IS Curve Definition & Derivation with Diagram

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IS- Curve (Investment-Savings Curve)

The IS in the IS curve stands for Investment-Savings. It is a component of the IS-LM macroeconomic model. 

The IS-Curve represents the real sector/product market equilibrium of the economy, which shows the various combinations of interest and income required to maintain such equilibrium. So, an IS-curve is the curve that is the locus of a point that shows the various combinations of interest rate and income that maintain the real sector equilibrium of the economy (Aggregate Demand = Aggregate Supply).

To derive the IS curve, consider a simple two-sector economy where the household sector makes consumption (C) and the business sector makes investment (I). So, the aggregate demand of the economy is given as

AD = C + I ————- (i)

Here, C is assumed to be a positive non-proportional function of income, and so the consumption function is given as

C = Ca + bY ————— (ii)

Where,

  • Ca = autonomous consumption, Ca > 0
  • b = marginal propensity to consume (MPC)  0 < b < 1 [आयमा भएको एक इकाइ वृद्धिबाट उपभोगमा कति प्रतिशत वा अंश खर्च गरिन्छ भन्ने दर]

Similarly, I is assumed to be the inverse function of interest rate.

i.e. I = Ia- dr —————– (iii)

Where,

  • Ia = autonomous investment (Ia>0)
  • d = interest elasticity of investment (d>0)

The aggregate output or income of the economy represents the aggregate supply itself.

i.e. AS = Y —————- (v)

Where, Y = aggregate output or income. Now, the real sector of the economy is said to be in equilibrium when

AD = AS.

C + I = Y (from equation i & iv)

  • or, Ca + bY + Ia – dr = Y
  • or, -dr = – Ca – Ia + Y – bY
  • or, dr = Ca + Ia -Y + bY
  • or, r = (Ca+Ia)/d – (1 -b)Y/d ———— (v)

Thus, equation (v) shows the relationship between r and Y when the real sector is in equilibrium. So, this equation (v) itself represents the IS curve with (Ca+Ia)/d as the intercept and -(1-b)/d as the slope. This means the IS-curve has a positive intercept and a negative slope. Its slope depends on the two parameters: b and d.

Since, b ot MPC is assumed to be given. So, the slope of the IS curve mainly depends on d or interest elasticity of investment. The higher the value of “d”, the flatter or more elastic the IS curve.

Slope = (a – b`)/d

  • d↑, slope ↓ = flatter or more elastic IS-curve
  • d↓, slope ↑ = steeper or less elastic IS-curve.
  • d high = a small fall of “r” can increase investment largely.
  • d low = a large fall of “r” increases investment minimally or insignificantly.

For the graphical derivation of the IS-curve, investment is the inverse function of interest rate, and saving is the positive function of income, where the economy attains real sector equilibrium when investment and saving are equal.

IS curve derivation

Here,

  • — Panel I shows the investment function,
  • — Panel II shows the real sector equilibrium (I =S )
  • — Panel III shows the saving function
  • — Panel IV derives the IS curve with the help of other panels

As in Panel I, if the interest rate is ro then investment demand is Io. To maintain the real sector equilibrium, saving should be So such that Io = So. This is shown by Panel II for the So level of saving, income should be Yo as shown by Panel III. It means if the interest rate is ro and income is Yo, then the real sector is in equilibrium, where the point A in panel IV represents this specific combination of interest rate and income.

Similarly, point B in Panel IV shows that the real sector is in equilibrium if the interest rate is r1 and income is Y1. Now, if we join A and B in panel IV, we get the IS-curve, which is downward sloping, implying that to maintain real sector equilibrium, there is an inverse relationship between interest rate and income.

If r↓, I↑ for equilibrium S↑ only if Y↑

If r↑, I↓ for equilibrium S↓ only if Y↓

Shifts of the IS Curve:

Shifts of IS curve

i) Change in government expenditure:

If government expenditure is increased, the IS curve shifts upward. An increase in government expenditure (G) raises aggregate demand in the economy.
At any given interest rate, higher government spending leads to a higher level of income/output, so equilibrium in the goods market occurs at a higher income level.

As a result, the IS curve shifts upward (or to the right) in the IS–LM model, showing higher income for each interest rate

ii) Change in tax:

  • Increase in taxes ( T↑):
    Disposable income falls → consumption decreases → aggregate demand decreases.
     The IS curve shifts downward (or to the left).

  • Decrease in taxes (T↓ ):
    Disposable income rises → consumption increases → aggregate demand increases.
    The IS curve shifts upward (or to the right).

iii) Change in savings:

  • Increase in savings (↑ S):
    More savings means less consumption at every income level → aggregate demand falls.
    The IS curve shifts downward (or to the left).

  • Decrease in savings (↓ S):
    Less saving means more consumption → aggregate demand rises.
     The IS curve shifts upward (or to the right).

iv) Change in investment:

  • Increase in investment (↑ I):
    Aggregate demand rises at every interest rate → higher equilibrium income.
    The IS curve shifts upward (or to the right).

  • Decrease in investment (↓ I):
    Aggregate demand falls → lower equilibrium income.
    The IS curve shifts downward (or to the left).

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