Suppose the initial conditions of the economy are characterized by the following equations. In this problem, we assume that prices are fixed at 1 (the price index is 100 and when we deflate, we use 1.00) so that nominal wealth equals real wealth.

1) C = a₀+ a₁(Y - T) + a₂(WSM) + a₃(WRE) + a₄(CC) + a₅(r)

1') C = a₀+ a₁(Y - 200) + a₂(10,000) + a₃(15,000) + a₄(100) + a₅(3)

2) I = b₀+ b₁AS + b₂CF + b₃(r)

2') I = b₀+ b₁(170) + b₂(2000) + b₃(3)

3) G = G

3') G = 300

4) X - M = X - M

4') X - M = - 100

Where: a₀= 200 , a₁= . 6 , a₂= .05, a₃= .10, a₄= .8, a₅= - 500, b₀= 380 , b₁= .5, b₂= .5, b₃= - 200

a.Derive an expression for the consumption function and graph it .Show all work.

b.Derive an expression for the aggregate expenditure curve and graph it onsheet labeling this initial equilibrium output as point A. Also, add this point A to your consumption function.Show all work.

Draw an aggregate demand and an aggregate supply curve in the right hand graph on sheet identifying this initial point as point A.

NOTE:We are holding the price level fixed at 100 in this problem. Also, note that you that you cannot derive an expression for the aggregate demand curve, just draw it with a negative slope going through point A.

c.We now let G rise to 400 as the Federal Government (fiscal policy) authorities are not happy with the level of GDP. Solve for the new equilibrium output and label as point B on all three of your diagrams. Please be sure to label your diagrams completely and show all work.

d.What is the government spending multiplier in this problem and what does this government spending multiplier depend on?