Question

# In the Keynesian Cross, assume that the consumption function is given by: C = 200 +...

In the Keynesian Cross, assume that the consumption function is given by: C = 200 + 0.8 (Y-T).

Assume that: I = I ̅= 100, G = G̅ =100, T = T̅ =100.

a) Use graphical analysis to demonstrate the determination of equilibrium income.

b) What is the equilibrium level of income?

c) If government spending increase to 125, what is the new equilibrium income?

d) Now instead of assuming T = T̅ , assume that T = T̅ + tY, where T̅ and t are parameters of the tax code. The parameter t is the marginal tax rate: if income rises by \$1, taxes rise by t x \$1. Derive the new government spending multiplier under this system and explain how this tax system alters the slope of the IS curve.

a.

b.

The equilibrium income is determined by solving the two equations:

AE = PE

Y = 200 + 0.8(Y - 100) + 100 + 100

Y = 1600

c.

Delta Y= (125-100)/(1-MPC)

=25/(1-0.8)

=125

New equilibrium income = 1600 + 125 = 1725

d.

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