Answer to Question #225694 in Macroeconomics for Sara

Question

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)
a. What is the equation that describes the IS curve?
b. What is the general definition of the IS curve?
c. What is the equation that describes the LM curve?
d. What is the general definition of the LM curve?
e. What are the equilibrium levels of income and the interest rate?

Answer 1

(a)

$Y=C+I+G$

$=0.8(1-t)Y+900-50R+800=0.6Y+900-50R+800$

$=0.8Y+1700.8-50R$

$Y-0.6Y=1700-50R$

$0.4Y=1700-50R$

$Y=4250-125R$

(b)

The IS curve describes the equilibrium of the product market and a reflection of the relationship between the market interest rate R and the income level Y that arise in the market of goods and services.

The IS curve is derived from a simple Keynesian model, that is the equilibrium model of total expenditures but it differs in that part of total expenditures. In this case, investment expenditure is dependent on interest.

(c)

$IS=4250-125R$

$LM=0.004Y-8$

$Y=4250-125(0.004Y-8)$

$Y=4250-0.5Y+1000$

$Y+0.5Y=5250$

$1.5Y=5250$

$Y=3500$

(d)

The LM curve describes the money market that exists when the demand for money is equal to the money supply. Demand for money is dependent on the interest rate and therefore there is the liquidity money curve , each point being a combination of income and interest rates and ensuring monetary equilibrium is maintained.

(e)

$0.25Y-62.5R=500$

$0.25Y-500=62.5R$

$R=0.004Y-8$

$LM=0.004Y-8$

$IS=4250-125R$

$Y=4250-125(0.004Y-8)$

$Y=4250-0.5Y+1000$

$Y+0.5Y=5250$

$1.5Y=5250$

$Y=3500$

$\therefore$ $R=0.004\times3500-8$

$=6$