What happens to Keynesian Multiplier in an Open Economy?

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In Keynes’ model equilibrium output can be calculated as follows:

Since C – a + bY and AE – C + I = a + bY + l, and since in equilibrium, aggregate expenditure equals income,

AE = Y, we have

Y₀ = a + bY + I or, Y₀ = a + 1/1 – b.

For example, if a = Rs 2 crores, I = Rs 1 crores and b = 1/2, Y = Rs 6 crores.

To calculate the multiplier, let us assume that I increases by Re 1. Now, Y₁ = a + I + 1/1 – b.

The change in Y, i.e., Y₁ – Y₀ is found by subtraction:

Y₁ – Y₀ = 1/1 – b 

The smaller (larger) b, the MPC, is the flatter (steeper) the aggregate expenditure schedule will be, and the smaller (lower) correspondingly is the multiplier. If b = 0.2, the multiplier is 2. If b = 0.8, the multiplier is 5.

Multiplier with Government:

When we add government, the equation for aggregate expenditures be­comes:

AE = C + I + G = a + Yd + I + G

where Yd is disposable income. For simplicity, let us assume that a given fraction, t, of income is paid in taxes.

So, we have:

Yd = Y (1 – t)

Hence, in equilibrium, with aggregate expenditure equaling income

AE = Y = a + bY (1 – t) + I + G

Y = a + I + G/1 – b (1 – t)

Hence, multiplier = 1/1 – b (1 – t)

If m = 0.8, t = 0.25, the multiplier is 2.5. By contrast, the multiplier without taxes is 5, twice as large. The reason is simple. Without taxes every rupee of extra income translates into 80 paise of extra expenditure. With taxes, when income goes up by a rupee, consumption increases by only 0.8 × (1 – 0.25) = 60 paise.

Open Economy Multiplier:

When we add foreign trade, aggregate expenditures are given by:

AE = C + I + G + X – M Imports are now related to disposable income by the import function

M = MPI × Y_d

where MPI is the marginal propensity to import; exports are exogenous and are thus assumed to remain fixed.

Hence, aggregate expenditures are:

AE = a + b Y (1 – t) + I + G + X – MPI (1 – t) Y

Since aggregate expenditures equal income, in equilibrium, we have:

Y = a + I + G + X /1 – (1 – t) (b – MPI)

So, the multiplier is:

1/1 – (1 – t) (b – MPI)

If t = 0.25, b = 0.8, MPI = 0.1, then the multiplier is

1/1 – 0.75 (0.80 – 0.1) = 2.1

much smaller then in the absence of foreign trade. This new multiplier is called open economy multiplier.