Question

1. Consider the economy described by the following equations:

Y = 2400;

C = 100 + 0.75(Y – T) – 10r;

I = 450 – 15r;

G = 250;

NX = 0;

T = 0;

1. Use the information above to calculate an expression (equation) for national saving S as a function of the real interest rate r.
2. Calculate the goods market equilibrium real interest rate, and levels of desired national saving and investment, and consumption.
3. Calculate government (or public) saving. Comment on how this could relate to crowding out.

Answer 1

(a) National Saving: S = Y- C - G

=> S = 2400 - (100 + 0.75(Y-T) -10r) - 250

=> S = 2400 - 100 - 0.75 (2400 -0) + 10r - 250

=> S = 2050 - 0,75 (2400) + 10r

=> S = 2050 - 1800 + 10r

=> S = 250 + 10r

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(b) At goods market equilibrium point;

Y = C + I + G + NX

=> Y = 100 + 0.75(Y-T) -10r + 450 - 15r + 250 + 0

=> Y = 800 + 0.75 (Y-0) -25r

=> Y = 800 + 0.75Y - 25r

=> 25r = 800 + 0.75Y - Y

=> 25r = 800 - 0.25Y

=> 25r = 800 - 0.25(2400)

=> 25r = 800 - 600

=> 25r = 200

=> r = (200 /25)

=> r = 8

Thus, equilibrium interest rate is 8%

S = 250 + 10r

=> S = 250 + 10(8)

=> S = 330

Level of desired national saving is 330

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I = 450 -15r

=> I = 450 - 15(8)

=> I = 330

Equilbrium investment is 330

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C= 100 + 0.75(Y-T) -10r

=> C = 100 + 0.75(2400 -0) -10 (8)

=> C = 100 + 1800 - 80

=> C = 1820

Equilibrium consumption is 1820

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(c) Public saving = T - G

=> Public saving = 0 - 250

=> Public saving = -250

The public saving is -250.

A negative public saving will decrease the national saving, which leads to leftward shift of the loanable funds supply curve and increase the interest rate. An increase in interest rat leads to decrease in investment in the economy.

So, an increase in Government spending (G) will increase the AD in the economy (but at the same time leads to fall in public saving). But this increase in AD leads to decrease in investment (through rise of interest rate). Hence, there is a crowding out effect.