According to Keynes's national income determination theory, the change of consumption will lead to the change of national income in the same direction, while the change of savings will lead to the change of national income in the opposite direction. However, according to the theory that the change of savings causes the change of national income in the opposite direction, it is evil to increase savings and reduce national income and make the economy decline; Reducing savings will increase national income and make the economy prosperous, which is a good thing. This contradiction is called "savings paradox".

The paradox of savings is a conclusion derived from Keynes's national income determination theory, which exists in the case that resources are not fully utilized and is short-term. In the long run, or when resources are fully utilized, the paradox of saving does not exist. Keynes's analysis of national income determination is a short-term static analysis under the premise of involuntary unemployment. In addition, it should be noted that Keynes's analysis is a total analysis, and there is no specific analysis of consumption structure and income structure.

1936 Keynes put forward the famous paradox of saving in the General Theory of Employment, Interest and Money. He quoted an old fable: there is a nest of bees that is very prosperous. Every bee eats and drinks all day. Later, a philosopher taught them not to be so extravagant and wasteful, but to practise economy. After listening to the philosopher's words, the bees found it very reasonable, so they quickly implemented it and tried to be a model of saving. But the result was unexpected, and the whole colony declined rapidly.

The scene during the Great Depression is a vivid and sad example of economic paradox. As people have no hope for the future, everyone tries to save as much as possible. However, their psychology and behavior of not wanting to spend led to the continuous decline of their income. The condition of its national income balance is I=S, that is, investment = savings.

Where S=Y-C, that is, savings = national income-consumption.

The consumption hypothesis is a linear function: c = c. +cY, where c is the marginal propensity to consume for spontaneous consumption that is not affected by income, that is, the proportion of consumption increase to income increase. Because assuming that the marginal propensity to consume remains unchanged, C is also the average propensity to consume, that is, the proportion of consumption to income.

So there is: s =-C.+(1-C) y.

It is also assumed that the investment is fixed, that is, I = I

Then the national income determination equation of the two-sector economy is obtained:

Me. =-C .+( 1-c)Y

Solution:

Balance national income y * = (c. +I .)/( 1-c)

In this formula, as the marginal propensity to consume, C is a number less than 1. When c becomes larger, the value of 1/( 1-c) becomes larger, and the national income Y* increases. When c becomes smaller, the value of 1/( 1-c) becomes smaller, and the national income Y* becomes smaller.

This means that when citizens increase the proportion of consumption in income, it will lead to more national income and make the whole economy prosperous; When citizens reduce the proportion of consumption in income, it will cause the decline of national income and make the whole economy fall into recession. In short, profligacy leads to prosperity and frugality leads to depression.

It should be pointed out that this is because under the basic theoretical premise that income is not a problem in modern society, consumption restricts production, not production restricts consumption. If we don't consume or reduce consumption, the movement of capital will stagnate, and then the demand for labor will stagnate, which will eventually lead to the stagnation of production.