According to the theory of Keynes, an increase in investment triggers the multiplier process, which is reflected in the increase in national income by a greater amount than the original increase in investment. This effect Keynes called the effect of the multiplier. k (multiplier) = growth income / growth investments. Marginal propensity to savings and consumption depends on the strength of the effect of the multiplier. If the values of these parameters relatively constant, to determine the multiplier is not difficult.
To calculate the multiplier, assume that:
I – investments; C – consumption; Y – national income; the MPS is the marginal propensity to save and MPC is the marginal propensity to consume.
Since Y = C + I, the increase in income(Y) will be equal, respectively, to the amount of growth of consumption(C) and investment growth(I).
According to the formula, the marginal propensity to consume: MPC = C / Y, we get: C = Y * Mrs.
Substitute this expression into the equation above (Y = C + I).
Will get: Y = Y * MPC + I.
Hence: Y * (1 - MPC) = I.
Next: the increase of income Y = (1 / 1 – MPS) * a rate of investment I, but since k = increase in Y / increase I, therefore gain Y = k * increment I. This means that k = 1 / 1 – MPS = 1 / MPS where k is the multiplier of the investment.
Thus, the multiplier of investment is the reciprocal of the relative to the marginal propensity to save. The multiplier operates in both forward and back.