The Goods Market

Goods Market Equilibrium & the Multiplier

coreExam · highTA · PS1-Q1

Equilibrium in the goods market requires production Y equal demand Z. With a linear consumption function, solving Y = Z yields Y* = (c₀ − c₁T + I + G)/(1−c₁). The denominator (1−c₁) generates the spending multiplier: a £1 increase in autonomous spending raises output by 1/(1−c₁) > 1.

Derivation

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Intuition

The goods market equilibrates when production equals demand. The key insight is that when firms produce more, they generate income, which generates more demand, which generates more production — a multiplier process.

With MPC $c_1 = 0.6$ : every £1 of government spending raises income by £2.50. With $c_1 = 0.8$ : every £1 raises income by £5. Higher MPC → stronger multiplier.

The Equilibrium Condition

Demand for goods:

Z \equiv C + I + G = c_0 + c_1(Y - T) + I + G

Setting production equal to demand $Y = Z$ and solving:

Y^* = \frac{1}{1 - c_1}(c_0 - c_1 T + I + G)

What Shifts Equilibrium?

Rightward (higher Y*): increase in $G$ , $I$ , $c_0$ ; decrease in $T$ .

Leftward (lower Y*): decrease in $G$ , $I$ , $c_0$ ; increase in $T$ .

Each shift is amplified by the multiplier $1/(1-c_1)$ for spending changes, or $c_1/(1-c_1)$ for tax changes.

Limitation

This model keeps the interest rate and price level fixed. Chapter 4 (IS–LM) endogenizes investment as $I(Y, i)$ , making the goods-market equilibrium a curve in $(Y, i)$ space — the IS curve.

Worked Example

c₀=150, c₁=0.75, T=100, I=200, G=300. Find Y* and the effect of ΔG=+40.

Y* = (150 − 0.75×100 + 200 + 300)/(1−0.75) = (150 − 75 + 200 + 300)/0.25 = 575/0.25 = 2300.
Multiplier = 1/(1−0.75) = 1/0.25 = 4.
ΔY* = 40 × 4 = 160. New Y* = 2300 + 160 = 2460.

Equilibrium output is 2300; after ΔG=+40 it rises by 160 to 2460. The spending multiplier is 4.

Common Mistakes

—Using ΔY = ΔG instead of ΔY = ΔG/(1−c₁) — forgetting to multiply by the multiplier.
—Applying the spending multiplier 1/(1−c₁) to a tax change; the correct tax multiplier is −c₁/(1−c₁).
—Confusing endogenous Y and exogenous G, T in the equilibrium equation.

Exam Cues

→If c₁ = 0.8, multiplier = 5. If c₁ = 0.6, multiplier = 2.5. These values come up frequently.
→Balanced-budget theorem: ΔG = ΔT → ΔY* = ΔG (multiplier = 1). Always testable.
→The simple model here keeps I exogenous; Ch 4 endogenizes I via the IS curve.