Question

Consider the following model

i) C = 1650 + mpc (Y - tY)
ii) I = 800
iii) G = 500
iv) X - M = 500 - mpi (Y)

where: t = the (flat) tax rate

mpc = the marginal propensity to consume
mpi = the marginal propensity to import

Suppose mpc = 0.60, t = 0.15, mpi = 0.2 Given the information above, solve for the equilibrium output:_________

a. Y* = 3450
b. Y* = 5000
c. Y* = 5500
d. Y* = 1650

Answer 1

The correct option is b. Y* = 5000.

Step-by-step explanation:

Y = C + I + G + (X - M) ................ (1)

Substituting the defined equations into equation (1), we have:

Y = 1650 + mpc (Y - tY) + 800 + 500 + 500 - mpi (Y) ............. (2)

Since we are given:

mpc = 0.60

t = 0.15

mpi = 0.2

We also substitute them into equation (2) and solve for Y* as follows:

Y = 1650 + (0.60 (Y - 0.15Y)) + 800 + 500 + 500 - 0.2Y

Y = 1650 + 0.60Y - 0.09Y + 800 + 500 + 500 - 0.2Y

Y - 0.60Y + 0.09Y + 0.2Y= 1650 + 800 + 500 + 500

Y(1 - 0.60 + 0.09 + 0.2) = 3,450

Y0.69 = 3,450

Y* = 3,450 / 0.69

Y* = 5,000

Therefore, the correct option is b. Y* = 5000.