Consider the following behavioral equations:

Y=C+I+G

C = Co + C1Yd

Yd=Y-T

T=to+t1 Y

I= bo + b1 Y - b2 i

i = -

i

G is exogenously given and constant. Assume that C1, b1, and t1 are between 0 and 1, and that

Co = Autonomous consumption, i.e., consumer confidence

C1 = Marginal propensity to consume

bo = Autonomous investment, i.e., business confidence

b1 = Marginal propensity of invest

to = Constant autonomous lump-sum tax

t1 = tax rate, i.e., the proportion of income tax

a. Solve for equilibrium output.

b.Show and illustrate the equilibrium level of output for this economy on a 22-Y graph (i.e., a graph that includes the ZZ line and 45-degree line with Z-demand- on the vertical axis and Y on the horizontal axis),

i. On your graph,show the equilibrium output level on the horizontal axis, and the point at the ZZ line crosses the vertical axis (i.e., y-intercept).

ii. Explain what variables determine the slope of the ZZ line and what variables determine the value of the point ZZ lines hit the vertical axis?

iii. Explain why the slope of the ZZ line is important?

c. What is the multiplier in this economy? What is the value of autonomous spending?

When does the economy respondmore to changes in autonomous spending? Explain.

d. ???For the multiplier to be positive, what conditions must be satisfied? What would happen if they were not satisfied? Explain your answers.

e. ???Using the result you obtained in (a) solve for the equilibrium level of investment. What variables in your solution have a positive relationship with investment? What are the variables in your solution that have negative relationships with investment?

Q1 ['70 points] Consider the following behavioral equations: Y=C+I+G C=Co+01YD YDT-Y-T T=to+t1Y I=bo+b1Y-b21 1:1 G is exogenously given and constant. Assume that Cl, b1 and t1 are between 0 and 1, and that co = Autonomous consumption, i.e., consumer confidence 01 = Marginal propensity of consume 130 = Autonomous investment, i.e., business confidence bl = Marginal propensity of invest to = Constant autonomous lump-sum tax t1 = tax rate, i.e., proportion of income tax