Question

Suppose that 

 C = 60 + 0.8YD

 I = 150 - 10r

G = 250

T = 200

Ms

= 100

 Md

= 40 + 0.1Y - 10r

 a. Write the equations for the IS and LM schedules. 

 b. Find the equilibrium values for income ( Y0 ) and the interest rate ( r0 ). 

Answer 1

a. The condition of t he equilibrium of the market of goods in the Keynesian model: the income of the economic system at the point of equilibrium is equal to expenses. We find the equation of the line IS, which determines all the points of equilibrium of the market of goods.

$Y=C+I+G$

$Y=60 + 0.8\times YD+150-10\times r+250$

$Y=60 + 0.8(Y-T)+150-10r+250$

$Y=60 + 0.8(Y-200)+150-10r+250$

$Y=300+ 0.8\times Y-10r$

$Y-0.8\times Y=300-10\times r$

$0.2\times Y=300-10\times r$

$Y=1500-50\times r$ the IS equation

Ms=Md

$100=40 + 0.1\times Y - 10\times r$

$60= 0.1\times Y - 10\times r$

$600+100\times r=Y$ the LM equation

b.IS=LM

$1500-50\times r=600+100\times r$

r=6%

$Y=1500-50\times r=1500-50\times6=1500-300=1200$