Answers to Text Questions and Problems. Chapter 22. Answers to Review Questions


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1 Answers to Text Questions and Problems Chapter 22 Answers to Review Questions 3. In general, producers of durable goods are affected most by recessions while producers of nondurables (like food) and services are affected least. Automobiles are durable goods, so the automobile producer would probably see its profits reduced the most, while the barbershop (which provides a service) will see the smallest decline in profit. Boots and shoes are semidurable, since a pair of shoes may last for several years and people can put off purchases of these for a while if necessary. Thus the boot manufacturer s losses are likely to fall in between those of the other two firms. 4. The natural unemployment rate is the sum of structural and frictional unemployment and excludes cyclical unemployment. Hence, the natural unemployment rate by definition should not be affected by a recession. Also by definition, the cyclical unemployment rate rises in recession. Inflation tends to decline in the period following a recession. Finally, poll ratings of presidents tend to be strongly correlated with the state of the economy, so a recession will probably reduce a president s popularity. 5. Potential output, or potential GDP, is the maximum sustainable amount of output (real GDP) that an economy can produce. Because inputs can be used at greater than normal rates for a time (for example, workers can work overtime and machines can be used at night or on weekends), it is possible for the economy to produce an amount exceeding potential output. 7. False. When output equals potential output, the unemployment rate equals the natural unemployment rate. Cyclical unemployment is zero when output equals potential output, but frictional and structural unemployment still exist. Answers to Problems 3. NOTE: this is different than in the galley proofs. We decided to extend the data to The data from the problem along with the output gap, the type of gap and the growth rate of real GDP are given in the table below: Year Real GDP Potential GDP Output gap Type of gap Growth rate of real GDP 999 $9,470 $9, % expansionary 2000 $9,87 $9, % expansionary 3.7% 200 $9,89 $9, % recessionary 0.8% 2002 $0,049 $0, % recessionary.6% 2003 $0,30 $0,50 .9% recessionary 2.5% 2004 $0,676 $0, % recessionary 3.6% 2005 $,003 $, % recessionary 3.% 2006 $,39 $, % recessionary 2.9% 2007 $,567 $, % recessionary 2.2%
2 The growth rate of GDP slowed to 0.8% in 200; growth accelerated from 2002 to 2004, corresponding to the official dating of the recession. Note, however, that a recessionary gap continued throughout the period, meaning that despite the resumption of normal growth rates the economy never caught up with potential after the 200 recession. 5. Working with Okun s law: a. In 200, real GDP is 2% below potential GDP, so cyclical unemployment is %. Since the actual unemployment rate is 6%, the natural rate must be 5%. b. In 20, the natural rate equals the actual rate, so cyclical unemployment equals zero. Okun s law implies that the output gap is therefore zero, and potential output equals the actual output level of 8,00. c. In 202, cyclical unemployment equals 4%  4.5% = 0.5%, so by Okun s Law the output is gap is %. This implies that real GDP is % larger than potential GDP, so real GDP must equal 8,282 (= (.0)(8200)). d. In 203, the output gap is 2% since real GDP is 2% above potential GDP. Using Okun s law, this implies that cyclical unemployment is %. Since the natural unemployment rate is 5%, actual unemployment is 4%. Chapter 23 Answers to Review Questions. The key assumption of the basic Keynesian model is that in the short run, firms meet demand at preset prices. The fact that firms produce to meet demand implies that changes in demand affect output in the short run. 2. There are many possible examples. Goods that are standardized and are bought and sold in large quantities, such as wheat or other commodities, tend to have rapidly adjusting prices since the benefits of setting up active auction markets for such goods usually exceeds the costs. Goods such as dresses or skirts, which are not standardized (they vary in size, color, style) and which are usually sold in retail stores one by one, tend to have prices that are changed less frequently. 3. Planned aggregate expenditure (PAE) is total planned spending on final goods and services. It consists of consumption spending, investment spending, and government purchases of goods and services, and net exports (exports less imports). Changes in output are cause changes in the income received by producers, which in turn affects consumption spending through the consumption function. Since consumption is a component of PAE, changes in output lead to changes in PAE. 4. Planned spending includes planned additions to inventories to firms. When firms actual sales differ from planned sales, the resulting additions to inventory will differ from what was planned, and actual spending will differ from planned spending. For example, suppose a firm planned to produce 00 units, sell 90 units to the public, and add 0 units to its inventory. But in fact the firm sells only 80 units and thus must add 20 units to inventory. The firm s planned inventory investment (a component of investment and thus total spending) was 0 units, but its actual inventory investment was 20 units. So the firm s actual investment spending (inclusive of inventory investment) is greater than it planned. On the other hand, if the firm sold all 00
3 units, it would add nothing to inventory, and its actual investment (including inventory investment) would be less than planned. 5. Figure 23.2 shows a consumption function. Consumption (C), is on the vertical axis and disposable income (Y T), is on the horizontal axis. a. A movement from left to right along the consumption function shows that consumption increases as disposable income increases. b. A parallel shift upward of the consumption function indicates that people are consuming more at any given level of disposable income. This implies that some factor other than a change in disposable income is stimulating consumption. 6. Figure 23.4 shows the Keynesian cross diagram. The 45degree line captures the definition of shortrun equilibrium output, ; this implies that shortrun equilibrium output must lie on this line. The flatter line, the expenditure line, shows how planned aggregate expenditure depends on output. Because increased output raises disposable income, which in turn increases consumption and planned aggregate expenditure, the expenditure line is upward sloping. Autonomous expenditure is given by the intercept of the expenditure line, the marginal propensity to consume equals the slope of the expenditure line, and shortrun equilibrium output is the point on the horizontal axis corresponding to the intersection of the expenditure line and the line. To find induced expenditure, draw a horizontal line from the intersection of and the expenditure line to the vertical axis. The difference between the resulting point on the vertical axis (which equals actual output) and the intercept of the expenditure line (which equals autonomous expenditure) equals induced expenditure. 7. The two factors cited in the text as causes of the 200 recession were a fall in consumer confidence and a credit crunch. A fall in consumer confidence reduces consumers willingness to spend at each level of disposable income (a fall in C ). A credit crunch reduces planned investment, I. Each of these leads to a reduction in autonomous expenditure. Graphically, a decline in autonomous expenditure shifts the expenditure line downward and lowers shortrun equilibrium output. (See Figure 23.5 for an illustration.) 8. The multiplier tells us the effect of a oneunit increase in autonomous expenditure on shortrun equilibrium output. The multiplier is greater than one because a oneunit increase in autonomous expenditure directly increases output by one unit and increases producers incomes by one unit. The increase in income leads to further spending on the part of producers, which raises income of other producers and increases their spending. This multipleround process of spending and income creation leads to a final increase in output that is greater than the oneunit initial impact. 9. The increase in government purchases raises autonomous expenditure by 50 units. The tax cut raises disposable income by 50 units, which also stimulates planned aggregate expenditure by increasing consumption spending. However, the tax cut raises autonomous expenditure by only 50 units times the marginal propensity to consume (mpc); since the mpc is less than one, the tax cut will increase autonomous expenditure by less than 50 units. Thus the increase in government purchases will have the greater impact on planned aggregate expenditure.
4 0. First, government spending and taxing decisions may affect potential output as well as planned aggregate expenditure. What the government spends its money on, as well as the incentive effects of changes in tax and transfer programs, need to be factored in when evaluating the effects of fiscal policy. The type of spending may affect longrun growth of potential output, as well as how tax policies affect labor supply decisions and investment decisions. Second, changes in government spending and taxing can affect the government s budget deficit, which in turn may affect longrun investment in capital goods and the growth of potential output. For example, an expansionary fiscal policy may boost planned aggregate expenditure in the short run, leading to increased output and employment, but it may also raise real interest rates if it reduces national saving (by increasing the government s budget deficit without an offsetting increase in private saving). The increased interest rates may reduce capital investment and longrun growth of output. Third, fiscal policy is relatively inflexible, with long legislative processes reducing the government s ability to quickly respond to output gaps. The delays in implementation may stem from the legislative process itself (budget recommendations are first presented to Congress by the President, then are often debated for months before finally becoming law, and may take effect months after this) or from political wrangling over spending and taxing priorities. Answers to Problems. Acme s planned investment in every case is $,500,000 (its planned expenditure on new equipment plus zero planned increase in inventories). The key to this problem is to find the amount of unplanned inventory investment Acme makes then add this to their planned investment to find Acme s actual investment. a. If Acme sells $3,850,000 worth of goods, it has unplanned inventory investment of $50,000 and total actual investment of $,650,000. b. If Acme sells $4,000,000 worth of goods as it planned, its actual investment of $,500,000 equals its planned investment. c. If Acme sells $4,200,000 worth of goods it must draw down $200,000 worth of goods from its existing inventory, implying that inventory investment is negative $200,000. Acme s actual investment in this case is $,500,000  $200,000 = $,300,000. Output equals shortrun equilibrium output in case b, where planned spending and actual spending are equal. 2. Working with the consumption function: a. Disposable income (beforetax income less taxes paid) and consumption are as follows: Beforetax income ($) Taxes paid ($) Disposable income ($) Consumption ($) 25,000 3,000 22,000 20,000 27,000 3,500 23,500 2,350 28,000 3,700 24,300 22,070 30,000 4,000 26,000 23,600
5 Graph: Consumption 24,000 23,500 23,000 22,500 22,000 2,500 2,000 20,500 20,000 9,500 2,000 22,000 23,000 24,000 25,000 26,000 27,000 Disposable income The marginal propensity to consume is the increase in consumption caused by a one dollar increase in disposable income. In this case, when disposable income increases by from 22,000 to 23,500, a rise of 500, consumption rises by 350. The mpc is therefore 350/500 = 0.9. We can confirm this by checking the other points on the consumption function. For example, when disposable income rises by another 800 (24,300 23,500), consumption rises by 720 (22,070 2,350), which is (0.9)(800). Similarly, if disposable income rises by yet another 700 (26,000 24,300), consumption rises by,530 (= (0.9)(700)). We can also find the intercept of the consumption function, C. Since the mpc is 0.9, we know the consumption function can be expressed as C = C + (0.9)(Y T). To find C, plug into the equation any of the numerical combinations of consumption and disposable income given above. For example, if we set C = 20,000 and Y T = 22,000, we get 20,000 = C + (0.9)(22,000), which implies C = 200. So the consumption function for the Simpsons is C = (0.9)(Y T). b. From the consumption function derived in part a, setting Y = 32,000 and T = 5,000, C = (0.9)(27,000) = 24,500. c. The consumption function shifts upward by 000 at each level of disposable income (that is, the vertical intercept, C, rises from 200 to 200.) The mpc is unaffected because the increase in consumption is the same at each level of disposable income. This implies that the graph makes a parallel upward shift and the slope, equal to the mpc, does not change. 3. Working with planned aggregate expenditure and its components: a. Begin with the definition of PAE: PAE = C + I p + G + NX
6 Next, substitute the components of PAE that are given in the problem: PAE = [800 + (0.6)(Y 500)] Collecting terms, we have: PAE = Y b. Autonomous expenditure is 3400 and induced expenditure is 0.6Y. 4. Finding shortrun equilibrium output in the basic Keynesian model: a. Numerical determination of shortrun equilibrium output: see the table below: Output (Y) Planned aggregate expenditure (PAE) Y  PAE? No No No YES No No No No No when output and PAE are equal to 8500, so Y = 8500 is the level of shortrun equilibrium output. b. From problem 3, we know that PAE = Y. To find shortrun equilibrium output we use the condition that defines shortrun equilibrium output, : Y = Y 0.4Y = 3400 Y = 8500 The result is the same as we found in part a. c. From problem 3 we know that full employment output (Y * ) is 9000, so the output gap, Y Y *, equals = As a percentage of full employment, the gap is  500/9000 = 5.6%. By Okun s Law, cyclical unemployment is minus one times onehalf of the output gap, or 2.8%. Since the natural rate is 4%, the actual unemployment rate is 4% + 2.8% = 6.8%. 5. Calculating the effects of changes in autonomous expenditure on shortrun equilibrium output: a. An increase in government purchases of 00 causes autonomous expenditure to rise from 3400 to Equilibrium output is found by setting :
7 Y = Y 0.4Y = 3500 Y = 8750 b. A decrease in tax collections of 00 causes autonomous expenditure to rise from 3400 to (Remember: the 00 unit decrease in T is multiplied by the mpc of 0.6 since the decrease in taxes affects consumption via disposable income.) Equilibrium output is found by setting : Y = Y 0.4Y = 3460 Y = 8650 c. A decrease in planned investment of 00 causes autonomous expenditure to fall from 3400 to Equilibrium output is found by setting : Y = Y 0.4Y = 3300 Y = 8250 All three examples demonstrate that the multiplier, equal to the change in output per  unit change in autonomous aggregate demand, is 2.5 for this economy. (For example, in part a, the 00 unit increase in government spending led to a 250 unit increase in shortrun equilibrium output.) We can verify this also by the formula for the multiplier, = = 2.5 mpc. In this economy, mpc = 0.6, so the multiplier is Using the multiplier to calculate changes in shortrun equilibrium output: a. The multiplier is given by mpc, where mpc is the marginal propensity to consume. = = 4 In this economy, mpc = 0.75, so the multiplier is Therefore, the recessionary gap will be four times the size of the fall in planned investment. b. To restore equilibrium at full employment, overall autonomous spending must increase to its previous level, so the increase in government spending required to close the recessionary gap will be just equal to the fall in planned investment. With a multiplier of 4, the change in output will be four times the change in government spending, offsetting the drop in output caused by the fall in planned investment. c. Again, to restore equilibrium at full employment, overall autonomous spending must increase to its previous level, but since consumers only spend 0.75 of any increase in disposable income, the reduction in taxes must be larger than the fall in planned investment. (If taxes were reduced by the amount of the change in planned investment, autonomous spending would increase by only 75% of this change, leaving the economy
8 with a recessionary gap.) Taxes therefore need to be reduced so that the resulting increase in autonomous consumer spending just equal the fall in planned investment. Mathematically, this implies the following: (0.75)(change in taxes) = (change in planned investment) Dividing both sides by 0.75, we have change in taxes = (.33)(change in planned investment) That is, taxes must be reduced by an amount that is 33% greater than the decline in planned investment that occurred. For example, if planned investment fell by $00 million, then taxes must be reduced by $33 million. With an increase of $33 in income, consumers will then spend 0.75 of this increase, leading to an increase in autonomous consumption of (approximately) $00 million. d. If the government increases government spending and taxes by the same amount, the result will be an increase in autonomous spending because the increase in government spending contributes fully to an increase in autonomous spending, while the decrease in taxes will only reduce autonomous consumer spending by 0.75 of the tax increase. Thus, for every dollar increase in government spending matched by a dollar increase in taxes (preserving the balanced budget), autonomous spending will increase by $0.25. To restore equilibrium in the economy, recall that overall autonomous spending must increase to its original level prior to the fall in investment spending. As a result, to move the economy to full employment, the government must increase spending (and taxes) by four times the fall in autonomous investment spending. The resulting increase in autonomous spending will just offset the fall in investment spending, restoring the original level of overall autonomous spending in the economy and increasing output back to the full employment level. 7. Working with the basic Keynesian model: a. To find planned aggregate expenditures (PAE), begin with the definition of PAE: PAE = C + I p + G + NX Next, substitute the components of PAE that are given in the problem: PAE = [40 + (0.8)(Y 50)] Collecting terms, we have: PAE = Y
9 b. The table below illustrates the level planned aggregate expenditure (PAE) for various output levels: Output (Y) Planned aggregate expenditure (PAE) Y  PAE Shortrun equilibrium output is 600 since this is the level of output at which. c. Since Y*=580, there is an expansionary output gap of 20. To eliminate the output gap, autonomous spending needs to be reduced or taxes raised. In the former case, with a multiplier of 5, government spending needs to be reduced by 4; this will lead to a decrease of 4 5 = 20 in output. In the latter case, overall autonomous spending needs to be reduced by 4; with an mpc of.8, an increase in taxes by 5 will lead to a reduction in autonomous spending of.8 5 = 4, which in turn will lead to reduction in output of 20, given the multiplier of 5. d. In the case where Y*=630, there is a recessionary gap of 30. To eliminate this output gap, autonomous spending needs to be increased or taxes reduced. In the former case, with a multiplier of 5, government spending needs to increase by 6; this will lead to an increase of 6 5 = 30 in output. In the latter case, overall autonomous spending needs to be increased by 6; with an mpc of.8, a reduction in taxes by 7.5 will lead to an increase in autonomous spending of = 6, which in turn will lead to an increase in output of 30, given the multiplier of 5. e. Graph:
10 Planned aggregate expenditure (PAE) Potential GDP = 580 Potential GDP = Working with the basic Keynesian model: a. To find planned aggregate expenditures (PAE), begin with the definition of PAE: PAE = C + I p + G + NX Next, substitute the components of PAE that are given in the problem: PAE = [3,000 + (0.5)(Y 2000)] +, , Collecting terms, we have: PAE = Y Autonomous expenditure is The multiplier is given by mpc, where mpc is the marginal propensity to consume. In = = = 2 this economy, mpc = 0.5 so the multiplier is mpc
11 Shortrun equilibrium output can be determined from a table showing the relationship between planned aggregate expenditure (PAE) or algebraically. In table form, Output (Y) Planned aggregate expenditure (PAE) Y  PAE 2,000 2, ,00 2, ,200 2, ,300 2, ,400 2, ,500 2, ,600 2, ,700 2, Equilibrium occurs at Y=2,400, i.e. where. Algebraically, equilibrium output is found by setting : Y = Y 0.5Y = 6200 Y = 2400 If Y* = 2,000, then there is an expansionary output gap of 400 in this economy. To eliminate this output gap, given the multiplier of 2, autonomous expenditure needs to be reduced by The role of net exports in recessions and expansions: a. We can find equilibrium output either using a table or using algebra. We present the algebraic solution here. Begin by finding planned aggregate expenditure (PAE): PAE = C + I p + G + NX PAE = [40 + (0.8)(Y 50)] PAE = Y Shortrun equilibrium output is found where : Y = Y 0.2Y = 0 Y = 550 b. Planned aggregate expenditures will then be given by PAE = C + I p + G + NX PAE = [40 + (0.8)(Y 50)] PAE = Y
12 Shortrun equilibrium output is found where : Y = Y 0.2Y = 20 Y = 050 Shortrun equilibrium output now 500 higher than the original equilibrium. This is what we would expect, since the multiplier for this economy is 5 (5 times the change in autonomous expenditure = (5)(00) = 500 = change in equilibrium output level.) c. Planned aggregate expenditures will then be given by PAE = C + I p + G + NX PAE = [40 + (0.8)(Y 50)] PAE = Y Shortrun equilibrium output is found where : Y = Y 0.2Y = 0 Y = 50 Shortrun equilibrium output now 500 lower than the original equilibrium. Again, this is what we would expect, since the multiplier for this economy is 5 (5 times the change in autonomous expenditure = (5)(00) = 500 = change in equilibrium output level.) d. Changes in autonomous spending in one country lead to changes in autonomous spending in other countries through NX. For example, suppose that U.S. consumers reduce their purchases when domestic income falls because of recession. Consumption spending (C) includes consumer purchases of both domestically produced goods and imported goods. (Remember: this is why NX is in PAE: we need to subtract out imported goods from PAE and add in foreign purchases of domestic goods so that PAE only includes purchases of domestic goods.) So, as U.S. imports decline, this causes exports from other countries to the U.S. to decline as well. This causes autonomous expenditure in other countries to fall, causing their shortrun equilibrium output levels to fall as well. Thus, a recession in the U.S. is spread to the rest of the world via changes in NX. The same reasoning works in the case of an expansion as well. 0. Automatic stabilizers and equilibrium output: a. We can solve for shortrun equilibrium output in the usual way, except that we will keep the equations in their general algebraic form (as in the Appendix to Chapter 23.) The first step is to find the relationship of aggregate demand to output:
13 PAE = C + I p + G + NX PAE = C + (mpc)(y T) + I + G + NX PAE = C + (mpc)(y ty) + I + G + NX PAE = C + I + G + NX + (mpc)( t)y Notice that, in this model, autonomous expenditure is expenditure is (mpc)(  t)y. C + I + G + NX and induced Shortrun equilibrium output is found where : Y = C + I + G + NX + (mpc)( t)y Y([ (mpc)( t)] = C + I + G + NX Y = (C + I + G + NX) (mpc)( t) The last line above gives an algebraic expression for shortrun equilibrium output in the model in which taxes are proportional to output. b. From the expression for shortrun equilibrium output in part a, we can see that a one unit increase in autonomous expenditure, C + I + G + NX, raises output by (mpc)( t) units, so (mpc)( t) is the multiplier. This multiplier is smaller than the standard multiplier, mpc, as can be verified algebraically or by trying numerical values for mpc and t. c. As we showed in part a, shortrun equilibrium output equals the multiplier times autonomous expenditure. For given fluctuations in autonomous aggregate demand, the smaller is the multiplier, the less output will fluctuate. So changes in the economy that reduce the multiplier, such as taxes that are proportional to output, tend to stabilize output for given fluctuations in autonomous expenditure. d. Plugging these values into the expression for output in part a, we get Y = ( ) 0.8( 0.25) Y = (4000) 0.6 Y = (2.5)(4000) = 0,000 = = = = 2.5 The multiplier is (0.8)( 0.25) (0.8)(0.75)
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