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Keynesian Consumption Function

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Demonstrate analytically and show graphically that, in the Keynesian consumption function, the average propensity of consumption is always bigger that the marginal propensity when the autonomous component of consumption is positive.

By using this result demonstrate analytically and show graphically why the average propensity of consumption decreases as income increases, whilst the Marginal propensity of consumption decreases as income increases, whilst the marginal propensity does not change with income

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Keynesian Consumption Function:

Early Keynesian models of the consumption function related current consumption expenditure to current levels of income or disposable income. These models took the form of:
C = a + bYd
where
C = Consumption Expenditure
a = Autonomous consumption i.e consumption expenditure independent of the level of income.
b = the Marginal Propensity to Consume 'MPC', which represents the fraction of each additional dollar of income devoted to consumption expenditure.
Yd = Current Disposable Income.
The above consumption function can be shown graphically as follows.

From the graph,
• The consumption function, C(Y), is drawn with price level held constant.
• Along 450 line, C = Q = Y, i.e., aggregate consumption equals total output equals total income.
• If income = 0, then C > 0 because people dissave. We see this by the intersection of the consumption function with the vertical axis. At zero income aggregate consumption is still positive. The only way to still have positive consumption when income is zero is to dissave.
• The fact that the consumption function is flatter than the 450means that as income rises, consumption rises but not as rapidly as income. Out of every dollar of income received a portion is consumed and a portion is saved. So ...

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