Ch22

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Chapter 22 Adding Government and Trade to the Simple Macro Model

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Learning Objectives 1. Describe how the government budget surplus is related to national income. 2. Explain how net exports are related to national income. 3. Distinguish between the marginal propensity to consume and the marginal propensity to spend. 4. Explain why the presence of government and foreign trade reduces the value of the simple multiplier. 5. Explain how government can use fiscal policy to influence the level of national income.

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22.1 Introducing Government Government Spending Government purchases of goods and services, G, are part of desired aggregate expenditures. Transfer payments (Tr) are not government purchases — they only affect aggregate expenditure through their effect on disposable income.

Tax Revenues Net tax revenue is defined as total tax revenue (Tx) received by the government minus total transfer payments (Tr) made by the government — it is denoted T. (T = Tx – Tr)

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The Budget Balance The budget balance is the difference between government revenue and government expenditures: T - G. When revenues exceed expenditures, there is a budget surplus. When expenditure exceeds revenues, there is a budget deficit.

The Public Saving Function We assume that G is autonomous with respect to national income, Y. However, as Y increases, net taxes rise — tax revenues rise (Tx) and transfers payments fall (Tr).

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Government Expenditure Function Desired government expenditure is treated as autonomous – completely unrelated to the current level of Y We can write

G=G

Were G is determined by – what governments do! the budget process! election cycles!

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Government Expenditure Function (what does it look like?)

Desires Government Expenditures

G

200

150 100 0

Government spending increases

G’ G Government spending cuts

G’’ Y Actual National Income

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Government Net Tax Function Desires Net Taxes

T = tY

T 200 T0 = tY0

Governments set the tax rate (t) but Y determines the total taxes paid (T)

150 T1 = tY1 100 0 -100 -150

Y1

Y0

Y Actual National Income

Recall Net taxes (T = Tx - Tr)

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Government Net Tax Function (what does it look like?) Desires Net Taxes

T

Net tax increases

T’ = t’Y T= tY T’’ = t’’Y

200 T0’ T0 T0’’

Net tax decrease

100 0 -100 -150

Y0

Y Actual National Income

Note: t’ > t > t’’

The Public Saving Function As national income rises, the budget surplus (public saving) increases. The slope of the public saving function is equal to the net tax rate.

Public Saving

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T-G 0

300

Y 150 300 525 600 900

600

900 Actual National Income

G T = 0.1 x Y T-G 51 15 -36 51 30 -21 51 52.5 1.5 51 60 9 51 90 39

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Provincial and Municipal Governments When measuring the overall contribution of government to desired aggregate expenditure and to public saving, all levels of government must be included. This is particularly important in Canada, where the combined purchases of provincial and municipal governments are larger than those of the federal government.

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Summary 1. All levels of government add directly to aggregate expenditure. 2. Governments also collect taxes and make transfer payments. 3. Government purchases and taxation, taken together, imply the public saving function, T-G.

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22.2 Introducing Foreign Trade The Net Export Function Canada’s exports are autonomous with respect to Canadian national income. In contrast, desired imports rise as Canadian national income increases. The marginal propensity to import is the change in imports that results from a $1 change in national income. IM = mY Where m is the marginal propensity to import Overall net exports, X – IM, falls as national income rises. This relationship is called the net export function.

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net exports, (NX = X – IM) is also referred to as the Balance of Trade if NX = X – IM > 0 NX = X – IM = 0 NX = X – IM < 0

then we have a trade surplus a trade balance a trade deficit

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Y 0 300 600 720 900

X 72 72 72 72 72

IM = 0.1 x Y 0 30 60 72 90

NX 72 42 12 0 -18

Imports and Exports

What Does the Net Export Function Look Like?

The NX function is drawn holding constant: • domestic and foreign prices, • and the exchange rate.

IM = 0.1Y

72

X = 72

48 24 0

300

600

900

Y

72 Net Exports

• foreign national income,

96

NX = 72 - 0.1Y

48 24 0

-24

300

600

900

Y

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Shifts in the Net Export Function Foreign Income An increase in foreign income, ceteris paribus, will lead to an increase in the quantity of Canadian goods demanded by foreign countries. This increases X and shifts up the NX function.

Relative International Prices A rise in Canadian relative to foreign prices reduces Canadian exports, decreasing X. The IM function also rotates up since Canadians now spend a higher fraction of income on foreign goods. The NX (=X-IM) function shifts down and also gets steeper.

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An important source of such relative prices changes is change in exchange rates. An appreciation of the Canadian dollar will increase Canadian prices relative to foreign prices.

IM´

IM X X´

Actual National Income Net Exports

This diagram illustrates the case of an increase in Canadian prices relative to foreign prices.

Imports and Exports

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(X - IM)

(X - IM)´ Actual National Income Copyright © 2005 Pearson Education Canada Inc.

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22.3 Equilibrium National Income Desired Consumption and National Income When taxes are included, disposable income (YD) is less than national income (Y). Suppose T = (0.1)Y. Then since YD = Y-T and since T = (0.1)Y is must be that YD = Y- (0.1)Y YD = (1 - 0.1) Y or YD = (0.9)Y How does this alter the simple consumption function?

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How does this alter the simple consumption function? C = 30 + (0.8)YD C = 30 + (0.8)(0.9)Y C = 30 + (0.72)Y

With income taxes, the MPC out of national income (0.72) is less than the MPC out of disposable income (0.8).

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The simple consumption function with taxes is written as: C = a + bYD where YD = Y - tY so that C = a + b(Y-tY) or C = a + b(1-t)Y If b = 0.8 and t = 0.1, then b(1-t) = 0.72 and C = a + 0.72Y C

a

Slope = b(1-t) Notice that the slope of the consumption function decreases as t (the marginal Slope = b(1-t’) tax rate) increases. This will cause the slope of the AE line to decrease also. Y

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The AE Function We can now expand the AE function to include net exports. AE = C + I + G + NX Recall that the slope of the AE function is the marginal propensity to spend out of national income — we call this z. Suppose Y rises by $1. Then an additional 72 cents is spent on consumption, but 10 cents of the extra consumption is on imports. Therefore, desired spending on domestic production rises by only 62 cents — z is 0.62.

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Equilibrium National Income As before, equilibrium occurs where desired aggregate expenditure equals actual national income. What happens if AE > Y? When households, firms, and governments try to spend their desired amounts, they will find that production is insufficient to meet their demand. This will deplete inventories and lead domestic firms to increase production. If AE < Y, then desired aggregate spending is less than current production. Inventories will build up, and firms will reduce their production.

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The Saving-Investment Approach This approach is more complicated with government and international trade. We must think about desired national saving and desired national asset formation. National Saving National saving is the sum of private saving and public saving (government’s budget surplus): National Saving = S + (T - G) As national income rises: • public saving rises (budget surplus), and • private saving rises (saving function). Copyright © 2005 Pearson Education Canada Inc.

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National Asset Formation In a closed economy, the only way to accumulate assets is to devote some of national product toward investment. In an open economy, however, there is an additional way to accumulate assets: we can purchase income-earning assets from foreigners (stocks or bonds). A country that exports more goods and services than it imports must use the “extra earnings” to buy income-earning assets such as stocks or bonds. So: National asset formation = I + (X - IM)

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Desired National Saving

Desired National Asset Formation

Saving Minus Asset Formation

Y

S+T-G

I + X - IM

0 300 600 900 1200

-81 3 87 171 255

147 117 87 57 27

(S+T-G) (I+X-IM) -228 -114 0 114 228

S + (T - G)

147

Desired Saving,

Equilibrium national income occurs where desired national saving is equal to desired national asset formation.

Desired Asset Formation

National Income

0 -81

• I + (X - IM) 300

600

Y

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The difference difference between desired aggregate expenditure and actual national income is always equal to the difference between desired national saving and desired national asset formation. Suppose the difference between desired national saving and desired national asset formation is equal to W. (S + T - G) - (I + X - IM) = W Recall that disposable income, Y - T, is equal to consumption plus saving: Y-T=C+S

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This implies:

INCORRECT S=T-Y–C

S=Y-T-C

Substituting this equation into our first equation gives: Y - (C + G + I + X - IM) = W Now note that the expression in brackets is AE. Y - AE = W Thus, the difference between desired national saving and desired national asset formation is exactly the same as the difference between national income and desired aggregate expenditure. Copyright © 2005 Pearson Education Canada Inc.

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22.4 Changes in Equilibrium National Income The Multiplier with Taxes and Imports With no government and no international trade, z is simply the marginal propensity to consume out of disposable income. But imports and income taxes make z smaller, and thus the simple multiplier is also smaller. The new value of z is given by: z = MPC(1-t) - m where t is the net tax rate and m is the marginal propensity to import. Copyright © 2005 Pearson Education Canada Inc.

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z = ∆AE / ∆Y Slope of the AE curve The value of z is determined by: z = MPC(1-t) - m

AE e0 ∆AE e1

where t is the net tax rate and m is the marginal propensity to import.

AE =Y E0

•

E1

Y1

∆Y For example, suppose MPC = 0.9 , t = 0.2 and m = 0.3

Y0

AE1

Y

Then z = 0.9 (1 - 0.2) – 0.3 = 0.42 z increases as MPC increases and decreases as t and m increase. Try different values for mpc, t, m

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A Realistic Value for the Multiplier The lower value of the multiplier with taxes and imports reflects that changes in autonomous expenditure bring about smaller changes in national income than before. Using realistic values of taxation and imports for Canada, the evidence shows that the value of the multiplier is closer to 1 than 2.

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Net Exports As with other elements of AE, if the net export function shifts upward, equilibrium national income will rise; if the net export function shifts downward, equilibrium national income with fall. Generally, exports are autonomous with respect to domestic national income. Foreigners’ demand for Canadian exports depends on foreign income, on foreign and domestic prices, on the exchange rate, and on consumer tastes.

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Fiscal Policy Fiscal policy involves the use of government spending and tax policies to influence desired aggregate expenditure so as to change the equilibrium level of national income. Any policy that attempts to stabilize national income at or near potential national income is called stabilization policy. Suppose the government reduces its purchases of all consulting services, saving $100 million annually. How much would equilibrium income change?

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A change in government purchases, ∆ G, will lead to a change in equilibrium national income, ∆ Y. The change will equal the multiplier times the change in government purchases.

AE

AE =Y E0

e0

•

∆G

e´1 e1

• Y1

•

AE0 AE1

E1

∆Y

Y0

Y

For example, suppose z = 0.62. The multiplier is then 1/.38 = 2.63. A $100 million decrease of government purchases will therefore reduce equilibrium national income by $263 million. Copyright © 2005 Pearson Education Canada Inc.

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Or, the government may decide to reduce taxes in an attempt to raise national income.

AE

AE=Y

E1

e2

A lower net tax rate raises the marginal propensity to consume out of national income and thus increases z — the AE function gets steeper.

e0

•

AE1 AE0

•E0 Y0

Y1

Y

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22.5 Demand-Determined Output The simple income-expenditure model is based on three central concepts: • equilibrium national income, • the multiplier, and • demand-determined output. The third concept — demand-determined output — is crucial. We (implicitly) assume that firms are able and willing to supply any amount of output at the given price level without requiring any changes in price. We therefore assume national income to be demand determined. Copyright © 2005 Pearson Education Canada Inc.

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There are two situations under which the assumption that output is demand determined is most reasonable. The first is when there are unemployed resources in the economy, so that output is below potential and firms have excess capacity. The second is when firms are price setters, which means that firms have some influence over price, either because of there are relatively few firms in the market, or because products are differentiated. If the economy’s resources are fully employed and firms are price takers, then the assumption of demand-determined output may not be reasonable. Copyright © 2005 Pearson Education Canada Inc.

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