Question

1. Consider the following national-income model.

Y = AE（1）
AE = C + I0 + G0（2）

C = C0 + bY 0 < ? < 1（3）

(a)Remaining in parametric form (do not sub in parameter values), build the equation for total spending AE (also known as aggregate demand).

(b) Continuing in parametric form, find the RFE for equilibrium national income Y* (also known as equilibrium national output).

(c) Using the parameter values ?0 = 25, ? = 0.75, ?0= 50, and ?0 = 25, find the total spending equation.

(d) Solve for the numeric value of ?

(e) Sketch a graph depicting this model. Label well.

(f) In 2-5 sentences, explain what will happen if this economy produces at an output level greater than its equilibrium level.

(h) Find the multiplier for this economy.

(i) Use the multiplier to find the new equilibrium level of national income if ?0 decreases to 15.

Answer 1

Consider the following national income model.

Y = AE（1）

AE = C + I0 + G0（2）

C = C0 + bY , 0 < ? < 1（3）

(a) AE is the aggregate demand function,

Putting equation (3) in equation (2), we get,

AE = C0 + bY + I0 + G0 (4)

The equation (4) shows the aggregate demand function or AE function.

(b) At the equilibrium level, Y = AE

Now putting equation (4) in equation (1) , we get,

Y = C0 + bY + I0 + G0

Y – bY = C0 + I0 + G0

Y(1 – b) = C0 + I0 + G0

Y^* = (C0 + I0 + G0)/ (1 – b) (5)

The above equation shows the RFE for equilibrium national income Y* or the equilibrium national output.

(c) From equation (4) we get,

AE = C0 + bY + I0 + G0

Putting the values of ?0 = 25, ? = 0.75, ?0= 50, and ?0 = 25 which are given, we get

AE = 25 +0.75Y + 50+ 25

AE = 100 +0.75Y

The above equation shows the total spending equation.

(d) From equation (5) we get,

Y^* = (25+ 50+25)/ (1 – 0.75)

Y^* = 100/0.25

Y^*= 400

The value of Y^* is the 400.

(e) The graph is as follows-

Figure 1

(f) If the economy produces an output which is greater than the equilibrium level or right side of the point A in the figure 1, then there will be excess supply. Any point right side of the equilibrium point implies excess supply where inventory is positive. At this situation the price of the goods falls until the point reaches at the equilibrium point.

In the graph we can see that, B is point of supply and C is the point of demand, there is a gap between demand and supply which implies inventory is positive and there exist excess supply.

Figure 2

(h)

From equation (5) we get,

Y(1 – b) = C0 + I0 + G0

Now we take the derivative with respect to g0

dY/dG0 = 1/(1 – b)

This is the multiplier value for the economy.

(i)

G0 decreases 25 to 15, so the change or dG0 =(15- 25) = -10

Changes in G0 do not affect the slope or b. using the multiplier

dY = dG0/(1-b)

dY = -10/ 0.25

dY = -40

Y₁ - Y^* = -40

Y₁ = -40 + 400

Y₁ = 360

The new equilibrium level of national income is 360. Due to fall in G0 the equilibrium level of income also falls from 400 to 360.