Chapter 16: Fiscal Policy

Transcription

1 Chapter 16: Fiscal Policy Yulei Luo SEF of HKU April 6, 2017

2 Learning Objectives 1. De ne scal policy. 2. Explain how scal policy a ects aggregate demand and how the government can use scal policy to stabilize the economy. 3. Use the dynamic aggregate demand and aggregate supply model to analyze scal policy. 4. Explain how the government purchases and tax multipliers work. 5. Discuss the di culties that can arise in implementing scal policy. 6. De ne federal budget de cit and federal government debt and explain how the federal budget can serve as an automatic stabilizer. 7. Discuss the e ects of scal policy in the long run.

3 What Fiscal Policy Is and What It Isn t I Fiscal policy (FP): Changes in federal taxes and purchases that are intended to achieve macroeconomic policy objectives: high employment, price stability, and high rates of economic growth. I The gov. can a ect the levels of both AD and AS through FP. Since WWII, the federal gov. has committed to intervening in the economy to promote maximum employment, production, and purchasing power. I Restrict the term scal policy to refer only to the actions of the federal gov (NOT state and local Gov.) because they are intended to a ect the national economy. I Not all actions of the federal gov are FP actions because some of them are not intended to achieve macro policy goals. I E.g., the increases in the defense and homeland security (HS) spending are not FP, but part of defense and HS policy.

4 How Much Government Spending Is Federal? Before the Great Depression of the 1930s, most government spending was at the state or local level; now the federal government s share is two-thirds to three-quarters. Figure 16.1 The federal government s share of total expenditures, of 68

5 Federal Expenditures as a Percentage of GDP As a percentage of GDP, federal expenditures are now higher than ever almost 25% of GDP. However a smaller proportion is now spent on government purchases of goods and services (mostly military spending). Figure 16.2 Federal purchases and federal expenditures as a percentage of GDP, of 68

6 What Does the Federal Government Spend Money On? Federal purchases consist of defense spending and everything else, like salaries of FBI agents, operating national parks, and funding scientific research. Around half of federal expenditures are spent on transfer payments, like Social Security, Medicare, and unemployment insurance. The rest is spent on grants to state and local governments to support their activities, like crime prevention and education; and on paying interest on the federal debt. Figure 16.3 Federal government expenditures, of 68

7 Where Does the Federal Government Get Money From? The majority of federal revenues come from taxes on individual employment: individual income taxes and payroll taxes earmarked to fund Social Security and Medicare. Taxes on corporate profits constitute about one-seventh of federal receipts. The remainder of federal revenue comes from excise taxes (on cigarettes, gasoline, etc.), tariffs on imports, and other fees from firms and individuals. Figure 16.4 Federal government revenue, of 68

8 Making the Connection Social Security and Medicare: Fiscal Time Bombs? Social Security and Medicare have helped to reduce poverty among the elderly, while Medicaid helps improve the health of poor people. But the aging population and rising health care costs are combining to put those programs in jeopardy. Through 2090, the budget shortfall for these programs is estimated to be enormous: almost $60 trillion. 10 of 68

9 Making the Connection Social Security and Medicare: Is There a Fix? How can these programs continue to exist? It is likely that a combination of these measures will eventually need to be adopted: Increasing taxes Decreasing benefits (including slower benefit growth, perhaps differently for different income groups) Decreasing eligibility (SSI age already increasing from 65 to 67) But perhaps the most important element will be finding a way to reduce medical costs. 11 of 68

10 Distinction bw. automatic stabilizers and discretionary FP I Automatic stabilizers: Government spending and taxes that automatically increase or decrease along with the business cycle: I I E.g., when the economy is in expansion, gov spending on UI payments to unemployed workers will automatically decrease. Similarly, during the expansion, income is rising, and the amount the gov collects in taxes will increase. I Discretionary FP: The gov. takes actions to change spending or taxes. E.g., the tax cuts passed by Congress in 2001.

11 An Overview of Government Spending and Taxes I Federal gov. expenditures include purchases plus all other federal gov. spending. I In addition to purchases, there are three other categories of federal gov. expenditures: I I I Interest on the national debt, which represents payments to holders of the bonds the federal gov. has issued to borrow money. Grants to state and local governments, which are payments made by the federal gov. to support government activity at the state and local levels. Transfer payments, which include Social Security, Medicare, unemployment insurance, and programs to aid the poor, is the largest and fastest-growing category of federal expenditures.

12 I The gov can also use stabilization policy through changes in gov. spending and taxes to o set the e ects of BC on the economy. I Changes in gov. spending and taxes lead to changes in AD, so they can a ect the levels of real GDP, employment, and the PL. I When the economy is in a recession, increases in gov. purchases or decreases in taxes will increase AD directly or indirectly. Consequently, the in ation rate may increase when AD is increasing faster than AS.

13 Expansionary Fiscal Policy in the AD-AS Model Expansionary fiscal policy involves increasing government purchases or decreasing taxes. Increasing government purchases directly increases aggregate demand. Decreasing taxes indirectly affects aggregate demand by increasing disposable income, and hence consumption spending. Figure 16.5a Fiscal policy If the government believes real GDP will be below potential GDP, it can enact expansionary fiscal policy in an attempt to restore longrun equilibrium decreasing unemployment. 13 of 68

14 Contractionary Fiscal Policy in the AD-AS Model Contractionary fiscal policy involves decreasing government purchases or increasing taxes. This works just like expansionary fiscal policy, only in reverse. Figure 16.5b Fiscal policy If the government believes real GDP will be above potential GDP, it can enact contractionary fiscal policy in an attempt to restore longrun equilibrium decreasing inflation. 14 of 68

15 Summarizing Fiscal Policy Problem Type of Policy Actions by Congress and the President Recession Expansionary Increase government spending or cut taxes Rising inflation Contractionary Decrease government spending or raise taxes Result Real GDP and the price level rise. Real GDP and the price level fall. Table 16.1 Countercyclical fiscal policy The federal government s actions described on the previous slides constitute a countercyclical fiscal policy. Bear in mind that: The effects described assume ceteris paribus: everything else is staying the same, including monetary policy. Contractionary fiscal policy is not really causing prices to fall; it s causing inflation to be lower than it otherwise would have been. 15 of 68

16 Static vs. Dynamic Model Our model of fiscal policy so far is static: it assumes long-run potential GDP does not change, and that the price level is constant. While the lessons from this model are still appropriate Congress and the president can use fiscal policy to affect real GDP and the price level our understanding of fiscal policy can be improved by seeing it in the dynamic aggregate demand and aggregate supply model. 17 of 68

17 Expansionary Fiscal Policy in the Dynamic AD-AS Model Initially, the economy is in long-run equilibrium. The federal government projects that aggregate demand will not rise by enough to maintain full employment. It enacts an expansionary fiscal policy to increase aggregate demand, hopefully to the full employment level. The price level is higher than it would have been without the expansionary fiscal policy. Figure 16.6 An expansionary fiscal policy in the dynamic model 18 of 68

18 Contractionary Fiscal Policy in the Dynamic AD-AS Model The economy starts once more in long-run equilibrium. The federal government projects that aggregate demand will rise so much that employment is beyond the fullemployment level, causing high inflation. It enacts a contractionary fiscal policy to decrease aggregate demand, again ideally to the full employment level. Figure 16.7 A contractionary fiscal policy in the dynamic model 19 of 68

19 The Government Purchases Multiplier I Economists refer to the initial increase in gov. purchases as autonomous because it is a result of a decision by the government and is not directly caused by changes in the level of real GDP. I The initial increase in gov. purchases (as a component of AD, autonomous expenditures) will lead to additional increases in income and spending. I E.g., when using $100 billion to build subways, the gov. hires private rms. These rms will hire more workers and the newly hired workers will increase their spending on consumption goods. Sellers of these goods will increase their production and employment. At each step, real GDP and income increases, thereby increasing consumption and AD. I Multiplier e ect The series of induced increases in consumption spending that results from an initial increase in autonomous expenditures.

20 The E ect of Changes in Tax Rates I A change in tax rates has more complicated e ects on real GDP than does a tax cut of a xed amount. I The higher the tax rate, the smaller the multiplier e ect. The reason is that the higher the tax rate, the smaller the available amount of any increase in income caused by an increase in gov purchases. I A cut in tax rates a ects equilibrium GDP through two channels: 1. A cut in tax rates increases the disposable income, which increases consumption, 2. a cut in tax rates increases the size of the multiplier e ect.

21 Aggregate Demand and the Multiplier Effect If the government increases its spending on goods and services, then aggregate demand increases immediately. This is the autonomous increase in aggregate demand. But then people receive this increased spending as increased income and increase their consumption spending accordingly. This is the induced increase in aggregate demand. The series of induced increases in consumption spending that results from the initial increase in autonomous expenditures is known as the multiplier effect. Figure 16.8 The multiplier effect and aggregate demand 21 of 68

22 Multiplier Effect of an Increase in Government Purchases Suppose each increase in spending induces half again as much consumption spending. Over time, a $100 billion increase in government purchases will result in an additional $100 billion in induced consumption spending. Figure 16.9 The multiplier effect of an increase in government purchases 22 of 68

23 Multipliers for Government Purchases and Taxes We can describe the total effect of a change (increase or decrease) in government purchases or taxes by measuring the change in equilibrium real GDP. Government purchases multiplier = Change in equilibrium real GDP Change in government purchases Tax multiplier = Change in equilibrium real GDP Change in taxes The tax multiplier will be a negative number: an increase in taxes will decrease equilibrium real GDP, and vice versa. We expect the tax multiplier to be smaller (in absolute value) than the government purchases multiplier. Why? A $100 billion increase in purchases initially increases spending by $100 billion, but a $100 billion tax cut is partially spent and partially saved. 23 of 68

24 The Multipliers Work in Both Directions I Increases in government purchases and cuts in taxes have a positive multiplier e ect on equilibrium real GDP. I Decreases in government purchases and increases in taxes also have a multiplier e ect on equilibrium real GDP, only in this case, the e ect is negative. I We look more closely at the government purchases multiplier and the tax multiplier in the appendix to this chapter.

25 Timing is also Important to Conduct Fiscal Policy I If the gov. decides to increase spending or cut taxes to ght a recession that is about to end, the e ect may be to increase the in ation rate. I If the gov. decides to reduce spending or increase taxes to slow down the economy that actually already moved into recession can make the recession longer and deeper. I The delays caused by the legislative process can be very long. Even after a change in scal policy has been approved, it takes time to implement the policy. I Getting timing right can be more di cult with FP than with MP. The Fed then plays a larger role in stabilizing the economy because it can quickly change MP i.r.t. changing economic conditions.

26 Does Government Spending Reduce Private Spending? I Using gov spending to increase AD cause a potential problem. I The size of the multiplier e ect may be limited if the increase in gov. purchases causes one of the nongovernment, or private, components of aggregate expenditures consumption, investment, or net exports to fall. I Crowding out: A decline in private expenditures (consumption, investment, or net exports) as a result of an increase in government purchases.

27 Taking into Account the Effects of Aggregate Supply An increase in aggregate demand will not only result in real GDP rising; it will also result in a price level increase, because the short-run aggregate supply curve is upward-sloping. Suppose that between the autonomous and induced effects, fiscal policy causes aggregate demand to increase by $1.2 trillion. The resulting real GDP increase is smaller only $1.0 trillion. The price level also rises. Figure The multiplier effect and aggregate supply 25 of 68

28 Crowding Out in the Long Run I Economists disagree on the extent of crowding out in the SR. Most economists agree that the LR crowding out e ect of a permanent increase in gov spending is complete and the decline in C, I, and NE, exactly o sets the increases in gov. purchases, and AD remains unchanged. I To understand crowding out in the LR, recall that in the LR, the economy returns to potential GDP. If gov purchases are increased permanently, in the LR, private expenditures must fall the same amount to keep the potential GDP at the same level.

29 Crowding Out in the Short Run Money Market A temporary increase in government purchases will cause the demand for money, and hence the interest rate, to rise. But with the higher interest rate, consumption, investment, and net exports all fall. Figure An expansionary fiscal policy increases interest rates 29 of 68

30 Crowding Out in the Short Run AD-AS Model A temporary increase in government purchases will cause the demand for money, and hence the interest rate, to rise. With the higher interest rate, consumption, investment, and net exports all fall. So the initial increase in spending is partially offset by the crowding out. Figure The effect of crowding out in the short run 30 of 68

31 Crowding Out in the Long Run In the long run, the increase in government purchases will have no effect on real GDP; the reduction in consumption, investment, and net exports will exactly offset the increase in government purchases. Why? Because in the long run, the economy returns to potential GDP, even without the government s intervention. The long run effect is simply to increase the size of the government sector within the economy. Bear in mind that the long run may be many years away, however, so the intermediate increase in real GDP may be worth the cost. 31 of 68

32 Fiscal Policy in Action: Did the Stimulus Package of 2009 Work? I Congress enacted a tax cut totaling $95 billion that took the form of rebates of taxes already paid that were sent to taxpayers between April and July I One-time tax rebates increase consumers current income but not their permanent income, which re ects their expected future income. I Since only a permanent decrease in taxes increases consumers permanent income, a tax rebate is likely to increase consumption spending less than would a permanent tax cut.

33 Fiscal Policy in Action: The Recession In early 2008, believing a recession was imminent, Congress authorized a tax cut: a one-time rebate of taxes already paid, totaling $95 billion. This resulted in a boost to consumers current incomes. Changes to current incomes result in smaller increases in spending than changes to permanent incomes, because people seek to smooth their consumption over time. Economists estimate that consumers spent about 33-40% of the rebates they received, so the tax cut resulted in about $35 billion in increased spending. 32 of 68

34 American Recovery and Reinvestment Act of 2009 Figure The 2009 stimulus package In 2009, Congress passed the stimulus package, a combination of increased government spending (about two-thirds) and decreased taxes (about one-third). At $840 billion, the stimulus package was by far the largest fiscal policy action in U.S. history. 33 of 68

35 The Effect of the Stimulus on the Federal Budget The effect of the stimulus package on federal expenditures and revenue was not immediate, but it mostly occurred over the following two years. (a) The effect on expenditures (b) The effect on revenues Figure The effect of the stimulus package on federal expenditures and revenue 34 of 68

36 How Effective Was the Stimulus Package? When the stimulus was passed, Obama administration economists believed that by the end of 2010, it would: Increase real GDP by 3.5% Increase employment by 3.5 million By the end of 2010, real GDP actually rose by 4.4% but employment fell by 3.3 million. Did the stimulus fail? To judge the effect of the stimulus package, we have to measure its effects holding constant all other factors affecting real GDP and employment. Isolating the effects of the stimulus package is very difficult; economists still differ in their views about how effective the stimulus package was. 35 of 68

37 CBO Estimates of the Effects of the Stimulus Year The Congressional Budget Office (CBO) is a non-partisan organization that estimates the effects of government policies. The table shows CBO estimates of the effect of the stimulus package on economic variables, relative to what would have happened without the stimulus package: The CBO s conclusion: the stimulus package reduced the severity of the recession but did not come close to bringing the economy back to full employment. Change in Real GDP Change in the Unemployment Rate Table 16.2 Change in Employment (millions of people) % to 1.8% 0.1% to 0.5% 0.3 to % to 4.1% 0.4% to 1.8% 0.9 to % to 2.3% 0.2% to 1.4% 0.6 to % to 0.8% 0.1% to 0.6% 0.2 to % to 0.4% 0% to 0.3% 0.1 to 0.5 CBO estimates of the effects of the stimulus package 36 of 68

38 Making the Connection Why Was the Recession of So Severe? The recession of was the worst recession to hit the United States since the Great Depression of the 1930s. Duration Decline in Real GDP Peak Unemployment Rate Average for postwar recessions 10.4 months 1.7% 7.6% Recession of months 4.1% 10.0% The Great Depression of the 1930s was accompanied by a financial crisis just like the recession of Are recessions generally worse when they are accompanied by a financial crisis? 37 of 68

39 Making the Connection The Recession of continued After studying recessions accompanied by financial crises worldwide, economists Carmen Reinhart and Ken Rogoff say that such recessions are much more severe than average: Economic Variable Average Change Average Duration of Change Number of Countries Unemployment rate +7 percentage points 4.8 years 14 Real GDP per capita 9.3% 1.9 years 14 Real stock prices 55.9% 3.4 years 22 Real house prices 35.5% 6 years 21 Real government debt +86% 3 years 13 Note: Data above do not include the U.S. recession of Most people did not see the financial crisis coming, so they also underestimated how severe the recession would be. 38 of 68

40 Estimates of the Size of Multipliers How large are the multipliers for government purchases and for taxes? This question is very difficult to answer, and different economists produce different estimates: Economist Congressional Budget Office Lawrence Christiano, Martin Eichenbaum, and Sergio Rebelo Tommaso Monacelli, Roberto Perotti, and Antonella Trigari, Universita Bocconi Ethan Ilzetzki, London School of Economics, Enrique G. Mendoza, and Carlos A. Vegh, University of Maryland Valerie Ramey, University of California, San Diego Robert J. Barro, Harvard University, and Charles J. Redlick, Bain Capital, LLC Type of Multiplier Government purchases Government purchases Government purchases Government purchases Military expenditure Military expenditure Size of Multiplier (when short-term interest rates are not zero); 3.7 (when short-term interest rates are expected to be zero for at least five quarters) 1.2 (after one year) and 1.5 (after two years) (after one year) and (after two years) Table 16.3 Estimates of the size of the multiplier 39 of 68

41 Estimates of the Size of Multipliers continued Economist Type of Multiplier Size of Multiplier John Cogan and John Taylor, Stanford University, and Tobias Cwik and Volker Wieland, Gothe University Christina Romer, University of California, Berkeley, and Jared Bernstein, chief economist and economic policy adviser to Vice President Joseph Biden Christina Romer (prior to serving as chair of the Council of Economic Advisers) and David Romer, University of California, Berkeley A permanent increase in government expenditures A permanent increase in government expenditures Tax 2 3 Congressional Budget Office Tax (two-year tax cut for lowerand middle-income people) and (one-year tax cut for higher-income people) Robert J. Barro, Harvard University, and Charles J. Redlick, Bain Capital, LLC Tax 1.1 Table 16.3 continued Estimates of the size of the multiplier 40 of 68

42 De cits, Surpluses, and Federal Government Debt I The Fed gov s budget shows the relationship bw its expenditures and its tax revenue. I Budget de cit: The situation in which the government s expenditures are greater than its tax revenue. I Budget surplus: The situation in which the government s expenditures are less than its tax revenue.

43 The Federal Budget Deficit, The U.S. federal government does not generally balance its budget. Sometimes its revenues are higher than its expenditure, but usually the reverse is true especially during wartime. Figure The federal budget deficit, of 68

44 How the Federal Budget Can Serve as an Automatic Stabilizer I Discretionary FP can increase the federal budget def. during recessions by increasing spending or cutting taxes to increase AD. I In fact, most of the increase in the federal budget def. during recessions take places without Congress or the president taking any action because of the e ect of Auto. Stabilizers: I During a recession, wages and pro ts fall, causing gov. tax revenues to fall. The gov. automatically increases its spending on transfer payments when the economy moves into recession. I Because budget def. automatically increase during recessions and reduce during expansions, economists often look at the Cyclically adjusted budget de cit or surplus which is the de cit or surplus in the federal gov s budget if the economy were at potential GDP. I It provides a better measure of the e ects of FP on the economy than the actual budget de cit or surplus.

45 Should the Federal Budget Always Be Balanced? I Many economists believe that it is a good idea for the federal government to have a balanced budget when the economy is at potential GDP. I Few economists believe that the gov should attempt to balance its budget every year: I During a recession (expansion), the federal budget automatically moves into de cit (surplus). To bring the budget back into balance, the gov would have to increase (cut) taxes or cut (increase) spending, but these actions would reduce (increase) AD, thereby making the recession worse (raising the risk of higher in ation).

46 Is the Government Debt a Problem? I Debt can be a problem for a gov for the same reasons that debt can be a problem for a HH or a rm. I If a family is unable to make the monthly payments on its house, it will have to default on the loan and will lose its house. The fed gov. is in no danger of defaulting on its debt because the gov. can raise the funds through taxes to make the interest payments on the debt. I Interest payments accounts for 10% of total federal expenditures. At this level, tax increases or signi cant cutbacks on other types of spending are not required. I In the LR, crowding out of investment means a lower capital stock may occur if an increasing debt drives up IRs. Lower investment reduces the capacity of the economy to produce G&S. I This e ect is somewhat o set if some of the gov. debt was incurred to nance improvements in infrastructure, such as bridges, highways, and ports; to nance education; or to nance R&D.

47 Making the Connection Did Fiscal Policy Fail during the Great Depression? Government expenditures increased after the Great Depression of the 1930s as part of the New Deal, enacted by Franklin D. Roosevelt. Similarly, there was a budget deficit each year in the 1930s (except 1937). However recovery from the Great Depression was painfully slow. Does this show that expansionary fiscal policy didn t work during the 1930s? In fact, when we cyclically-adjust the budget deficits of the 1930s, we find that the federal government was not using expansionary fiscal policy at all. It had a cyclically adjusted budget surplus instead. 45 of 68

48 Making the Connection Year Fiscal Policy during the Great Depression Federal Government Expenditures (billions of dollars) Actual Federal Budget Deficit or Surplus (billions of dollars) Cyclically Adjusted Budget Deficit or Surplus (billions of dollars) Cyclically Adjusted Budget Deficit or Surplus as a Percentage of GDP 1929 $2.6 $1.0 $ % E. Cary Brown: Fiscal policy, then, seems to have been an unsuccessful recovery device in the thirties not because it did not work, but because it was not tried. 46 of 68

49 Federal Government Debt When the federal government runs a budget deficit, it finances its activities by selling Treasury securities. The total value of those securities outstanding is known as the federal government debt, or the national debt. The national debt increased dramatically as a percentage of GDP during the two world wars and the two worst recessions. It is now at its highest level since Figure The federal government debt, of 68

50 The Long-Run E ects of Tax Policy I Because scal policy actions primarily a ect aggregate supply rather than aggregate demand, they are sometimes referred to as supply-side economics. I Some FP actions are intended to have LR e ects by expanding the productive capacity of the economy and increasing the rate of EG. I Tax wedge: The di erence between the pre-tax and post-tax return to an economic activity. I We can brie y look at the e ects on AS of cutting each of the following taxes: 1. Individual income tax. Reducing the marginal tax rates on individual income will reduce the tax wedge faced by: (1) workers, thereby increasing the quantity of labor supply; (2) savers, thereby increasing the amount saved; (3) entrepreneurs, thereby increasing the number of new businesses.

51 I 2. (Conti.) Corporate income tax. Cutting the marginal CI tax rate would encourage investment by increasing the return corporations receive from new investments. At the same time, it also increase the pace of technological process. 3. Taxes on dividends and capital gains. Lowering the tax rates on dividends and capital gains increases the supply of loanable funds from hhs to rms, increasing saving and investment and lowering the equilibrium real IR.

52 Tax Simpli cation I There are also gains from tax simpli cation because it can: I I reduces the resources used to deal with tax payments. E.g., some resources used by the tax preparation industry can be used to produce other G&S. increase economic e ciency by reducing the number of decisions made by hhs and rms to reduce their tax payments. The decisions of HHs and rms are distorted by the complexity of the tax code.

53 The Economic Effect of Tax Reform Tax reform has the potential to significantly increase real GDP in the long run beyond the increases that would otherwise occur. The magnitude of the effect is uncertain, however. For example, while people might like to work more if tax Figure The supply-side effects of a tax change rates are lowered, they might be constrained by employers expecting a particular work week (like 40 hours). Economists believe that more study is needed on the impact of tax reforms. 55 of 68

54 How Large Are Supply-Side E ects? I Most economists would agree that there are supply-side e ects to reducing taxes: I Decreasing marginal income tax rates will increase the quantity of labor supplied, cutting the corporate income tax will increase investment spending, and so on. I The magnitude of the e ects is the subject of considerable debate, however. Economists who are skeptical of their magnitude believe that tax cuts have their greatest e ect on AD rather than on AS. I Ultimately, the debate over the size of the supply-side e ects of tax policy may subside over time as more studies are conducted on the e ects of di erences in tax rates on labor supply and on saving and investment decisions.

55 A Closer Look at the Multiplier Our objective in this appendix is to develop an econometric model for how real GDP is determined. Then we will use that model to identify: 1. The government purchases and tax multipliers 2. How those multipliers are altered by tax rates 3. How those multipliers change in an open economy, i.e. when net exports change in response to income changes. Throughout, we will assume that price levels do not change. 59 of 68

56 Finding Equilibrium GDP (Simple Version) setup For simplicity, we will initially assume that taxes do not depend on income (i.e. they are a fixed amount), there are no government transfers to households, and there are no imports or exports. (1) C = 1, (Y T) Consumption function (2) I = 1,500 Planned investment function (3) G = 1,500 Government purchases function (4) T = 1,000 Tax function (5) Y = C + I + G Equilibrium condition These numbers are in billions of dollars, except the marginal propensity to consume (MPC) of (Y-T) is disposable income. Then we can write: Y = 1, (Y 1,000) + 1, , of 68

57 Finding Equilibrium GDP (Simple Version) cont. Y = 1, (Y 1,000) + 1, ,500 = 1, Y , ,500 Subtracting 0.75Y from both sides, we obtain: Y 0.75Y = 1, , , Y = 3,250 3,250 Y = = 13, Thus we conclude that according to our model, real GDP will be $13 trillion. 61 of 68

58 An Algebraic Expression for Equilibrium Real GDP Instead of inserting numbers, we could find an expression for real GDP algebraically. Let: (1) C = C + MPC(Y T) Consumption function (2) I = I Planned investment function (3) G = G Government purchases function (4) T = T Tax function (5) Y = C + I + G Equilibrium condition (The letters with bars represent fixed or autonomous variables.) Then: Y = C + MPC( Y T ) + I + G Y MPC( Y ) = C ( MPC T ) + I + G Y (1 MPC) = C ( MPC T ) + I + G Y = C ( MPC T ) + 1 MPC I + G 62 of 68

59 A Formula for the Government Purchases Multiplier Any change in an autonomous variable will change the value of real GDP (Y). We can make that explicit by writing the variables in change form: Y = C ( MPC T ) + I 1 MPC + G This uses the standard notation of for change. Keeping autonomous consumption (C), taxes (T), and investment (I) constant, we get: Y G = 1 MPC Divide both sides by G to obtain the government purchases multiplier: Y G 1 = 1 MPC For example, if MPC = 0.75, the government purchases multiplier will be: This image cannot currently be displayed. 63 of 68

60 A Formula for the Tax Multiplier Let s start again with the algebraic expression for real GDP: Y = C ( MPC T ) + I 1 MPC + G Now we will keep autonomous consumption (C), investment (I), and government purchases (G) constant: MPC T Y = 1 MPC Divide both sides by T to obtain the tax multiplier: Y MPC = T 1 MPC For example, if MPC = 0.75, the tax multiplier will be: 0.75 = A $10 billion increase in taxes decreases real GDP by $30 billion. 64 of 68

61 The Balanced Budget Multiplier Suppose we increase government spending and taxes both by $10 billion. What would happen to real GDP? Increase in real GDP from the 1 = $10 billion increase in government purchases 1 MPC Decrease in real GDP from the MPC = $10 billion increase in taxes 1 MPC Adding these effects and factoring out the $10 billion gives: $10 billion We can simplify this to: 1 MPC + 1 MPC 1 MPC 1 MPC $ 10 billion = $10 billion 1 MPC So the balanced budget multiplier is 1: equal dollar increases in government spending and taxes increase real GDP by that amount at least, in the short run. 65 of 68

62 Incorporating Tax Rates In our model, taxes were autonomous. Now, we will make them depend on income. Assuming a tax rate of t, consumers will now have disposable incomes of (1-t)Y. So the consumption function changes to: C = C + MPC( 1 t) Y Going through the same steps as before, we can obtain: Government purchases multiplier = If MPC = 0.75 and t = 0.2, then: Y G 1 = 1 MPC(1 t) Y 1 1 Government purchases multiplier = = = = G (1 0.2) If the tax rate t falls to 0.1, the multiplier becomes: Y 1 1 Government purchases multiplier = = = = 3.1 G (1 0.1) So lower tax rates yield larger multipliers of 68

63 The Multiplier in an Open Economy Now suppose we have imports and exports. Assume exports are autonomous, but the level of imports depends on income: Exports = Exports Imports = MPI Y Here MPI is the marginal propensity to import: the fraction of additional income spent on imported goods. Now we can write net exports as [ Exports ( MPI Y )] Inserting this into our equation for equilibrium real GDP we get: Y = C + MPC( 1 t) Y + I + G + [ Exports ( MPI Y )] Following the same process as before, we can obtain a new expression for the government purchases multiplier: Y Government purchases multiplier = G 1 = 1 [ MPC(1 t) MPI] 67 of 68

64 The Multiplier in an Open Economy continued Government purchases multiplier = Y G Let MPC = 0.75, t = 0.2, and MPC = 0.1. Then: 1 = 1 [ MPC(1 t) MPI] Y 1 1 Government purchases multiplier = = = = G 1 (0.75(1 0.2) 0.1) This is smaller than the multiplier from before; a portion of spending goes on imports, which do not feed back in to higher income in our country. 2 If MPI increases to 0.2, then we have: Y 1 1 Government purchases multiplier = = = = 1.7 G 1 (0.75(1 0.2) This is smaller still. An increase in the amount of additional income leaving the country as payments for imports decreases the multiplier effect of additional government purchases. 68 of 68