Answer to Question #109838 in Macroeconomics for Ashly

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  0.8(1  t ) Y (P1)
t  0.25 (P2)
I  900  50 i (P3)
−−
G  800 (P4)
L  0.25 Y  62.5 i (P5)
−−
M  −
P  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 (investment-savings) curve describes the equilibrium of the product market and reflects 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 (the equilibrium model of total expenditures or the Keynesian cross model), but differs in that part of the total expenditures and, above all, investment expenditures now depend on the interest rate.

c)

d)The LM curve (liquidity-money) characterizes the equilibrium in the money market that exists when the demand for money (primarily due to the absolute cash liquidity property) is equal to the money supply. Since the demand for money depends on the interest rate, there is a money market equilibrium curve - the LM (Liquidity preference = Money supply) curve, each point of which is a combination of income and interest rates, ensuring monetary equilibrium.

e)0.25Y-62.5R=500

0.25Y-500=62.5R

R=0.004Y-8

d) 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

R=0.004*3500-8=6