What does the importance of the multiplier depend on in a simple Keynesian model?

Investment multiplier k = 1 (1-marginal propensity to spend). Based on c = 100 + marginal propensity to consume so the investment multiplier is 1 ( = 5.).

The slope of the consumption function is still being investigated.

1.The emergence of the external multiplier theory The external multiplier theory refers to the Keynesian international theory put forward in the 30s of the 20th century, which tries to link the external multiplier theory with the employment theory, and explains the importance of protection from the perspective of increasing employment and increasing national income. Keynes (1883-1946) was the most famous British economist of our time and the founder of Keynesianism.

Keynes lived in a time of great change in the world economic system. The capitalist economy replaced free competition with monopoly, especially the outbreak of the unprecedentedly serious economic crisis in 1929 and 1933, the world market problem was further acute, and various countries successively abandoned the policy of freedom and changed to pursue a policy of protection, which strengthened the role of state power in intervening in the economy. In this context, Keynes's economic stance has also changed, from one in favor of freedom to one in favor of protection, and he actively provides a rationale for it.

In 1936, Keynes published his masterpiece "The General Theory of Employment, Interest and Money", in which he criticized the theory of liberalism, re-evaluated some policies of mercantilism, and founded a new theory of protecting domestic employment on the basis of insufficient effective demand, with the three so-called psychological laws of marginal consumption tendency, marginal capital efficiency and flexible preference as the core, and state intervention as the policy basis. In Keynes's economic theory and his followers in the development of his theory, a series of theoretical propositions of protection were put forward, the core of which is the external multiplier theory. 2.

The main content of the external multiplier theory The external multiplier theory was extended by Keynes's main followers, such as Mark Loop and Harold, on the basis of Keynes's investment multiplier theory. Keynes believed that the effect of increased investment on national income has a multiplier effect, that is, the increase in national income caused by increased investment is several times greater than the increase in investment. If y is used to denote an increase in national income, k denotes a multiplier, and i denotes an increase in investment, then:

y=k· i (1) The increase in national income is a multiple of the increase in investment because the demand for the means of production increases as a result of the increase in the demand for the means of production, which in turn leads to an increase in the incomes of those engaged in the production of the means of production. The increase in their incomes in turn leads to an increase in demand for consumer goods, which in turn leads to an increase in the incomes of those engaged in the production of consumer goods. By extrapolating this way, the result is that the increase in national income is equal to the increase in investment several times.

Assuming that the new investment i is $100, it is used to purchase the investment product and becomes the increased income of the producer (employer and worker) of the investment product; If the producer of investment goods consumes only 90 per cent of his new income, then the person who gives them the goods receives $90; If these people in turn consume 90% of their income, or $81, it becomes a ...... of increased income to the people who are giving their goodsIf this continues, so does the income. The sum of the increase in income is the following infinite proportional series:

On the basis of Keynes's propensity to consume, the economic implications of the multiplier principle can be summarized as follows: changes in investment have a greater impact on national income than changes in investment, and such changes tend to be multiples of changes in investment. Using the multiplier principle, Keynes obtained the exact relationship between national income (y) and the amount of investment (i).

In macroeconomics, multipliers have two meanings, broad and narrow:

Broadly defined, it refers to the ratio between the amount of change in equilibrium national income and the amount of change in the variable that causes this change.

In a narrow sense, it refers specifically to the investment multiplier, that is, under the condition of a certain marginal propensity to consume, an increase (or decrease) in investment can lead to an increase (or decrease) in national income and employment several times. The ratio of income increments to investment increments is the investment multiplier.

where k is the multiplier, y is the revenue increment, and i is the investment increment. At the same time, the increase in total income caused by the increase in investment also includes the increase in consumption (c) indirectly caused by it, that is, y= i + c, which makes the size of the investment multiplier closely related to the propensity to consume, and the relationship between the two can be deduced mathematically as follows:

k=△y/△i=△y/(△y-△c)=1/(1-△c/△y)

where c y is the marginal propensity to consume.

As can be seen from the above equation, the higher the marginal propensity to consume, the larger the investment multiplier, and vice versa, the smaller the investment multiplier.

Multiplier conditions: various resources in society are not fully utilized.

The multiplier theory was first proposed by the British economist Kahn, and later Keynes further popularized the theory. Kahn's multiplier is the ratio of the total employment caused by new investment to the initial employment directly caused by new investment, whereas Keynes's multiplier is the investment multiplier. Keynes's multiplier theory is a theory about the relationship between changes in investment and changes in income.

Keynes believed that when the total investment increases, the increase in income will be k times the increase in investment, and this k is the investment multiplier. Assuming an additional investment of $1 million in an economy and society, the marginal propensity to consume is 4 5. When $1 million is used to purchase investment goods, it is actually used to purchase the factors of production necessary for the manufacture of investment goods, so that the $1 million flows into the hands of the owners of the factors of production in the form of wages, interest, profits and rents, thus increasing the income of the population by $1 million.

This is the first increase in the income of the society resulting from an additional investment of $1 million.