Question

2) Given the following National Income Model:

Y = C + I0 + G0 + (X0 - M0)

C = 100 + 0.5(Y - T)

T = 10 + 0.2Y

a. How many endogenous variables are there?

b. Find Y*, T*, and C* if:

I0 = 17

G0 = 13

X0 = 100

M0 = 150

c. What are the economic meanings of (Y - T) and the coefficient 0.5 in the previous Keynesian consumption equation?

d. What is the value of the government spending multiplier?

e. If the government spending increases by 2 billion dollars, what is the amount of change in the national income?

Answer 1

a. In the set of equations, 3 variables are endogeneous. These are Y, C and T.

b. Y = C + I0 + G0 + (X0 - M0);

  C = 100 + 0.5(Y - T)

  T = 10 + 0.2Y

so, Y = 100 + 0.5(Y - T) + I0 + G0 + (X0 - M0)

or, Y = 100 + 0.5(Y - 10 - 0.2Y) + I0 + G0 + (X0 - M0)

or, Y = 100 +0.5 (0.8Y - 10) + 17 + 13 + (100 - 150)

or, Y = 100 +0.4Y - 5 + 30 - 50

or, 0.6Y = 75

or, Y = 75/0.6

or, Y = 125

so, T = 10 + 0.2Y = 10 + 0.2*125 = 10 + 25

and C = 100 + 0.5(Y - T) = 100 + 0.5 * (125 - 25) = 100 + 50 = 150

c. (Y - T) is the after tax income. This is also called the disposable income.

0.5 in the Keynesian consumption equation represents the Marginal Propensity to Consume. This is nothing but the measure which says the increase in consumption due to an unit increase in disposable income.

d.