Question

Consider an economy in the short-run described by the following equations:

AD = C + I + G

G = 500

TA = 700, TR = 200

C = 400 + 0.6(Y – TA + TR)

I = 600

1. What is the equilibrium condition that allows us to solve for Y. Find Y.  Compute private saving, public saving and total/national saving at this level of Y.
2. What is the value of the marginal propensity to consume? What is the value of the expenditure multiplier?  Explain the economic effect of the multiplier in words.
3. Now suppose that G rises to 600.  Find the new equilibrium value of Y.
4. Compute private saving, public saving and total/national saving at the new equilibrium.

Answer 1

(a)

In equilibrium, Y = AD.

Y = 400 + 0.6(Y - 700 + 200) + 600 + 500

Y = 1500 + 0.6(Y - 500)

Y = 1500 + 0.6Y - 300

0.4Y = 1200

Y = 3000

C = 400 + 0.6(3000 - 700 + 200) = 400 + 0.6 x 2500 = 400 + 1500 = 1900

Private saving (Sp) = Y - C = 3000 - 1900 = 1100

Public saving (Sg) = T - G = 700 - 500 = 200

National saving (S) = Sp + Sg = 1100 + 200 = 1300

(b)

MPC = 0.6

Multiplier = 1 / (1 - MPC) = 1 / (1 - 0.6) = 1/0.4 = 2.5

It means that as autonomous spending increases (decreases) by 1 unit, output (Y) increases (decreases) by 2.5 units.

(c)

Y = 400 + 0.6(Y - 700 + 200) + 600 + 600

Y = 1600 + 0.6(Y - 500)

Y = 1600 + 0.6Y - 300

0.4Y = 1300

Y = 3250

(d)

C = 400 + 0.6(3250 - 700 + 200) = 400 + 0.6 x 2750 = 400 + 1650 = 2050

Sp = Y - C = 3250 - 2050 = 1200

Sg = T - G = 700 - 600 = 100

S = Sp + Sg = 1200 + 100 = 1300