Answer to Question #147944 in Macroeconomics for Khanyisani Jila

Question

The following information is provided about an open economy with a government. Use the
information to answer the questions that follow:
C = 450 + 0.4Y
I = 350
G = 150
X = 70
Z = 35 + 0.1Y
T = 0.15Y
Yf = 1550
Q.2.1 Calculate the level of autonomous spending in this economy. (2)

Q.2.2 Calculate the size of the multiplier
(Note: Round your answer to two decimal places)
(4)
Q.2.3 Calculate the equilibrium level of income
(Hint: use the multiplier method)

Answer 1

Consumption (C) = 450 + 0.4Y where Y is income

Investment (I) = 350

Government spending (G) = 150

Exports (X) = 70

Imports (Z) = 35 + 0.1Y

Taxes (T) = 0.15Y

Full employment income (Yf) = 1550

Q.2.1

Y = C + I + G + X – Z

Y = 450 + 0.4Y + 350 + 150 + 70 – 35 – 0.1Y

Y = 985 + 0.4(Y – T) – 0.1Y

Y = 985 + 0.4(Y – 0.15Y) – 0.1Y

Y = 985 + 0.24Y

Autonomous Spending = 985

Q.2.2

Multiplier $= \frac{1}{[1 – c(1 – t)] + m}$

In the above c is marginal propensity to consume (mpc), m is marginal propensity to import (mpm) and t is the tax rate

$Multiplier = \frac{1}{[1 – 0.4(1 – 0.15)] + 0.1} \\ Multiplier = \frac{1}{[1 – 0.4(0.85)] + 0.1} \\ Multiplier = \frac{1}{0.76} \\ Multiplier = 1.31$

Q.2.3

Y = 985 + 0.24Y

Y – 0.24Y = 985

0.76Y = 985

Equilibrium level of income = 1296