Absolute Income Hypothesis (AIH) Derivation with Diagram

Theories of Consumption and Saving

What is the Consumption Function? 

• Functional relationship between the consumption and various determinants of it.
• Which means Consumption = f(income, taste, preference, price level, demographic characteristics, interest rate, expectation of customers, etc.)

Income is the main factor affecting consumption, and so consumption is generally expressed as a function of income.

i.e C = f(Y) 

Absolute Income Hypothesis (AIH)

• Developed by John Maynard Keynes in his 1936 book, The General Theory of Employment, Interest and Money.

This hypothesis argues that the consumption of any period depends on the absolute disposable income of the same period.

i.e. C_t = f(Y_d,t)

• Where, Y_d = Y – Tax (disposable Income)
• C_t = Consumption at ‘t’ period

This means the consumption of today depends on today’s disposable income. It implies that if we have a good income today, we consume more. SO, there is a positive relationship between consumption and income.

According to this hypothesis, there is a positive and non-proportional relation between the consumption and the absolute level of disposable income. When personal income increases, consumption also increases, but not in proportion to income. So, the short-run consumption function can be written as,

C_t = Ca + bY_d,_t ———– (i)

• Where,
• Ca = Autonomous consumption, Ca > 0
• b = Marginal Propensity to Consume (MPC), 0 < b <1

Now, average propensity to consume,

• APC = C_{t /} Y_d,_t
• APC = Ca + bY_d,_t / Y_d,_t
• APC = Ca/ Y_d,_t + b
• APC = Ca/Y_d,_t + MPC ——————-  (ii)

This shows that in the short run, APC > MPC, and APC declines as income increases. This means the APC of rich people is lower than the poor people. This implies a positive and non-proportional relationship between consumption and income in the short run. 

This shows that the short-run consumption function has +ve intercept and a constant positive slope (b). This means the short-run consumption is positive and non-proportional to income.

Keynes did not analyze the long-run relationship between consumption and income, but in 1946, S. Kutznet made an empirical study using long-run data on income and consumption of the US economy. He found that:

1. Consumption at any period depends on the absolute level of personal disposable income, which means Keynes’ hypothesis was acceptable (right).
2. In the short run, income and consumption are positive but non-proportional, which supports the Keynesian argument.
3. In the long run, as income increases, consumption also increases in the same proportion. Which means long-run consumption is positive and proportional to income. This is the extension of the hypothesis and also known as the Kuznets paradox. 

लामो समयमा संचित गरिएको पैसा सम्पति (asset) मा बदलिन्छ जुन पछी खपत गर्दा खर्च बढ्न जान्छ, बुढेसकालमा खर्च बढ्दा युवा अवस्थामा संचित गरिएको पैसा खर्च हुन्छ, Innovation & new arrival of new products, यी कारणहरुले long-run consumption is positive and proportional to income हुन्छ !

Now, the long-run consumption function (LRCF) can be written as:

C_t = bY_d,t

Where, b = MPC  0<b<1

The long run APC is Ct/Y_d,t

Or, APC = bY_d,t/Y_d,t => b => MPC

This shows that in the long run, APC and MPC are equal and constant. This means the long-run consumption is positive and proportional to income.

Reconciliation of Short-run and Long-run consumption

According to Keynes, saving is a luxury product, and its income elasticity is greater than 1. Therefore, when income increases in the short term, savings increase at a faster rate than income. It means that through income increases, consumption increases, but at a lower proportion than income in the short run. This makes the SRCF positive and non-proportional.

However, in the long run, income and consumption grow at the same rate for the following reasons.

1. Conversion of savings to assets and an increase in expenditure.
2. Increase the proportion of the old-age population
3. Arrival or innovation of new products
4. Increased cost of living due to rural-to-urban migration or urbanization of rural areas.

Here, initially, the economy is at Eo with OYo income and EoYo consumption. Now, assume that the income increases in the short run, which also increases consumption but follows the arrowwheels along SRCFo, implying a non-proportional growth rate due to increased saving in the short run. But when income increases to OY1, which takes a long period of time, then the short sun consumption function itself shifts upward from SRCFo to SRCF1 due to assets accumulation, increases the proportion of old age, innovation & arrival of new product, and increases the cost of living.

If we compare these two long-run points, Eo and E1, we find that both income and consumption are increased by the same proportion.

i.e., proportionate change in Y = Proportionate change in C.

or  (OY1 – OYo)/OYo = (E1Y1 – EoYo)/EoYo

Therefore, the consumption at any period depends on the absolute level of personal disposable income, and in the short ru,n there is +ve and non-proportional relation between them, whereas in the long run they are positive and proportional.