If bonds demand (Bd) is P = 1100-5Q, bonds supply (Bs) is P = 500+15Q, respective interest rate i* = (F-P)/P, assume F = 1000, money demand is L = 0.8Y-62.5i and real money balance is $1500m with fixed prices. Each sub-question carries 2½ marks.

(a)  Determine the interest rate using bonds market equations.

(b)  Show financial market dynamics in (BsBd), (MsMd) and (ISLM) spaces.

(c)   If IS was Y= 2240 -120r, derive the AD function if MP rule was r = 2 +0.5π

(d)  Use ADAS to determine RGDP if Phillips Curve was π = 10 + 0.5(Y-Y*) + ρ, where Y* (Potential RGDP) was 1500 and ρ (financial friction) was 2%.

 

1) Interest rate using bonds market equations

We take the bond demand and equate it to bond supply

Bd = Bs

Given p= 1100 - 5Q and p = 500 + 15Q, then;

1100 - 5Q = 500 + 15Q

20Q = 600

Q = 30 units

To calculate price, substitute value of Q in one equation as follows;

p= 1100 - 5 (30)

p = 1100 - 150

p = 950

The interest rate is computed using the below formula;

I* = (F - P)/P

I* = ( 1000 - 950)/ 950

I* = 50/950

I* = 0.053

2) Financial market dynamics in (BsBd), (MsMd) and (IS-LM) spaces

(This is explained with diagrams as shown in the attached)

3) If IS was Y= 2240 -120r, the AD function if MP rule was r = 2 +0.5π

The IS equation;

Y = 2240 - 120r

m/p = 0.8Y - 62.5 r = 1500

0.8Y - 62.5 ( r + π) = 1500

Given that r = 0.5 π + 2

Then r = I - π

Therefore, we compute it as follows;

0.8 Y = 1500 + 62.5 (r + π)

Y = 1500/0.8 + 62.5/0.8 (r + π)

Y = 1875 + 78.125 (1.5 π + 2)

This can further be simplified as follows;

Y = 2240 - 120r = 2240 - 120 (0.5 π + 2)

Y = 2240 - 240 - 60 π

Y = 2000 - 60 π

Equation Y = 1875 + 78.125 (1.5 π + 2) can be substituted in Y = 2000 - 60 π as follows;

1875 + 78.125 (1.5 π + 2) = 2000 - 60 π

Solving for π is done as follows;

Π = -31.25/177.1875

Π = - 0.1764

We can get Y* by substituting π in one equation as follows

Y* = 1875 + 78.125 {1.5 (-0.1764) + 2)}

Y* = 2,010.58

4) Using ADAS to determine RGDP if Phillips Curve was π = 10 + 0.5(Y-Y*) + ρ, where Y* is 1500 and ρ was 2%

Determining RGDP is computed as follows;

Π = 10 + 0.5 (Y - Y*) + P

Given p is 2%, Y* is 1500, then we can substitute them in Π equation as follows;

-0.1764 = 10 + 0.5 (Y - 1500) + 0.02

-0.1764 = 10 + 0.5 Y - 750 + 0.02

0.5Y = 739.8036

Y = 739.8036/0.5

Y = 1,479.6072

The RGDP is 1,479.6072

Please see the attached file for the complete solution