Chapter 27 - Basic Macroeconomic Relationships Chapter 27 Basic Macroeconomic Relationships QUESTIONS 1. What are the variables (the items measured on the axes) in a graph of the (a) consumption schedule and (b) saving schedule? Are the variables inversely (negatively) related or are they directly (positively) related? What is the fundamental reason that the levels of consumption and saving in the United States are each higher today than they were a decade ago? LO1 Answer: (a) Consumption schedule: The variable on the vertical axis (y-axis) is consumption and the variable on the horizontal axis (x-axis) is disposable income (see Figure 27.2a). These variables are directly (positively) related because they move in the same direction. (b) Saving schedule: The variable on the vertical axis (y-axis) is saving and the variable on the horizontal axis (x-axis) is disposable income (see Figure 27.2b). These variables are directly (positively) related because they move in the same direction. The level of consumption and saving in the United States is higher today than a decade ago because real GDP and income are higher. 2. Precisely how do the MPC and the APC differ? How does the MPC differ from the MPS? Why must the sum of MPC and the MPS equal 1? LO1 Answer: MPC refers to changes in spending and income at the margin. Here we compare a change in consumer spending to a change in income: MPC = change in C / change in Y. APC is an average whereby total spending on consumption (C) is compared to total income (Y): APC = C/Y. When your income changes there are only two possible options regarding what to do with it: You either spend it or you save it. MPC is the fraction of the change in income spent; therefore, the fraction not spent must be saved and this is the MPS. The change in the dollars spent or saved will appear in the numerator and together they must add to the total change in income. Since the denominator is the total change in income, the sum of the MPC and MPS is one. 3. In what direction will each of the following occurrences shift the consumption and saving schedules, other things equal? LO2 a. A large decrease in real estate values, including private homes. b. A sharp, sustained increase in stock prices. c. A 5-year increase in the minimum age for collecting Social Security benefits. d. An economy-wide expectation that a recession is over and that a robust expansion will occur. e. A substantial increase in household borrowing to finance auto purchases. Answer: (a) The consumption schedule will shift downward and the saving schedule will shift upward given the decrease in wealth. 27-1 © 2012 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. Chapter 27 - Basic Macroeconomic Relationships (b) The consumption schedule will shift upward and the saving schedule will shift downward given the increase in wealth. (c) The consumption schedule will likely shift upward and the saving schedule will likely shift downward given that individuals will need to work 5 more years before retiring. There is less need to save for retirement. (d) The consumption schedule will shift upward and the saving schedule will shift downward because individuals expect to be earning higher income in the future. (e) The consumption schedule will shift upward and the saving schedule will shift downward as individuals borrow (decrease saving) and purchase the automobiles (increase consumption). 4. Why does a downshift of the consumption schedule typically involve an equal upshift of the saving schedule? What is the exception to this relationship? LO2 Answer: If, by definition, all that you can do with your income is use it for consumption or saving, then if you consume less out of any given income, you will necessarily save more. This being so, when your consumption schedule shifts downward (meaning you are consuming less out of any given income), your saving schedule shifts upward (meaning you are saving more out of any given income). The exception is a change in personal taxes. When these change, your disposable income changes, and, therefore, your consumption and saving both change in the same direction and opposite to the change in taxes. If your MPC, say, is 0.9, then your MPS is 0.1. Now, if your taxes increase by $100, your consumption will decrease by $90 and your saving will decrease by $10. 5. Why will a reduction in the real interest rate increase investment spending, other things equal? LO3 Answer: Firms will only make an investment purchase if the expected return is greater than or equal to real interest rate at which it can borrow. The logic is as follows. If you borrow a $100 at an interest rate of 10%, then at the end of the year you will owe $110. Now, if you can earn a rate of return of 20% on the borrowed $100, then you will have $120 from your investment at the end of the year. You pay off the $110 loan and keep $10. This is a good investment. However, if you can earn a rate of return of 5% on the borrowed $100, then you will have $105 from your investment at the end of the year. You pay off the $110 loan and lose $5. This is a bad investment. Using this logic, a reduction in the real interest rate will make previously unprofitable investments profitable. Thus, other things equal, this will increase investment. For example, if the real interest rate fell from 10% to 3% it would be a good investment to borrow at 5% now, where it wasn't before when the real interest rate was 10%. 6. In what direction will each of the following occurrences shift the investment demand curve, other things equal? LO4 a. An increase in unused production capacity occurs. b. Business taxes decline. c. The costs of acquiring equipment fall. 27-2 © 2012 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. Chapter 27 - Basic Macroeconomic Relationships d. Widespread pessimism arises about future business conditions and sales revenues. e. A major new technological breakthrough creates prospects for a wide range of profitable new products. Answer: (a) This will decrease investment demand causing the investment curve to shift to the left. The increase in unused capacity reduces the need (expected return) for capital. (b) This will increase investment demand causing the investment curve to shift to the right. The decrease in business taxes increase after-tax expected returns (which determines investment decisions). (c) This will increase investment demand causing the investment curve to shift to the right. The expected return increases due to the declining cost. (d) This will decrease investment demand causing the investment curve to shift to the left. Widespread pessimism about future business conditions and sales revenues reduces expected returns. (e) This will increase investment demand causing the investment curve to shift to the right. The major new technological breakthrough increases expected returns. 7. How is it possible for investment spending to increase even in a period in which the real interest rate rises? LO4 Answer: As long as expected rates of return rise faster than real interest rates, investment spending may increase. This is most likely to occur during periods of economic expansion. 8. Why is investment spending unstable? LO4 Answer: Investment is unstable because, unlike most consumption, it can be put off. In good times, with demand strong and rising, businesses will bring in more machines and replace old ones. In times of economic downturn, no new machines will be ordered. A firm can continue for years with, say, a tenth of the investment it was carrying out in the boom. Very few families could cut their consumption so drastically. Also, new business ideas and the innovations that spring from them do not come at a constant rate. This is another reason for the irregularity of investment. Profits and the expectations of profits vary. Since profits, in the absence of easy access to borrowed money, are essential for investment and since, moreover, the object of investment is to make a profit, investment, too, must vary. 9. Is the relationship between changes in spending and changes in real GDP in the multiplier effect a direct (positive) relationship or is it an inverse (negative) relationship? How does the size of the multiplier relate to the size of the MPC? The MPS? What is the logic of the multiplierMPC relationship? LO5 Answer: The key relationship is as follows: Change in Real GDP = multiplier x change in spending From this equation we can see that there is direct relationship between changes in spending and changes in real GDP. When spending increases real GDP increases and when spending decreases real GDP decreases. They both move in the same direction. 27-3 © 2012 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. Chapter 27 - Basic Macroeconomic Relationships To answer the next part of the question we use the following relationships. MPC + MPS = 1 and Multiplier = 1/ (1-MPC) or Multiplier = 1/ MPS. From above, we see that an increase in the MPC increases the multiplier and a decrease in the MPC reduces the multiplier. For the MPS, we see that an increase in the MPS decreases the multiplier and a decrease in the MPS increases the multiplier. The reason we see an increase in the multiplier when the MPC increases is because the initial change in spending results in greater consumption spending at each stage of the expansion process. Thus, the higher the MPC the greater the change in real GDP following an increase in spending. The same logic applies to a decrease in spending. 10. Why is the actual multiplier in the U.S. economy less than the multiplier in this chapter’s example? LO5 Answer: The actual multiplier (estimated to be about 2) is smaller because it includes other leakages from the spending and income cycle besides just saving. Imports and taxes reduce the flow of money back into spending on domestically produced output, reducing the multiplier effect. 11. LAST WORD What is the central economic idea humorously illustrated in Art Buchwald’s piece, “Squaring the Economic Circle”? How does the central idea relate to economic recessions, on the one hand, and vigorous economic expansions, on the other? Answer: The central idea illustrated is the multiplier effect that exists in a market economic system. One independently determined change in spending has an effect on another’s income, which then sets in motion a chain of events whereby spending changes directly with the income changes. A decline in spending begins a chain of declines, or, in other words, the initial decrease in spending is multiplied in terms of the final effect of this single decision. This occurs because of the observation that any change in income causes a change in spending that is directly proportional to it. The multiplier effect helps us understand why there is a business cycle as opposed to a stable level of output growth from year to year. In the Buchwald piece, a “downturn” for one person became a downturn for everyone in that fictional economy. Likewise, if the story had begun with a burst of optimism and an increase in spending, it might have rippled through to expand everyone’s fortunes. The multiplier intensifies the effect of a spending change, whether it is an increase or decrease. PROBLEMS 1. Refer to the incomplete table below. LO1 27-4 © 2012 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. Chapter 27 - Basic Macroeconomic Relationships a. Fill in the missing numbers in the table. b. What is the break-even level of income in the table? What is the term that economists use for the saving situation shown at the $240 level of income? c. For each of the following items indicate whether the value in the table is either constant or variable as income changes: the MPS, the APC, the MPC, the APS. Answers: (a) data in the completed table; (b) $260, dissaving; (c) constant, variable, constant, variable. Feedback: Consider the following example. Refer to the nearby incomplete table. Part a: Fill in the missing numbers in the table. 27-5 © 2012 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. Chapter 27 - Basic Macroeconomic Relationships Level of Output and Income (GDP=DI) $240 260 280 300 320 340 360 380 400 Consumption $244 $260 $276 $292 $308 $324 $340 $356 $372 Saving -$4 0 4 8 12 16 20 24 28 APC 1.0167 1 0.9857 0.9733 0.9625 0.9529 0.9444 0.9368 0.93 APS -0.0167 0 0.0143 0.0267 0.0375 0.0471 0.0556 0.0632 0.07 MPC 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 MPS 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 To find the level of consumption (column 2): Consumption = Income - Saving Example: at Income $300 Consumption = $300 - $8 = $292 To find the Average Propensity to Consume (APC) (column 4): APC = Consumption/Income Example: at Income $300 APC = $292/$300 = 0.9733 To find the Average Propensity to Save (APS) (column 5): APS = Saving/Income Example: at Income $300 APS = $8/$300 = 0.0267 To find the Marginal Propensity to Consume (MPC) (column 6): MPC = Δ Consumption/Δ Income Example: at Income $300 (from $280) MPC = $16/$20 = 0.8 To find the Marginal Propensity to Save (MPS) (column 7): MPS= Δ Saving/Δ Income Example: at Income $300 (from $280) MPS = $4/$20 = 0.2 Part b: What is the break-even level of income in the table? What is the term that economists use for the saving situation shown at the $240 level of income? 27-6 © 2012 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. Chapter 27 - Basic Macroeconomic Relationships Break-even level of income is where saving equals zero (consumption equals income). Thus, the break-even level of income is $260. At the level of income $240 saving is negative. Economists refer to this as dissaving. Part c: For each of the following items indicate whether the value in the table is either constant or variable as income changes: the MPS, the APC, the MPC, the APS. MPS: Constant (does not change with income) APC: Variable (changes with income) MPC: Constant (does not change with income) APS: Variable (changes with income) 2. Suppose that disposable income, consumption, and saving in some country are $200 billion, $150 billion, and $50 billion, respectively. Next, assume that disposable income increases by $20 billion, consumption rises by $18 billion and saving goes up by $2 billion. What is the economy’s MPC? Its MPS? What was the APC before the increase in disposable income? After the increase? LO1 Answers: .9; .1; .75; .764. Feedback: Consider the following example. Suppose that disposable income, consumption, and saving in some country are $200 billion, $150 billion, and $50 billion, respectively. Next, assume that disposable income increases by $20 billion, consumption rises by $18 billion and saving goes up by $2 billion. What is the economy’s MPC? Its MPS? What was the APC before the increase in disposable income? After the increase? What is the economy’s MPC? To find the Marginal Propensity to Consume (MPC): MPC = Δ Consumption/Δ Income MPC = $18/$20 =0.9 What is the economy’s MPS? To find the Marginal Propensity to Save (MPS): MPC = Δ Saving/Δ Income MPS = $2/$20 =0.1 What was the APC before the increase in disposable income? To find the Average Propensity to Consume (APC): APC = Consumption/Income APC = $150/$200 = 0.75 What was the APC after the increase in disposable income? 27-7 © 2012 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. Chapter 27 - Basic Macroeconomic Relationships Disposable Income after the change equals $220 (=$200 +$20) Consumption after the change equals $168 (= $150 +$18). The MPC is 0.9, so consumption increases by $18 given the increase in disposable income of $20. APC = $168/$220 = 0.7636 3. Advanced Analysis Suppose that the linear equation for consumption in a hypothetical economy is C = 40 + .8Y. Also suppose that income (Y) is $400. Determine (a) the marginal propensity to consume, (b) the marginal propensity to save, (c) the level of consumption, (d) the average propensity to consume, (e) the level of saving, and (f) the average propensity to save. LO1 Answer: (a) 0.8; (b) 0.2; (c) $360; (d) 0.9; (e) $40; (f) 0.1. Feedback: Consider the following example. Suppose that the linear equation for consumption in a hypothetical economy is C = 40 + .8Y. Also suppose that income (Y) is $400. Determine (a) the marginal propensity to consume, (b) the marginal propensity to save, (c) the level of consumption, (d) the average propensity to consume, (e) the level of saving, and (f) the average propensity to save. Determine (a) the marginal propensity to consume: The marginal propensity to consume is the slope of the linear equation, which equals 0.8. Determine (b) the marginal propensity to save: The marginal propensity to save is one minus the slope of the linear equation, which equals 0.2 (=1 - 0.8). Determine (c) the level of consumption: To find the level of consumption, substitute income into the linear equation. This results in a level of consumption of $360 (= $40 + 0.8 x $400 = $40 + $320 =$360). Determine (d) the average propensity to consume: To find the average propensity to consume, divide consumption by income. This results in an average propensity to consume of 0.9 (= $360/$400). Determine (e) the level of saving: To find the level of saving, subtract consumption from income. This results in a level of saving of $40 (= $400 -$360). Determine (f) the average propensity to save: To find the average propensity to save, divide saving by income. This results in an average propensity to consume of 0.1 (= $40/$400). 4. Advanced Analysis Linear equations for the consumption and saving schedules take the general form C = a + bY and S= -a + (1-b)Y where C, S, and Y are consumption, saving, and national income, respectively. The constant a represents the vertical intercept, and b represents the slope of the consumption schedule. LO1, LO2 a. Use the following data to substitute numerical values for a and b in the consumption and saving equations. 27-8 © 2012 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. Chapter 27 - Basic Macroeconomic Relationships b. What is the economic meaning of b? Of (1 - b)? c. Suppose that the amount of saving that occurs at each level of national income falls by $20 but that the values of b and (1 - b) remain unchanged. Restate the saving and consumption equations inserting the new numerical values, and cite a factor that might have caused the change. Answer: (a) C = $80 + 0.6xY; S = -$80 + 0.4xY (b) b is the slope of the consumption function, the marginal propensity to consume (MPC), or the change in consumption relative to the change in income. (1-b) is the slope of the saving function, the marginal propensity to save (MPS), or the change in saving relative to the change in income. (c) C = $100 + 0.6xY; S = -$100 + 0.4xY Feedback: Consider the following example. Part a: Use the following data to substitute numerical values for a and b in the consumption and saving equations. Finding the consumption function: The intercept a is the level of consumption when income is zero. Thus, a = $80. The slope of the consumption function b is found by looking at the change in consumption relative to the change in income. This is the marginal propensity to consume (MPC). b = MPC = Δ Consumption/Δ Income = $60/$100 =0.6 C = $80 + 0.6xY Finding the saving function: The intercept -a is the level of saving when income is zero. If consumption is positive when income is zero there must be dissaving. Thus -a =-$80. 27-9 © 2012 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. Chapter 27 - Basic Macroeconomic Relationships The slope of the saving function (1-b) is found by looking at the change in saving relative to the change in income. This is the marginal propensity to save (MPS). MPS = (1-b) = 1-MPC = 1- 0.6 = 0.4 = Δ saving/Δ Income = $40/$100 S = -$80 + 0.4xY Part b: What is the economic meaning of b? Of (1 - b)? The slope of the consumption function b is the marginal propensity to consume (MPC). b = MPC = Δ Consumption/Δ Income = $60/$100 =0.6 This implies that $0.60 of every additional dollar of disposable income will be consumed. The slope of the saving function (1-b) is the marginal propensity to save (MPS). MPS (1-b) = 1-MPC = 1- 0.6 = 0.4 = Δ saving/Δ Income = $40/$100 This implies that $0.40 of every additional dollar of disposable income will be saved. Part c: Suppose that the amount of saving that occurs at each level of national income falls by $20 but that the values of b and (1 - b) remain unchanged. Restate the saving and consumption equations inserting the new numerical values, and cite a factor that might have caused the change. If saving falls by $20 at every level of national income this implies consumption increases by $20 at every level of income. Thus, the intercept of the consumption function a will increase by $20 and the intercept of the saving function -a will fall by $20. C = $100 + 0.6xY S = -$100 + 0.4xY 5. Use your completed table for problem 1 to solve this problem. Suppose the wealth effect is such that $10 changes in wealth produce $1 changes in consumption at each level of income. If real estate prices tumble such that wealth declines by $80, what will be the new level of consumption at the $340 billion level of disposable income? The new level of saving? LO2 Answers: $316; $24. Feedback: Consider the following example. Use your completed table for problem 1 to solve this problem. Suppose the wealth effect is such that $10 changes in wealth produce $1 changes in consumption at each level of income. If real estate prices tumble such that wealth declines by $80, what will be the new level of consumption at the $340 billion level of disposable income? The new level of saving? 27-10 © 2012 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. Chapter 27 - Basic Macroeconomic Relationships TABLE FROM PROBLEM 1 Level of Output and Income (GDP=DI) $240 260 280 300 320 340 360 380 400 Consumption $244 $260 $276 $292 $308 $324 $340 $356 $372 Saving -$4 0 4 8 12 16 20 24 28 APC 1.0167 1 0.9857 0.9733 0.9625 0.9529 0.9444 0.9368 0.93 APS -0.0167 0 0.0143 0.0267 0.0375 0.0471 0.0556 0.0632 0.07 MPC 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 MPS 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 If real estate prices tumble such that wealth declines by $80 and the wealth effect is such that a $10 change in wealth produce a $1 change in consumption at each level of income, then consumption will fall by $8 at every level of income (= 0.1 x $80). This implies consumption equals $316 at the income level of $340. Consumption was originally $324 at this income level and the decline in wealth results in a fall in consumption of $8. To find the new level of savings after the decline in wealth we subtract the NEW level of consumption (=$316) from disposable income (=$340), which equals $24 (= $340 $316). The household increases savings to offset the decline in wealth. 6. Suppose a handbill publisher can buy a new duplicating machine for $500 and the duplicator has a 1-year life. The machine is expected to contribute $550 to the year’s net revenue. What is the expected rate of return? If the real interest rate at which funds can be borrowed to purchase the machine is 8 percent, will the publisher choose to invest in the machine? Will it invest in the machine if the real interest rate is 9 percent? If it is 11 percent? LO3 Answers: 10 percent; yes; yes; no. Feedback: Consider the following example. Suppose a handbill publisher can buy a new duplicating machine for $500 and the duplicator has a 1-year life. The machine is expected to contribute $550 to the year’s net revenue. What is the expected rate of return? If the real interest rate at which funds can be borrowed to purchase the machine is 8 percent, will the publisher choose to invest in the machine? Will it invest in the machine if the real interest rate is 9 percent? If it is 11 percent? The expected rate of return equals the expected net revenue less cost divided by the cost of the machine. Expected return = (net revenue - cost)/cost = ($550 - $500)/$500 = $50/$500 = 0.1 27-11 © 2012 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. Chapter 27 - Basic Macroeconomic Relationships In percentage terms 10% (= 100 x 0.1). The firm will only make this purchase if the expected return is greater than or equal to interest rate at which it can borrow. The logic is as follows. If you borrow a $100 at an interest rate of 10%, then at the end of the year you will owe $110. Now, if you can earn a rate of return of 20% on the borrowed $100, then you will have $120 from your investment at the end of the year. You pay off the $110 loan and keep $10. This is a good investment. However, if you can earn a rate of return of 5% on the borrowed $100, then you will have $105 from your investment at the end of the year. You pay off the $110 loan and lose $5. This is a bad investment. Back to our problem: So, if the real interest rate at which funds can be borrowed to purchase the machine is 8 percent, will the publisher choose to invest in the machine? Yes, 10% is greater than 8% Will it invest in the machine if the real interest rate is 9 percent? Yes, 10% is greater than 9%. If it is 11 percent? No, 10% is less than 11%. 7. Assume there are no investment projects in the economy that yield an expected rate of return of 25 percent or more. But suppose there are $10 billion of investment projects yielding expected returns of between 20 and 25 percent; another $10 billion yielding between 15 and 20 percent; another $10 billion between 10 and 15 percent; and so forth. Cumulate these data and present them graphically, putting the expected rate of return (and the real interest rate) on the vertical axis and the amount of investment on the horizontal axis. What will be the equilibrium level of aggregate investment if the real interest rate is (a) 15 percent, (b) 10 percent, and (c) 5 percent? LO3 Answer: 27-12 © 2012 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. Chapter 27 - Basic Macroeconomic Relationships (a) $20 billion (b) $30 billion (c) $40 billion Feedback: Consider the following example. Assume there are no investment projects in the economy that yield an expected rate of return of 25 percent or more. But suppose there are $10 billion of investment projects yielding expected returns of between 20 and 25 percent; another $10 billion yielding between 15 and 20 percent; another $10 billion between 10 and 15 percent; and so forth. Cumulate these data and present them graphically, putting the expected rate of return (and the real interest rate) on the vertical axis and the amount of investment on the horizontal axis. What will be the equilibrium level of aggregate investment if the real interest rate is (a) 15 percent, (b) 10 percent, and (c) 5 percent? The firm will only make an investment if the expected return is greater than or equal to interest rate at which it can borrow. At an interest rate of 25% investment is zero (no project yields an expected rate of return of 25% or more) At an interest rate of 20% investment is $10 billion (these are projects with expected rates of return between 20% and 24.99%) At an interest rate of 15% investment is $20 billion (these are projects with expected rates of return between 15% and 24.99%. There are $10 billion between 15% and 19.99% and $10 billion between 20% and 24.99%. Investment is cumulative) At an interest rate of 10% investment is $30 billion (logic above applies) At an interest rate of 5% investment is $40 billion (logic above applies) At an interest rate of 0% investment is $50 billion (logic above applies) See the graph below. 27-13 © 2012 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. Chapter 27 - Basic Macroeconomic Relationships (a) If the rate at which firms can borrow is 15% (real interest rate), then aggregate investment is $20 billion. (b) If the rate at which firms can borrow is 10% (real interest rate), then aggregate investment is $30 billion. (c) If the rate at which firms can borrow is 5% (real interest rate), then aggregate investment is $40 billion. 8. Refer to the table in Figure 27.5 in the book and suppose that the real interest rate is 6 percent. Next, assume that some factor changes such that that the expected rate of return declines by 2 percentage points at each prospective level of investment. Assuming no change in the real interest rate, by how much and in what direction will investment change? Which of the following might cause this change: (a) a decision to increase inventories; (b) an increase in excess production capacity? LO4 Answers: $5 billion decrease; (b). Feedback: Consider the following example. Refer to the table below and suppose that the real interest rate is 6 percent. Next, assume that some factor changes such that that the expected rate of return declines by 2 percentage points at each prospective level of investment. Assuming no change in the real interest rate, by how much and in what direction will investment change? Which of the following might cause this change: (a) a decision to increase inventories; (b) an increase in excess production capacity? 27-14 © 2012 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. Chapter 27 - Basic Macroeconomic Relationships Since the expected rate of return has fallen by 2 percentage points investment at each real interest rate will decrease. The investment schedule will shift to the left. The next question is by how much? To answer this question we use the following logic. Initially investment at the real interest rate of 6% is $25 billion (see figure 27.5 above). Since the expected rate of return has fallen by 2 percentage points, the return on the last dollar invested of the $25 billion (the $25 billionth dollar) has fallen to 4%. The real interest has not changed, it is still at 6% so this investment is no longer made. This is true for every investment dollar beyond $20 billion because the return has fallen by 2 percentage points and the return is now below 6% (originally below 8%). The marginal return on the $20 billionth (dollar) is 6% because the original return was 8%. All of the investment dollars before the $20 billionth (dollar) also earns a return greater than 6%. So investment at the 6% real interest rate is now $20 billion. The investment schedule shifts in by $5 billion at every real interest rate. Which of the following might cause this change: (a) a decision to increase inventories; (b) an increase in excess production capacity? The answer is (a). An increase in excess production capacity will reduce investment demand because each new machine does not add as much to output (firm already has significant excess capacity). 27-15 © 2012 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. Chapter 27 - Basic Macroeconomic Relationships 9. What will the multiplier be when the MPS is 0, .4, .6, and 1? What will it be when the MPC is 1, .90, .67, .50, and 0? How much of a change in GDP will result if firms increase their level of investment by $8 billion and the MPC is .80? If the MPC instead is .67? LO5 Answer: Multiplier when the MPS is 0: infinity or undefined; when the MPS is 0.4: 2.5; when the MPS is 0.6: 1.6667; when the MPS is 1: 1; when the MPC is 1: infinity or undefined; when the MPC is 0.90: 10; when the MPC is 0.67: 3.0303 (could also answer 3); when the MPC is 0.50: 2; when the MPC is 0: 1. Change in GDP when level of investment increases by $8 billion and the MPC is .80: $40 billion. If the MPC were instead 0.67, the change GDP = $24 billion. Feedback: Consider the following example. What will the multiplier be when the MPS is 0, .4, .6, and 1? What will it be when the MPC is 1, .90, .67, .50, and 0? How much of a change in GDP will result if firms increase their level of investment by $8 billion and the MPC is .80? If the MPC instead is .67? The multiplier = 1/MPS = 1/(1-MPC) What will the multiplier be when the MPS is 0? infinity or undefined What will the multiplier be when the MPS is 0.4? 2.5 (= 1/0.4) What will the multiplier be when the MPS is 0.6? 1.6667 (= 1/0.6) What will the multiplier be when the MPS is 1? 1 (= 1/1) What will the multiplier be when the MPC is 1? infinity or undefined What will the multiplier be when the MPC is 0.90? 10 (= 1/(1-0.9) = 1/0.1) What will the multiplier be when the MPC is 0.67? 3.0303 (= 1/(1-0.67) = 1/0.33) Could also answer 3. What will the multiplier be when the MPC is 0.50? 2 (= 1/(1-0.5) = 1/0.5) What will the multiplier be when the MPC is 0? 1 (= 1/1) How much of a change in GDP will result if firms increase their level of investment by $8 billion and the MPC is .80? The multiplier here is 5 (1/(1-0.8)). We multiply this times the initial change in investment to find the complete effect on GDP. GDP will change by $40 billion (= 5 x $8 billion). If the MPC were instead 0.67 the change GDP equals $24 billion (approx). The multiplier is 3 (approx) in this case. 27-16 © 2012 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. Chapter 27 - Basic Macroeconomic Relationships 10. Suppose that an initial $10 billion increase in investment spending expands GDP by $10 billion in the first round of the multiplier process. If GDP and consumption both rise by $6 billion in the second round of the process, what is the MPC in this economy? What is the size of the multiplier? If, instead, GDP and consumption both rose by $8 billion in the second round, what would have been the size of the multiplier? LO5 Answers: .6; 2.5; 5. Feedback: Consider the following example. Suppose that an initial $10 billion increase in investment spending expands GDP by $10 billion in the first round of the multiplier process. If GDP and consumption both rise by $6 billion in the second round of the process, what is the MPC in this economy? What is the size of the multiplier? If, instead, GDP and consumption both rose by $8 billion in the second round, what would have been the size of the multiplier? The initial $10 billion increase in investment spending expands GDP by $10 billion and income by $10 billion. Since consumption increases by $6 billion after the $10 billion increase in income the marginal propensity to consume equals 0.6. MPC = Δ Consumption/Δ Income = $6 billion/$10 billion =0.6 Given the MPC we can find the multiplier, which equals 2.5. The multiplier = 1/(1-MPC) = 1/(1-0.6) = 1 /0.4 If instead, GDP and consumption rose by $8 billion after the $10 billion increase, the MPC would have been 0.8. MPC = Δ Consumption/Δ Income = $8 billion/$10 billion =0.8 Given the MPC we can find the multiplier, which equals 5. The multiplier = 1/(1-MPC) = 1/(1-0.8) = 1/0.2 27-17 © 2012 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.