The formula is used to derive the expression of the equilibrium output of the three sectors

First, in the three-sector economy in which it participates, national income includes consumption and purchases from the perspective of total expenditure, while from the perspective of total income, it includes consumption, savings and taxes, and taxes here refer to the net tax amount obtained after the total tax subtract transfer payments.

Second, total expenditure = total income then c + i + g = c + s + t i + g = s + t This formula is the condition of macroeconomic equilibrium in the three-sector economy.

1. When the tax is a quantitative tax, y=(a+i+g- t) (1- ).

2. When the tax is proportional y=(a+i+g- t0) [1- (1-t)].

3.When there is a transfer payment, y=(a+i+g- t0+ tr) [1- (1-t)].

Extended Materials. 1. Expressions are combinations obtained by meaningful arrangement methods such as numbers, operators, numeric grouping symbols (parentheses), free variables, and constraint variables. Constraint variables have a numeric value specified in the expression, while free variables can have a numeric value specified in addition to the expression.

2. Giving some numerical designation to a free variable can give an expression value, even if for the value of some free variables, the expression may not be defined. Thus, an expression represents a function, the input of which is a fixed value of a free variable, and its output is the value of the expression that is produced by the result.

For example, the expression x y sets the free variables x and y at 10 and 5, respectively, and its output is the number 2; However, when the y value is 0, it is not defined. The assignment of an expression is related to the definition of an operator and the definition of a numeric value.

If two expressions are said to be equivalent, it means that for any fixed value of a free variable, both expressions will have the same output, i.e., they represent the same function.

3. An expression must be combined. That is, each of its operators must have the correct number of inputs, in the right place. For example, the expression 2+3 is combined; The expression *2+ is not a conjunctive, at least not a general notation of arithmetic.

Expressions and their assignments were formulated in the thirties of the twentieth century by Alonzo Church and Stephen Kleene in their calculus. Calculus has had a significant impact on the development of modern mathematics and computer programming languages.

4. Arithmetic expressions: Arithmetic expressions are the most commonly used expressions, also known as numerical expressions. It is a mathematical formula that performs operations through arithmetic operators.

Three-sector economic equilibrium formula: from the perspective of expenditure, national income is equal to consumption + investment + ** purchase payment, that is, y=c+i+g; From the perspective of income angle slip allocation degree, national income is equal to consumption signal + savings + ** net income, that is, y=c+s+t.

If the leakage w remains constant and the injection j increases, the equilibrium amount of national income increases; Conversely, if the injection decreases, the amount of equilibrium national income decreases. It can be inferred from the composition of the injections that an increase in investment, ** purchases and/or net exports will lead to an increase in equilibrium national income, and a decrease in investment, ** purchases and (available) net exports will lead to a decrease in equilibrium national income.

Equilibrium income is equilibrium national income, which is the gross national product equal to aggregate demand. Fully employed national income refers to the national income that corresponds to aggregate demand at the state of natural unemployment.

1. In the two-sector economy, the equilibrium national income is the national income when investment and savings are equal, y=c+i. When the consumption function c= +y is assumed, then the equilibrium income formula is y=(i) (1- ) and the investment is a function of the interest rate, i.e., i=e-dr, at which point the equilibrium income formula becomes y=( e-dr) (1- ).

2. In the economy of the three ministries of knowledge, the formula for determining the equilibrium national income is: y=c+i+g.

3. In the four-sector economy, the formula for determining the equilibrium national income is: y=c+i+g+nx (nx is the net export, nx=x-m).

In the three-sector economy, national income includes consumption, investment, and purchases from the perspective of total expenditure.

From the perspective of total income, it includes consumption, savings and taxes, where taxes refer to the net tax amount obtained after the total tax subtract the transfer payment.

Total expenditure = total income then c+i+g=c+s+t

i+g=s+t This formula is the condition of macroeconomic equilibrium in the three-sector economy1, when the tax is a quantitative tax.

y=(a+i+g-βt）/（1-β)

2. When the tax is proportional tax.

y=(a+i+g-βt0)/[1-β(1-t)]3.When there is a transfer payment.

y=(a+i+g-βt0+βtr)/[1-β(1-t)]

(1) The composition of the income of the Chinese people in the three-sector economy.

From the perspective of supply, the composition of the income of the Chinese people in the three-sector economy is in addition to the supply of various factors of production in the two-sector economy. The supply refers to the provision of "public goods" such as national defense, legislation, and infrastructure for the whole society. Since these "public goods" are provided and there is a corresponding income-tax, the tax can be used to represent the supply.

In this way: total supply = supply of various factors of production + supply of **.

Salary + Profit + Rent + Interest + Taxes.

Consumption + Savings + Taxes.

If t is used to represent the tax, it can be written in:

y=c+s+t

From the demand side, in addition to the consumption demand and investment demand of the two sectors of the economy, the demand is added, and the demand can be represented by the purchase expenditure. Such.

Total demand = consumption demand + investment demand + ** demand.

Consumption expenditure + investment expenditure + purchase expenditure of **.

If g represents ** purchase expenditure, it can be written:

y=c+i+g

2) The decision to equalize national income.

In the trisectoral economy, the equilibrium conditions for national income remain the following:

Total supply = total demand.

This condition can also be written as:

c+s+t=c+i+g

If c is eliminated on both sides at the same time, it is obtained:

s+t=i+g

This formula is the equilibrium condition for the income of Chinese citizens in the three-sector economy. Therefore, when s+t=i+g, the equilibrium national income is determined.

According to Keynes's theory, the equilibrium national income is equal to aggregate demand, so the equilibrium national income in the three-sector economy can also be determined according to the method of y=c+i+g.