Given the following model YCIGXZ CabY ZZ0 zY where I90 G65

Given the following model: Y=C+I+G+X-Z

C=a+bY

Z=Z₀ + zY

where I=90, G=65, X=80, a=70, Z₀=40, b=.9, z=.15

What is the equilibrium level of income Y*? SHOW ALL STEPS.

Solution

GIVEN    Y=C+I+G+X-Z

      C=a+by

                 Z=Z₀+zY

Where I=90, G=65, X=80, a=70, Z₀=40, b=.9, z=.15

Y=C+I+G+X-Z

Y = (a+bY)+I+G+X-(Z₀+ZY)

Y = 70+9Y+90+65+80-40-15Y

Y = 265-6Y

7Y = 265

Y = 37.85