Answer to Question #214038 in Macroeconomics for Kay

Question

Q.1 Consider the following information about a hypothetical economy:

1. Y = A (0.025K − 0.5N) N

2. A=2/3

3. K=2000

4. N^s=-18+(18/5)w

5. C=200+(2/3)(Y-T)-300r

6. T=-75+(1/4)Y

7. I =100−100r

8. G=100

9. L = 0.5Y − 200i

10. M=6300

11. π^e=0.10

Now using this information, answer the following: 

(e) Beginning from the initial classical equilibrium, suppose that the central bank increases the money supply 

by 420 while price remains fixed at its initial long run equilibrium level. What will be the impact of this 

policy on all endogenous variables in short run and long run? 

(f) Compare the equilibrium positions in (d) and (e) in one graph indicating all points. 

Answer 1

a

$Y=\frac{2}{3}[(0.025×2000)-0.5N]N\\Y=\frac{2}{3}(50-0.5N)N\\Y=\frac{100N}{3}-\frac{1}{3}N^2$

equilibrium income

$T=-75+\frac{1}{4}Y\\T=-75+\frac{25y}{3}-\frac{y^3}{12}$

taxes

$C=300+\frac{2}{3}(Y-T)-300r\\C=300+\frac{2}{3}(Y-(-75+\frac{1}{4}y))-300r\\C=-300r+\frac{y}{2}+250\\C=-300r+250+\frac{\frac{100N}{3}-\frac{N^3}{3}}{2}$

consumption

$N=-18+\frac{18}{5}W\\Y=\frac{594}{5}W-594\\Y-594=\frac{594}{5}W\\W=\frac{5(Y-594)}{594}\\N=-18+\frac{18}{5}(\frac{5(Y-594)}{594})\\N=\frac{Y-1188}{33}$

$I=100-100r\\r=\frac{1000-r}{100}\\interest \space rates\\$

any change in in values affects each other because they are corelated. the economy depends on several factors to be at equilibrium.

b

the endogenous variables include Y

and exogenous variables C, I,T,C