# Econ: Multiplier Effect

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6.
To fully explain the multiplier effect, we need first to define the Injections and Withdrawals, preferably through the model of Circular flow of income:

It is a simple economic model describing a circulation of income between producers (firms) and consumers (households.). It consists of direct inner flow between firms and households and outer flow. The outer flow is caused by the fact that households do not spend all of their income on consumption; part of their income is withdrawn as net savings, Net taxes and Import expenditure. This happens through another three agents: Banks, Government and Abroad. These agents also represent part of the demand for firm’s output. It is an additional component of aggregate demand called
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The equilibrium will move from point a to point b on the new point when withdrawals equals the new injections J2. Thus the income will rise from Y1 to Y2. Thus, if we want to derivate a multiplier, we see that it is a change in national income divided by the change in injections:

So as we can see from the graph, the size of multiplier depends on the slope of the W function which is given by the marginal propensity to withdrawn mpw. That is the proportion of an increase in national income that is withdrawn from the circular flow.
The steeper the line (and hence the higher the mpw), the smaller will be the rise in national income and the smaller will be the multiplier.
According to this, the less is withdrawn each time a new extra income is generated, the more will be recirculated and hence the bigger will be the rise in national income.
By this, we get another formula of multiplier showing multiplier as the inverse of mpw: k= 1/mpw
In practice, however, the withdrawals curve is likely to get progressively steeper. In other words, the mpw is likely to rise as national income rises. The reason is that people on higher incomes can afford to save a larger proportion of their income (the mps rises as incomes rise) and, assuming a progressive taxation system, will have to pay a higher proportion of their income in taxes (the mpt rises as incomes rise). Thus the value of the multiplier will tend to fall as national income rises.