# Management Info System

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We know that the (national income) multiplier (K) is greater than 1, and that it can be computed from two different formulae; K = ΔY / ΔA K = 1 / [1 – z] How did we arrive at this result? We know that AE = C + I + G + NX The right hand side (RHS) can be rewritten to reflect the assumptions regarding autonomous and induced spending. AE = c0 + cYD + I + G + X – mY We also know that YD = (1-t)Y So AE = c0 + c(1-t)Y + I + G + X – mY = c0 + I + G + X + c(1-t)Y – mY Equilibrium means that AE = Y So we have Y = c0 + I + G + X + c(1-t)Y – mY By moving all the terms with national income (Y) to the LHS, we have Y[ 1 - c(1-t) + m ] = c0 + I + G + X Denoting the RHS (the sum of the autonomous components) with the symbol A, we have Y = 1 / [1 - c (1-t) + m]* A which gives us the equilibrium level of national income, but can also be expressed as changes: ΔY = 1 / [1 - c (1-t) + m]* ΔA

The expression { 1 / [1 - c (1-t) + m] } is the multiplier (K). Dividing both sides of the above equation by ΔA
ECON 1002 Feb 2013

We have ΔY / ΔA = 1 / [1 - c (1-t) + m]

which gives us our first formula for K.

What about the second formula? What is z? It is the marginal propensity to spend out of national income, which include the propensity to consume and the propensity to import. As we saw above, consumption spending comes out of disposable income, and therefore, the propensity to consume out of national income is c(1-t). We also assumed that imports represent a leakage from the circular flow, therefore, – m represents the propensity to import. We therefore have z = [c(1-t) – m] Notice that the minus sign in front of z in the multiplier formula will change the sign of its two terms and gives us the exact expression of K we derived above. What is obvious from the multiplier? From this expression we derived for K, we see that when c increases, the multiplier will increase, and when t and m…...

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