This equation appears to be a simple macroeconomic model that contains elements of the IS equation and the LM equation.

First, let’s explain the part in brackets: y?20?0.2y

This part actually describes the concept of aggregate demand. Among them:

y represents gross domestic product (GDP) or total income.

20 represents personal savings, the portion of income an individual retains.

0.2y represents personal consumption, where 0.20.2 is the proportion of consumption, which increases with the increase of total income, but not all income is consumed, and the remaining part is used for savings.

Therefore, y?20?0.2y actually describes the remainder after total income minus personal savings and consumption, which can be understood as investment or other expenditures, that is, aggregate demand.

Next, we will give the specific forms of the IS equation and the LM equation.

1. The IS equation describes the relationship between aggregate demand and aggregate output. In the model you gave, the IS equation can be expressed as:

Y=C+I+G

Where:

Y represents gross domestic product (GDP) or total output.

C stands for consumption.

I stands for investment.

G stands for government spending.

After replacing C with y?20?0.2y, the IS equation becomes:

Y=y?20?0.2y+I+G

After simplification, we get:

Y=0.8y?2I+G

2. The LM equation describes the equilibrium relationship between money supply and money demand. In the model you gave, the LM equation can be expressed as:

M/P=L(r,Y)

Where:

M represents money supply.

P represents the price level.

L represents a function of money demand that depends on the interest rate r and gross domestic product Y.

Abbreviate M/P as M and assume that the money demand function is L(r,Y)=kY?hr, where k and ?h are positive constants.

Then the LM equation can be expressed as:

M=kY?hr

Substitute the expression 0.8y?2I+G for Y in the model you gave, and the LM equation becomes is:

M=k(0.8y?2I+G)?hr

The above are the IS and LM equations derived based on the model you provided