IS Curve

August 31, 2024 Economics

The IS curve shows interest-rate and output combinations where planned expenditure equals production in the goods market.

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The IS curve shows combinations of the interest rate and output at which planned expenditure equals production in the goods market. In the traditional IS-LM model, lower interest rates support interest-sensitive spending, so goods-market equilibrium generally occurs at a higher level of output; this gives the curve its downward slope.

“IS” refers to the investment-saving equilibrium behind the model, but the most reliable definition is planned expenditure equals output. In an open economy with government, the accounting relationships are broader than literal private investment equaling private saving.

Key Takeaways

Each point on the IS curve is a modeled goods-market equilibrium, not a forecast or observed market price.
A change in the interest rate produces a movement along a given IS curve when other assumptions stay fixed.
A change in autonomous consumption, investment, government purchases, taxes, or net exports can shift the whole curve.
The slope depends on spending sensitivity to interest rates and on multiplier assumptions.
The classic IS-LM curve and a modern New Keynesian IS equation are related but not identical models.
Analysts should not infer an exact output response from the diagram without an estimated model, time horizon, policy rule, and financial-conditions assumptions.

Goods-Market Equilibrium

Start with the expenditure identity:

$$ Y = C + I + G + NX $$

For a simple closed-economy illustration, let consumption depend on disposable income and investment depend negatively on the interest rate:

$$ C = C_0 + c(Y-T) $$

$$ I = I_0 - br $$

Substituting into equilibrium output gives:

$$ Y = C_0 + c(Y-T) + I_0 - br + G $$

Solving for output:

Y = \frac{C_0-cT+I_0+G-br}{1-c}

where:

Y is real output or income;
r is the interest rate used by the model;
C_0 is autonomous consumption;
c is the marginal propensity to consume;
T is taxes under the simplified assumption;
I_0 is autonomous investment;
b measures investment sensitivity to the interest rate; and
G is government purchases.

Holding the other terms fixed:

\frac{dY}{dr} = -\frac{b}{1-c}

The negative sign explains the downward slope. A larger b or a stronger multiplier makes modeled output more responsive to the interest rate. These parameters are assumptions or estimates, not permanent constants.

IS curve diagram showing a movement along the curve and a rightward shift from higher autonomous spending.

The figure is directional. It does not imply that every rate change produces the same output response or that policymakers can select any point without affecting inflation, expectations, exchange rates, credit spreads, or financial stability.

Worked Example

Assume a hypothetical closed economy with all amounts in billions and r measured in percentage points:

$$ C = 100 + 0.75(Y-200) $$

$$ I = 300 - 20r $$

$$ G = 250 $$

Goods-market equilibrium is:

$$ Y = 100 + 0.75(Y-200) + 300 - 20r + 250 $$

Rearranging:

$$ Y = 2{,}000 - 80r $$

At an interest rate of 4%, modeled equilibrium output is:

$$ Y = 2{,}000 - 80(4) = 1{,}680 $$

If government purchases increase by $50 billion while the interest rate and other assumptions remain fixed, the simple spending multiplier is:

\frac{1}{1-c} = \frac{1}{1-0.75} = 4

The IS curve shifts right by a modeled $200 billion, producing:

$$ Y = 2{,}200 - 80r $$

At 4%, output would be $1.88 trillion in this simplified exercise. This is not a real-world forecast. Taxes, imports, inflation, financing conditions, policy reactions, capacity constraints, and confidence can reduce, delay, or reverse the modeled effect.

Movement Along the Curve vs. Shift of the Curve

Change	Typical diagram effect	Reason
Interest rate rises	Move up and left along the existing curve	Interest-sensitive planned spending falls
Interest rate falls	Move down and right along the existing curve	Interest-sensitive planned spending rises
Government purchases rise	Curve shifts right	Autonomous planned expenditure rises
Taxes rise	Curve generally shifts left	Disposable income and consumption generally fall
Business confidence raises autonomous investment	Curve shifts right	Planned investment rises at each modeled rate
Foreign demand raises net exports	Curve shifts right in an open-economy model	Domestic planned expenditure rises
Credit spreads widen at an unchanged policy rate	Often shifts or alters the effective relationship	Borrower financing costs can rise without a matching policy-rate move

The last row is important in finance. A model using only a policy rate can miss changes in bank lending standards, bond spreads, collateral values, or market access. The financially relevant rate may be a real borrowing rate rather than the quoted central-bank target.

What Shifts the IS Curve?

Fiscal Policy

Higher government purchases or lower taxes generally shift the simple IS curve right; the reverse generally shifts it left. The eventual effect depends on the fiscal multiplier, financing method, economic slack, import leakage, monetary response, and household or business behavior.

Private Demand

Changes in expected income, wealth, financing access, capacity utilization, or business confidence can alter consumption and investment demand. A fall in policy rates may have little effect if borrowers are constrained or firms see no profitable projects.

External Demand and Exchange Rates

In an open-economy model, foreign output, exchange rates, trade prices, and import sensitivity affect net exports. Exchange-rate effects depend on invoicing, pass-through, hedging, trade composition, and the response of domestic demand.

Traditional IS Curve vs. Modern New Keynesian IS Equation

Feature	Traditional IS-LM treatment	Modern New Keynesian treatment
Output variable	Level of income or output	Often the output gap
Rate variable	Interest rate in a static diagram	Expected real rate relative to a natural or neutral rate
Expectations	Often simplified or fixed	Expected future output and inflation are central
Companion equations	LM curve for money-market equilibrium	Phillips curve and monetary-policy reaction rule
Main use	Comparative statics and introductory policy analysis	Dynamic forecasting and policy-model analysis

A common modern form is:

x_t = E_t x_{t+1} - \sigma(i_t-E_t\pi_{t+1}-r_t^n) + \varepsilon_t

Here, x is an output gap, i is a nominal interest rate, expected inflation converts it to an expected real rate, r^n is a natural-rate estimate, and epsilon represents demand disturbances. This equation is conceptually related to the classic IS curve, but it should not be inserted into a traditional level model without reconciling definitions and units.

Why the IS Curve Matters in Finance

The model provides a disciplined way to ask how rate and spending assumptions interact. It can help frame:

earnings sensitivity for cyclical businesses;
loan demand and borrower cash-flow scenarios;
fiscal-policy effects on output and sovereign revenue;
links between the natural rate of interest and demand;
credit-spread or lending-standard shocks; and
scenario consistency across growth, inflation, rates, and exchange rates.

It is a framework for organizing assumptions, not a trading signal. A downward-sloping curve does not prove that a specific rate cut will raise a security’s price, a company’s revenue, or an economy’s output by a known amount.

Common Mistakes and Limitations

Defining the curve only as I = S and ignoring government and foreign-sector balances.
Treating an accounting identity as a behavioral forecast.
Mixing nominal rates, real rates, policy rates, and borrower rates.
Moving the curve when only the interest rate changed, or moving along it when autonomous spending changed.
Assuming a fixed multiplier regardless of inflation, imports, taxes, capacity, and monetary response.
Ignoring expectations, lags, credit rationing, and financial frictions.
Reading a stylized diagram as evidence of current equilibrium output.
Combining a classic IS-LM equation with a New Keynesian output-gap equation without aligning variables.

IS-curve analysis is educational and model-dependent. It does not provide an output forecast, rate forecast, policy recommendation, or personalized investment advice.

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FAQs

Why does the IS curve slope downward?

In the basic model, a lower interest rate increases interest-sensitive planned spending. Goods-market equilibrium therefore occurs at a higher level of output, holding the curve’s other assumptions fixed.

What shifts the IS curve to the right?

An increase in autonomous planned expenditure can shift it right. Examples include higher government purchases, lower taxes under standard assumptions, stronger autonomous investment, or higher net exports. The actual effect depends on the model and financial conditions.

Is the IS curve still used?

Yes, both as an introductory comparative-statics tool and in modified form within modern macroeconomic models. Modern versions often focus on the output gap, expectations, and the expected real interest rate rather than the classic static IS-LM diagram.

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