§2 The Goods Market

The Composition of AD (GDP)

• Consumption, $C$: goods and services purchased by consumers.
• Investment, $I$: the sum of nonresidential and residential investment (goods and services...).
• Government spending, $G$: purchases of goods and services by the federal, state, and local governments, excluding government transfers.
• Exports, $X$: purchases of U.S. goods and services by foreigners.
• Imports, $IM$: purchases of foreign goods and services by U.S. consumers, U.S. firms, and the U.S. government.
• Inventory investment: difference between production and sales.

The Demand for Goods

• Aggregate demand is:

  $$Z \equiv C+I+G+X-IM$$

• In closed economy:

  $$Z \equiv C+I+G$$

• Behavioral assumptions:

  • Exogenous:

    $$I=\bar I$$

    $$G,T$$

    • Note: $G$ and $T$ describe fiscal policy.

  • Endogenous:

    $$C=C(Y_D)$$

The Consumption Function

• Let’s assume that the consumption function is a linear function:

  $$C=c_0+c_1Y_D$$

• The parameter $c_1$ is the marginal propensity to consume; i.e. how much additional consumption is generated by an additional dollar of disposable income.

• The parameter $c_0$ is autonomous consumption and captures many unmodeled factors (e.g. wealth).

• Disposable income:

  $$Y_D\equiv Y-T$$

• To imply:

  $$C=c_0+c_1(Y-T)$$

The Determination of Equilibrium Output

• Recall that aggregate demand (in closed economy) is:

  $$Z=C+I+G$$

• Replacing our functional forms, we have

  $$Z=c_0+c_1(Y-T)+\bar I+G$$

• Equilibrium in the goods markets requires:

  $$Y=Z$$

  Important: this is an equilibrium condition (not a function)

• Let’s now find what is the equilibrium level of output (GDP)

  $$\begin{aligned}Y &= Z \\ &= c_0 + c_1(Y - T) + \bar{I} + G \end{aligned}$$

• Solving for output, $Y$, yields:

  $$Y = \frac{1}{1 - c_1} \left[ c_0 - c_1 T + \bar{I} + G \right]$$

• The term $1/(1 - c_1)$ is known as the multiplier.

• There is an alternative way to find equilibrium output: it’s the output such that investment is equal to saving (John Maynard Keynes).

• Private and public saving:

  $$S \equiv Y_D - C = Y - T - C$$

  $$S^G \equiv T - G$$

• In equilibrium:

  $$\begin{aligned} I &= S + S^G \\ &= Y - T - C + T - G \\ &= Y - C - G \end{aligned}$$

  this is known as the IS relation, and it implies

  $$Y = C + I + G$$

The Paradox of Saving

• We are told of the virtues of thrift as we grow up, but not so for macroeconomics in the short run

  $$\bar{I} = S(Y) + \bar{S}^G$$

• If $S(Y)$ shifts up, then $Y$ must decline to restore equilibrium...

— Apr 10, 2025

§2 The Goods Market by Lu Meng is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. Permissions beyond the scope of this license may be available at About.