7. A closed economy is described by the following simple IS-LM system:

C = a + b(1 – t)Y – dR
I = I
G = G
L = kY – hR

To understand and solve the IS-LM system for a closed economy, let's break it down step by step.

1. Define the variables:
- C: Consumption
- I: Investment
- G: Government spending
- Y: National income (or output)
- R: Interest rate
- a, b, t, d, k, h: Constants or coefficients

2. The IS (Investment-Saving) curve relates the national income (Y) to the interest rate (R):
C = a + b(1 – t)Y – dR
I = I
S = Y – C - G

The equation for consumption (C) consists of four terms:
- "a" represents autonomous consumption, which is the amount of consumption when income is zero.
- "b(1 – t)Y" represents the consumption that varies with income. It can be thought of as the fraction (b) of disposable income (1 – t)Y that is consumed.
- "dR" represents the influence of interest rates on consumption. A higher interest rate reduces consumption.

The equation for investment (I) is assumed to be exogenous or independent of the interest rate and income.

The equation for savings (S) is derived by subtracting consumption (C) and government spending (G) from national income (Y).

3. The LM (Liquidity Preference-Money Supply) curve represents the equilibrium of the money market:
L = kY – hR
M/P = L(Y, R)

The equation for money demand (L) consists of two terms:
- "kY" represents the demand for money as a function of national income. It reflects the need for money to carry out transactions in an expanding economy.
- "hR" represents the demand for money as a function of the interest rate. A higher interest rate reduces the demand for money, as people prefer to hold less of it.

The equation for money supply (M) is assumed to be exogenous or independent of national income and the interest rate.

4. Find the equilibrium output (Y) and interest rate (R):
To find the equilibrium output and interest rate, we need to find the point where the IS and LM curves intersect. At this point, both the goods market and the money market are in equilibrium.

This can be done by simultaneously solving the IS and LM equations, considering the values of the parameters (a, b, t, d, k, h), investment (I), and government spending (G).

By solving the system of equations, we can find the equilibrium values of national income (Y) and the interest rate (R).

Overall, the IS-LM system describes the interaction between the goods market and the money market in a closed economy. It helps to understand how changes in government spending, investment, or the interest rate affect the equilibrium level of national income.