The Consumption Function

 

Consumption function for a household shows the level of consumption at each level of income. Whenever consumers income rise, their consumption also increases. As consumers income rise, they tend to spend more than they did before. However, the rise in income is not the same as the rise in consumption. A typical consumer will spend less than his\her increased income. That is a consumer only consumes a fraction of his \ her increased income. So, consumption is a fraction of income.

For example, Lets say a Household’s total income is GH₵ 100.00 and they spend 20% on consumption, then the household consumes GH₵ 20.00 of their total income. Now, assume the household income increases to GH₵ 120.00 and still consumes 20% of the income then, the amount being spent on consumption will be GH₵ 24.00, which means the consumers consumption has increased by GH₵4.00.

Now, let “c” be the fraction that a household consumes of their income. Since the household does not consume all of its income then “c” must be between 0 and 1 (i.e. 0<c<1). Let ΔY be an increased in income and ΔC be an increase in consumption. From the example above

GH₵ 24.00 = GH₵ 120.00 × 0.2 → ΔC =ΔY×c .

ΔC = GH₵ 24.00

ΔY = GH₵ 24.00

c = 0.2 (Note: 20% was converted into fraction 0.2)

So a change in consumption is equal to the fraction consumed of income.
Thus, consumption Function is C =cY

Hence ΔC = c × ΔY → ΔC/ ΔY = c. where “c” is a slope. And “c” is called the Marginal Propensity to Consume (MPC). Thus, Marginal Propensity to Consume is a fraction of income consumed.

Moreover, if only a fraction of increased income is consumed then the remaining fraction of the income must be saved. It follows that, if c is the fraction consumed , then 1-c = s must be the fraction that is saved and its called the Marginal Propensity to Save(MPS). Therefore

MPC + MPS = 1

Now, if C =cY, then if c increases then C will also increase so as an increase in Y will also cause C to increase.

MPC = ΔC/ ΔY

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