDP = -50 (c) Net exports = -\$ 20; -\$ 20; -\$ 20; -\$ 20; -\$ 20; -\$ 20; -\$ 20; -\$ 20; Equilibrium GDP = 0 (d) 5 Feedback: Consider the following example. The data in columns 1 and 2 in the accompanying table are for a private closed economy: Part a: a. Use columns 1 and 2 to determine the equilibrium GDP for this hypothetical economy. Equilibrium for this economy occurs where Aggregate Expenditures for the Private Closed Economy equals Real Gross Domestic Product. Thus, equilibrium is \$400 billion. Part b: b. Now open up this economy to international trade by including the export and import figures of columns 3 and 4. Fill in columns 5 and 6 and determine the equilibrium GDP for the open economy. What is the change in equilibrium GDP caused by the addition of net exports? To find net exports we subtract imports from exports. These answers are reported in column 5 below. To find aggregate expenditures for the open economy add net exports to the aggregate expenditures for the closed economy. These values are reported in column

10 (1) Real domestic output (GDP=DI) (2) Aggregate Expenditures, private closed economy, (3) Exports, (4) Imports, (5) Net exports, private economy (6) Aggregate expenditures, open 0 \$250 0 \$350 \$400 \$450 \$500 \$550 \$240 \$280 \$320 \$360 \$400 \$440 \$480 \$520 \$ 230 \$ 270 \$ 310 \$ 350 \$ 390 \$ 430 \$ 470 \$ 510 Equilibrium for this economy occurs where Aggregate Expenditures for the Private Open Economy equals Real Gross Domestic Product. Thus, equilibrium is \$350 billion. The change in equilibrium GDP is a decrease of \$50. Part c: c. Given the original billion level of exports, what would be net exports and the equilibrium GDP if imports were \$10 billion greater at each level of GDP? If Imports were \$10 billion greater at each level of GDP we would have the following table. (1) Real domestic output (GDP=DI) (2) Aggregate Expenditures, private closed economy, (3) Exports, (4) Imports, (5) Net exports, private economy (6) Aggregate expenditures, open 0 \$250 0 \$350 \$400 \$450 \$500 \$550 \$240 \$280 \$320 \$360 \$400 \$440 \$480 \$520 \$40 \$40 \$40 \$40 \$40 \$40 \$40 \$40 -\$ 20 -\$ 20 -\$ 20 -\$ 20 -\$ 20 -\$ 20 -\$ 20 -\$ 20 \$ 220 \$ 260 \$ 300 \$ 340 \$ 380 \$ 420 \$ 460 \$ 500 Equilibrium for this economy occurs where Aggregate Expenditures for the Private Open Economy equals Real Gross Domestic Product. Thus, equilibrium is 0 billion. Part d: d. What is the multiplier in this example? 28-10

11 To find the multiplier for this example we could use the standard approach using the marginal propensity to consume or using the change in real GDP that results from the change in net exports. We will use the latter approach here. The change in net exports equals -\$10 billion. The change in real GDP associated with the change in net exports is -\$50. Multiplier = Δ real GDP/ Δ net exports = -\$50 billion/-\$10 billion = 5 6. Assume that, without taxes, the consumption schedule of an economy is as follows: LO4 a. Graph this consumption schedule and determine the MPC. b. Assume now that a lump-sum tax is imposed such that the government collects \$10 billion in taxes at all levels of GDP. Graph the resulting consumption schedule and compare the MPC and the multiplier with those of the pretax consumption schedule. Answer: (a) MPC = 0.8 (b) Multiplier before tax = 5 Consumption after Tax = \$112; 192; 272; 352; 432; 512; 592 MPC after tax = 0.8; Multiplier after tax = 5; Comparison is the same Feedback: Consider the following example. Assume that, without taxes, the consumption schedule of an economy is as follows: Refer to Figures 27.1, 27.2, and 28.6 for the graphs for (a) and (b) respectively

12 28-12

13 28-13

14 Part a: a. Graph this consumption schedule and determine the MPC. Use the values in the table above for graph. The size of the MPC is 80/100 or.8 because consumption changes by 80 when GDP changes by 100. Part b: b. Assume now that a lump-sum tax is imposed such that the government collects \$10 billion in taxes at all levels of GDP. Graph the resulting consumption schedule and compare the MPC and the multiplier with those of the pretax consumption schedule. To find the level of consumption after the tax we first find out by how much consumption will decrease because of the tax. The tax is \$10 billion, since the marginal propensity to consume is 0.8 the household will reduce consumption by \$8 billion (= 0.8 x \$10 billion tax). The other \$2 billion will come from a reduction in saving. The new level of consumption after the tax equals the original level of consumption minus the reduction above. These values are reported in column 4 below. GDP, Billions Consumption before Tax Tax Consumption after Tax \$100 \$120 \$10 \$ The graph of the new after tax level of consumption will lie \$8 billion below the original level of consumption (part a) for each level of GDP. 7. Refer to columns 1 and 6 in the table for problem 5. Incorporate government into the table by assuming that it plans to tax and spend billion at each possible level of GDP. Also assume that the tax is a personal tax and that government spending does not induce a shift in the private aggregate expenditures schedule. What is the change in equilibrium GDP caused by the addition of government? LO4 Answer: 28-14

15 Feedback: Consider the following example. Refer to columns 1 and 6 in the table for problem 5. Incorporate government into the table by assuming that it plans to tax and spend billion at each possible level of GDP. Also assume that the tax is a personal tax and that government spending does not induce a shift in the private aggregate expenditures schedule. What is the change in equilibrium GDP caused by the addition of government? (1) Real domestic output (GDP=DI) (2) Aggregate Expenditures, private closed economy, (3) Exports, (4) Imports, (5) Net exports, private economy (6) Aggregate expenditures, open 0 \$250 0 \$350 \$400 \$450 \$500 \$550 \$240 \$280 \$320 \$360 \$400 \$440 \$480 \$520 \$ 230 \$ 270 \$ 310 \$ 350 \$ 390 \$ 430 \$ 470 \$ 510 (NOTE: Use marginal propensity to consume and multiplier found in problem 5) Before G is added, open private sector equilibrium will be at \$350. The addition of billion of government expenditures and billion of personal taxes increases equilibrium GDP from \$350 to \$370 billion. The addition of government expenditures G to our analysis raises the aggregate expenditures (C + I g +X n + G) schedule and increases the equilibrium level of GDP. This change in government spending is subject to the multiplier effect. Thus, the increase in Government spending increasing the equilibrium GDP to \$450 (5 (multiplier) x ). The billion increase in T reduces initially reduces consumption by \$16 billion at every level of output (= 0.8 (MPC) x ). This \$16 billion decline in turn reduces equilibrium GDP by \$80 billion (= 5 (multiplier x \$16). The net change from this balance between government spending and taxes is billion (= \$100 billion (increase due to increase in G) - \$80 billion (decrease due to increase in T)). 8. Advanced Analysis Assume that the consumption schedule for a private open economy is such that consumption C = Y. Assume further that planned investment Ig and net exports Xn are independent of the level of real GDP and constant at Ig = 30 and Xn = 10. Recall also that, in equilibrium, the real output produced (Y) is equal to aggregate expenditures: Y = C + Ig + Xn. LO4 a. Calculate the equilibrium level of income or real GDP for this economy. b. What happens to equilibrium Y if Ig changes to 10? What does this outcome reveal about the size of the multiplier? 28-15

16 Answer: (a) 450 (b) 350; 5 Feedback: Consider the following example. Assume that the consumption schedule for a private open economy is such that consumption C = Y. Assume further that planned investment Ig and net exports Xn are independent of the level of real GDP and constant at Ig = 30 and Xn = 10. Recall also that, in equilibrium, the real output produced (Y) is equal to aggregate expenditures: Y = C + Ig + Xn. Part a: a. Calculate the equilibrium level of income or real GDP for this economy. In equilibrium we have the following relationship: Y = C+I g+x n = Y = Y solving for Y, Y - 0.8Y = 90 which gives us 0.2Y = 90 (= (1-0.8)Y = 90), or Y = 90/0.2. Thus, the answer is: Y = 450 Part b: b. What happens to equilibrium Y if Ig changes to 10? What does this outcome reveal about the size of the multiplier? If Investment falls from 30 to 10, we follow the same procedure (except let I g=10). In equilibrium we have the following relationship: Y = C+I g+x n = Y = Y solving for Y, Y - 0.8Y = 70 which gives us 0.2Y = 70 (= (1-0.8)Y = 70), or Y = 70/0.2. Thus, the answer is: Y = 350 The multiplier can be found by dividing the change in output (Y) by the change in investment (I g). multiplier = ΔY/ΔI g = 100/20 =5 9. Refer to the accompanying table in answering the questions that follow: LO5 a. If full employment in this economy is 130 million, will there be an inflationary expenditure gap or a recessionary expenditure gap? What will be the consequence of this gap? By how much would aggregate expenditures in column 3 have to change at each level of GDP to eliminate the inflationary expenditure gap or the recessionary expenditure gap? What is the multiplier in this example? 28-16

17 b. Will there be an inflationary expenditure gap or a recessionary expenditure gap if the fullemployment level of output is \$500 billion? By how much would aggregate expenditures in column 3 have to change at each level of GDP to eliminate the gap? What is the multiplier in this example? c. Assuming that investment, net exports, and government expenditures do not change with changes in real GDP, what are the sizes of the MPC, the MPS, and the multiplier? Answer: (a) Recessionary expenditure gap; 20 billion shortfall of employment; ; 5 (b) Inflationary expenditure gap; -; 5 (c) MPC = 0.8; MPS = 0.2; multiplier = 5 Feedback: Consider the following example. Refer to the accompanying table in answering the questions that follow: Part a: a. If full employment in this economy is 130 million, will there be an inflationary expenditure gap or a recessionary expenditure gap? What will be the consequence of this gap? By how much would aggregate expenditures in column 3 have to change at each level of GDP to eliminate the inflationary expenditure gap or the recessionary expenditure gap? What is the multiplier in this example? The equilibrium in this economy is at \$600 billion, real domestic output equals aggregate expenditures (this is where the economy will take us). Since full employment is at 130 million, this implies that full employment real domestic output is at \$700 billion. Given that aggregate expenditures is only \$680 billion at this level of employment we have a recessionary expenditure gap. That is, aggregate expenditures is billion below real domestic output. If aggregate expenditures increased by billion the new equilibrium would be at \$700 billion, which is at full employment (add billion to each level of aggregate expenditures in the table above). The multiplier can be found by dividing the change in equilibrium real domestic output by the change in aggregate expenditures. multiplier = Δ real domestic output/δ aggregate expenditures = \$100 billion/ billion = 5 Part b: b. Will there be an inflationary expenditure gap or a recessionary expenditure gap if the full-employment level of output is \$500 billion? By how much would aggregate expenditures in column 3 have to change at each level of GDP to eliminate the gap? What is the multiplier in this example? 28-17

18 Again, the equilibrium in this economy is at \$600 billion, real domestic output equals aggregate expenditures (this is where the economy will take us). Since full employment real domestic output is \$500 billion and given that aggregate expenditures is \$520 billion at this level of real domestic output we have an inflationary expenditure gap. That is, aggregate expenditures is billion above real domestic output. If aggregate expenditures decreased by billion, for this case, the new equilibrium would be at \$500 billion, which is at full employment (subtract billion from each level of aggregate expenditures in the table above). The multiplier can be found by dividing the change in equilibrium real domestic output by the change in aggregate expenditures. multiplier = Δ real domestic output/δ aggregate expenditures = -\$100 billion/- billion = 5 (note the changes are negative in this case) Part c: c. Assuming that investment, net exports, and government expenditures do not change with changes in real GDP, what are the sizes of the MPC, the MPS, and the multiplier? To find the marginal propensity to consume (MPC) divide the change in aggregate expenditures by the change in real domestic output (assuming that investment, net exports, and government expenditures do not change with changes in real GDP). MPC = Δ aggregate expenditures/δ real domestic output = \$40/\$50 = 0.8 With the MPC we can find the marginal propensity to save (MPS). MPS = 1 - MPC = = 0.2 We can also use the MPC (or MPS) to find the multiplier. multiplier = 1/(1-MPC) = 1/(1-0.8) = 1/0.2 = 5 This is consistent with the answers above. 10. Answer the following questions, which relate to the aggregate expenditures model: LO5 a. If C is \$100, Ig is \$50, Xn is \$10, and G is, what is the economy s equilibrium GDP? b. If real GDP in an economy is currently 0, C is \$100, Ig is \$50, Xn is -\$10, and G is, will the economy s real GDP rise, fall, or stay the same? c. Suppose that full-employment (and full-capacity) output in an economy is 0. If C is \$150, Ig is \$50, Xn is \$10, and G is, what will be the macroeconomic result? Answer: (a) \$170 (b) fall (c) Inflationary expenditure gap and employment levels are above the full employment level Feedback: Consider the following example. Answer the following questions, which relate to the aggregate expenditures model: Part a: a. If C is \$100, Ig is \$50, Xn is \$10, and G is, what is the economy s equilibrium GDP? Equilibrium occurs where real output (Y) equals aggregate expenditures (AE), where AE = C + I g + G +X n. Using this relationship, we have the equilibrium value: Y = AE = C + I g + G +X n = \$100 + \$50 +(-\$10) + = \$170 Part b: 28-18

19 b. If real GDP in an economy is currently 0, C is \$100, Ig is \$50, Xn is -\$10, and G is, will the economy s real GDP rise, fall, or stay the same? If real GDP is 0, aggregate expenditures of \$170 will result in positive unplanned inventory investment. GDP will fall as firms respond to the inventory build-up by reducing output. Part c: c. Suppose that full-employment (and full-capacity) output in an economy is 0. If C is \$150, Ig is \$50, Xn is \$10, and G is, what will be the macroeconomic result? Here we can use the same approach as in part (a) AE = C + I g + G +X n = \$150 + \$50 +(-\$10) + = \$220 Since full-employment (and full-capacity) output in the economy is 0 there is an inflationary expenditure gap and employment levels are higher than the full employment level

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