The economy begins in equilibrium at point E, representing the real interest rate r1 at which saving S1 equals desired investment I1. What will be the new equilibrium combination of real interest rate, saving, and investment if the government cuts spending, holding other factors constant?

The new equilibrium combination will be at increases I1 to I2, S1 to S2, and r1 to r2.

Explanation:

Saving or national saving of an economy is amount  of national income or gross domestic product (GPD) that is not spent by the government. Using a simple example of a closed economy, i.e. an economy with no foreign trade in terms and imports, this statement can be mathematically as follows:

Y = C + I + G (1)

Where,

Y denotes national income (GDP), C denotes consumption, I denotes Investment, and G denotes government spending.

To get investment, equation (1) can be rewritten by making I the subject of the formula as follows:

I = Y - C - G (2)

In economics, saving (S) is always equal to investment (I). Therefore, equation (2) can be rewritten by equating it with I as follows:

I = Y - C - G = S

I = S

Both I and S can be written as initial saving (S1) and initial Investment (I1), and we therefore have

I1 = S1 (3)

Equation (3) is an equilibrium E which implies that Investment (I1) is equal to saving (S1) at the initial real interest rate (r1). Real interest here denotes the price for saving and investment.

Since saving of an economy is amount  of national income or GDP that is not spent by the government, a cuts in the government spending will cause saving to rise, i..e. to S2. Since saving and Investment is always equal to investment, Investment will also rise, i.e. to S2. Increase in I1 to I2 and also in S1 to S2, will cause the real interest rate to rise to r2 at E2 which is the new equilibrium combination of real interest rate, saving, and investment

Therefore, the new equilibrium combination of real interest rate, saving, and investment if the government cuts spending, holding other factors constant, will be at increases in I1 to I2, S1 to S2, and r1 to r2.

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