Question

1. The following equations describe an economy. (Think of C , I , G , etc., as being measured in
billions and i as a percentage; a 5 percent interest rate implies i = 5.)
C 5 0.8(1 2 t ) Y (P1)
t 5 0.25 (P2)
I 5 900 2 50 i (P3)
−−G 5 800 (P4)
L 5 0.25 Y 2 62.5 i (P5)
−−My−
P 5 500 (P6)
*An asterisk denotes a more difficult problem.
2. Continue with the same equations.
a. What is the value of aG which corresponds to the simple multiplier (with taxes) of
Chapter 10 ?
b. By how much does an increase in government spending of D −−G increase the level of
income in this model, which includes the money market?
c. By how much does a change in government spending of D −−G affect the equilibrium
interest rate?
d. Explain the difference between your answers to parts a and b .

Answer 1

From the model above we can compute the IS and LM curve to help us answer the asked questions

Y = C+I+G = 0.8(1-0.25) Y +900-50i +800

Y = (2.5) (1700-50i)

From this the Multiplier is 2.5

Therefore, goods market (IS)curve is $4250-125i$

Money market

LM curve is described as $Y=2000+250i$

IS = LM

Equating the IS and LM curves and solving them we get

i = 6

Y = 3500

a.    

 Hence from the calculated multiplier the value of change in G which corresponds to the simple multiplier with taxes is 2.5

$Y=4250-125i + 750$ (Equation from 1a)) $Y = 5000-125i$

From IS curve and LM curve the interest is 8 

$2000 + 250x8$

Income = 4000

ΔY = 500 (increased by 500 compared to 1e)

$(ΔY) ÷ ( ΔG) = 450 ÷ 150 = 3$

$α1 = (ΔY) ÷ ( ΔG)$

$= 500÷150 = 3.33$

b.      

It increases the income by 375

ΔG = 150

 $ΔIS = 2.5 x 150 = 375$

c.       

The equilibrium interest increases by 2 points from 6 to 8% due to the change in government spending of 150.

 

d.      

α = 3 in 2a represents horizontal shift of the IS curve incase autonomous spending deviates by 1 unit. In 2a) if income increases it leads to a subsequent increase in the demand for money which again increases the rate of interest. 

In 2b) the effect of the multiplier is much higher than in 2a the multiplier increased from 3 to 3.33.