Consider the following model of a very simple economy. Household saving and investment behavior depend in part on wealth (accumulated savings and inheritance). In the late 1990's many were concerned with very large increase in stock value (a form of wealth) and it's possible effect on saving and investment.

The following consumption function incorporate wealth (W) as a determinant of consumption. We have the following information on consumption (C) and investment (I):

C=45+0.60Y+0.05W
I=100
W=800

We are ignoring the fact that saving adds to the stock of wealth.

Calculate the value of equilibrium Y, C, and savings (S). (Enter you responses as Integers. )

Equilibrium Y = 462.5 , Equilibrium C = 362.5 , Equilibrium S = 100

Explanation:

[ AD = C + I ] = [ AS = C + S = Y ]

45 + 0.6Y + 0.05 W + 100 = Y → 45 + 0.6Y + 0.05 (800) + 100 = Y

45 + 40 + 100 + 0.6Y = Y → Y ; 185 + 0.6Y = Y

Y - 0.6Y = 185

0.4Y = 185

Y = 185 / 0.4 = 462.5  

Putting Y value : C = 45 + 0.6 (462.5) + 0.05 (800) → C = 45 + 277.5 + 40

C = 362.5

Hence , S = Y - C → 462.5 - 362.5 = 100

Alternatively : As  C + I = C + S

Hence, I = S

Equilibrium Savings = Given Investment = 100

start by isolating the variable on one side by adding 43w^2 to both sides.   the equation will read:

25w^2+5=0

*subtract 5 from both sides*

25w^2=-5

*divide both sides by 25*

w^2=-1/5

*take the square root of both sides*

w=√(-1/5)

the square root of -1 is i.   the square root of 5 remains √5

the answer is i/√5.

hope this