Chapter 7: Adding Government and Trade to the Simple Macro Model – Study Notes

Adding Government and Trade to the Simple Macro Model

Overview and Learning Objectives

This chapter explores how government activities and international trade affect the macroeconomic model, focusing on aggregate expenditure, national income, and equilibrium. Students will learn to analyze fiscal policy, the role of exports and imports, and the impact of taxes and government purchases on the economy.

• Government purchases and tax revenues: Their relationship to national income.

• Exports and imports: How they relate to national income.

• Marginal propensity to consume vs. marginal propensity to spend: Key distinctions.

• Multiplier effect: How government and trade reduce its value.

• Fiscal policy: How government can influence national income.

• Demand-determined output: Why output is determined by aggregate demand in the simple macro model.

Government in the Macro Model

Government Purchases

Government purchases (G) refer to the acquisition of goods and services by the government, directly increasing aggregate demand for the economy's output.

• Transfer payments: Payments such as pensions or unemployment benefits, which affect aggregate expenditure indirectly through household income.

• Aggregate Expenditure (AE): Only G is included directly, not transfer payments.

• Autonomy: G is assumed to be autonomous with respect to national income (Y).

Tax Revenues

Net taxes (T) are total tax revenues minus transfer payments. They are modeled as a function of national income:

• Equation: $T = t \cdot Y$

• t: Net tax rate (autonomous policy variable).

• As Y rises, net tax revenue increases.

Budget Balance

The budget balance is the difference between net taxes and government purchases, ignoring debt-service payments.

• Budget surplus: $G < T$ (government buys back debt).

• Budget deficit: $G > T$ (government borrows by issuing debt).

Provincial and Municipal Governments

All levels of government contribute to aggregate expenditure. In Canada, provincial and municipal purchases often exceed those of the federal government.

Foreign Trade in the Macro Model

Exports and Imports

Exports (X) are treated as autonomous with respect to Canadian GDP, depending mainly on foreign demand and exchange rates. Imports (IM) increase with Canadian income.

• Import function: $IM = mY$

• m: Marginal propensity to import.

Net Exports

Net exports (NX) are the difference between exports and imports:

• Equation: $NX = X - mY$

• As Y rises, NX falls; as Y falls, NX rises.

• The net export function shows the relationship between Y and NX.

Net Export Function

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

Actual National Income (Y)	Exports (X)	Imports (IM = 0.1Y)	Net Exports (NX = X - IM)
300	72	30	42
600	72	60	12
720	72	72	0
900	72	90	-18

Shifts in the Net Export Function

• Increase in foreign income: Raises X, shifts NX upward.

• Rise in Canadian prices (relative to foreign prices): Decreases X, increases IM, shifts NX downward and makes it steeper.

Equilibrium National Income

Disposable Income and Consumption

Disposable income ($Y_d$) is national income minus net taxes. Consumption depends on disposable income:

• Equation: $Y_d = Y - T$

• If $T = 0.1Y$, then $Y_d = 0.9Y$

• Consumption function: $C = 30 + 0.8Y_d = 30 + 0.8(0.9)Y = 30 + 0.72Y$

• Marginal propensity to consume out of national income (0.72) is less than out of disposable income (0.8).

Aggregate Expenditure (AE) Function

The AE function sums the four components of desired aggregate expenditure:

• General form: $AE = C + I + G + NX$

• Expanded: $AE = a + b(1-t)Y + I + G + (X - mY)$

• Rearranged: $AE = [a + I + G + X] + [b(1-t) - m]Y$

• Autonomous expenditure is the sum of all terms not multiplied by Y; induced expenditure is the term multiplied by Y.

Marginal Propensity to Spend (z)

The slope of the AE function is the marginal propensity to spend out of national income, denoted as z:

• Equation: $z = b(1-t) - m = MPC(1-t) - m$

• Both taxes (t) and imports (m) reduce z compared to the simple model.

• Example: If $MPC = 0.8$, $t = 0.1$, $m = 0.1$, then $z = 0.8(1-0.1) - 0.1 = 0.62$

Equilibrium Condition

Output is demand determined: equilibrium occurs where actual national income equals desired aggregate expenditure.

• Equilibrium: $Y = AE(Y)$

• If $AE \neq Y$, inventories change and firms adjust production.

Saving-Investment Approach to Equilibrium

Closed vs. Open Economy

• Closed economy equilibrium: $S = I$

• Open economy with government: $S + (T - G) = I + (X - IM)$

National Asset Formation

Investment adds to national assets; net exports determine the rate at which a country acquires claims on foreigners.

• If $X > IM$, Canada accumulates foreign assets (currency, stocks, bonds, factories).

Equilibrium Condition (Saving-Investment)

• Equilibrium when desired national saving equals desired national asset formation.

• Equation: $Y - (C + G + I + X - IM) = W$ (W = difference between saving and asset formation)

• At equilibrium, $Y = AE$

Multiplier with Taxes and Imports

Effect of Taxes and Imports

Both taxes and imports reduce the marginal propensity to spend and thus the value of the simple multiplier.

• Equation: $z = MPC(1-t) - m$

• Higher m or t leads to a lower multiplier.

Calculating Multipliers

• Without government and trade: $z = MPC$

• Simple multiplier: $\text{Multiplier} = \frac{1}{1-z}$

• With government and trade: $z = MPC(1-t) - m$

• Simple multiplier: $\text{Multiplier} = \frac{1}{1 - [MPC(1-t) - m]}$

Fiscal Policy and Shocks

Fiscal Policy

Fiscal policy uses government spending and taxation to influence national output.

• Increase in G or decrease in t shifts AE upward, increasing equilibrium income.

• Decrease in G or increase in t shifts AE downward, decreasing equilibrium income.

Stabilization Policy

• Recessionary gap: $Y < Y^*$

• Inflationary gap: $Y > Y^*$

• Stabilization policy aims to keep $Y$ near $Y^*$.

Effects of Changes in Government Purchases

• Change in equilibrium income: $\Delta Y = \Delta G \times \text{multiplier}$

• Example: If $z = 0.25$, multiplier = 1.3, $\Delta G = 100$ million, $\Delta Y = 130$ million.

Effects of Changing the Net Tax Rate

• Lower t makes AE steeper (greater response to income).

• Higher t makes AE flatter (less response to income).

Exports and Equilibrium Income

• Upward shift in NX increases equilibrium Y.

• Downward shift in NX decreases equilibrium Y.

• Exports depend on foreign income, prices, exchange rates, and tastes.

• Change in equilibrium income: $\Delta Y = \Delta X \times \text{multiplier}$

Effects of Changing the Marginal Propensity to Import

• Lower m makes AE steeper (higher multiplier).

• Higher m makes AE flatter (lower multiplier).

Examples of Shocks and Policies

• Tariffs: Example of U.S. raising tariffs on Canadian goods, affecting exports and equilibrium income.

• "Buy Canada" initiatives: Encourage domestic consumption, support affected industries.

• Government transfers: Support for industries hit by trade shocks.

Demand-Determined Output

The simple macro model assumes output is determined by aggregate demand, with a constant price level. This is reasonable when output is below potential and firms can increase production without raising costs. In reality, price levels may vary, which is addressed in more advanced models.