Part 1: AE problem

Suppose the initial conditions of the economy are characterized by the following equations in black font. We then shock the economy as shown in the red font.

1) C = a₀ + a₁ (Y-T) + a_{2 (}WSM) + a₃ (WRE) + a₄ (CC) + a₅ (r)

1') C = a₀ + a₁ (Y-200) + a₂ (10,000) + a₃ (15,000) + a₄ (120) + a₅ (4)

1'') C = a₀ + a₁ (Y-200) + a₂ (12,000) + a₃ (15,000) + a₄ (160) + a₅ (4)

2) I = b₀ + b₁AS + b_­2CF + b₃ (r)

2') I = b₀ + b₁ (140) + b₂ (1500) + b₃ (4)

2') I = b₀ + b₁ (180) + b₂ (2000) + b₃ (4)

3) G = G

3') G = 200

4) X-M = X-M

4') X-M = -200

4') X-M = -400

5) AE = C + I + G + X-M

Where: a₀ = 50, a₁ = .60, a₂ = .05, a₃ = .10, a₄ = .5, a₅ = -400, b₀ = 100, b1 = .5, b₂ = .2, b₃ = -50

a) Given the initial conditions, find expression for consumption function and provide a completely labeled diagram. Please show all work.

b) Given the initial conditions, find an expression for the aggregate expenditure curve (AE in terms of Y), solve for equilibrium output and provide a graph of this aggregate expenditure curve labeling this initial equilibrium as point A. Please add point A to your consumption function diagram, being sure to label this point completely. Please show all work. 

c) We now incur shocks as provided in red font. Solve for a new expression of the consumption function and aggregate expenditure curve, solve for the new equilibrium output and add this new equilibrium point to both of your diagrams (label as point B). Please show all work.

d) Are your results consistent with the new economy? Why or why not? Explain in detail.