Answer to Question #118262 in Economics for michael

Question

1. Consider an economy with the following equations.
C= 0.8 (1- t) Y
t= 0.25
I= 900 – 50i
G = 800
L= 0.25Y – 62.5i
M=2,500
P= 5
Where;
C is Consumption function, t is Marginal propensity to tax, I is Investment function, G is
autonomous Government expenditure, L is liquidity Preference, M is money stock and P is the
average price level.
a) Derive the IS curve relation for this economy. [3 marks]
b) Derive the LM curve relation for this economy. [3 marks]
c) Based on your answer in a) and b), interpret the nature of slopes of the IS and the LM curves.
[3 marks]
d) Determine the equilibrium output and real interest rate for this economy? [3 marks]
e) Suppose government increases its expenditure to 1,000. Calculate the new equilibrium
output and new interest rate at this level. [3 marks]

Answer 1

a) Derive the IS curve relation for this economy. [3 marks]

The is derived as follows:

$\text{Y=C+I+G}$

$\text{Y}=0.8(1-t)Y+900-50i+800$

$\text{Y}=0.8(1-0.25)Y+900-50i+800$

$\text{Y}=0.6Y+1700-50i$

$\text{Y}-0.6Y=1700-50i$

The is equation therefore, becomes:

$\text{Y}=4250-125i$

b) Derive the LM curve relation for this economy. [3 marks]

The LM curve is computed by equating money supply to be equal to the demand of money.

$2500=0.25Y-62.5i$

$-0.25Y=-62.5i-2500$

The LM equation is therefore:

$Y=10000+250i$

c) Based on your an answer in a) and b), interpret the nature of slopes of the IS and the LM curves.

The IS curve has a negative slope meaning as that for the national income to increase the rate of interest must decrease to discourage savings and encourage investment. On the other hand, the LM curve has a positive slope. This means that as the national income increases that interest rate also increases

d) Determine the equilibrium output and real interest rate for this economy?

$10000+250i=4250-125i$

$\text{i}=\dfrac{5750}{375}=15.33\%$

e) Suppose government increases its expenditure to 1,000. Calculate the new equilibrium

output and new interest rate at this level.

$\text{Y}=0.8(1-0.25)Y+900-50i+1000$

$\text{Y}=0.6Y+1900-50i$

$Y=4750-125i$

Equilibrium interest rate is:

$4750-125i=250i+10000$

$i=\dfrac{5250}{375}=14\%$

Equilibrium national income will therefore, be:

$Y=4750-125\times 0.14=4732.5$