Answer to Question #219140 in Macroeconomics for RuDavis

Question

Consider the following economy

 

C=0.8(1-t)Y , t=0.25,I=900-50i, G=800, L=0.25Y-62.5i, M/P=500

 

a. Find the equilibrium income and interest rate. 

b. What is the value of the multiplier? 

c. How much does a unit change in G change the equilibrium income and interest rate?

d. How much does a unit change in M/P change theequilibrium Income and 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. It reflects the relationship between the market interest rate R and the income level Y that arise in goods and services. The IS curve is derived from a simple Keynesian model( the equilibrium model of total expenditures or Keynesian cross model). Still, it differs in that part of total expenditures and above all investment expenditures now depend on the interest rate.

(c)

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.

(d)

$0.25Y-62.5R=500$

$0.25Y-500=62.5R$

$R=0.004Y-8$

$IS=4250-125R$

$LM=0.004Y-8$

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

$Y=4250-0.5Y+1000$

$Y+0.5Y=5250$

$1.5Y=5250$

$Y=3500$

$R=0.004\times3500-8=6$