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: 

(a) Briefly explain the meaning of each equation in the above model. What are the values of d Y C , r I , LY and 

S Nw . Give economic interpretation of each. 

(b) Add all relevant identities and equilibrium conditions to complete the model. Write down the endogenous 

and exogenous variables.

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