C=15+0.50Y+0.0.5W
I=100
W=1,200
Calculate the values of equilibrium Y,C,and S
To calculate the values of equilibrium Y (income/output), C (consumption), and S (saving), we need to use the given equations and values.
The given consumption function is:
C = 15 + 0.50Y + 0.5W
We are also given that investment (I) is equal to 100 and W (wealth) is equal to 1,200.
To find the equilibrium values, we need to set Y (income/output) equal to C (consumption) + I (investment) and then solve for Y.
So, the equation becomes:
Y = C + I
Substituting the given values, we have:
Y = (15 + 0.50Y + 0.5W) + 100
Now, substitute the given value of W (wealth):
Y = (15 + 0.50Y + 0.5(1,200)) + 100
Y = (15 + 0.50Y + 600) + 100
Simplifying the equation, we get:
Y = 715 + 0.50Y
Next, we subtract 0.50Y from both sides:
0.50Y = 715
Dividing both sides by 0.50, we find:
Y = 1,430
Now, we have the value of Y (income/output) at equilibrium.
To calculate the values of C (consumption) and S (saving), substitute the value of Y into the consumption function equation:
C = 15 + 0.50Y + 0.5W
C = 15 + 0.50(1,430) + 0.5(1,200)
C = 15 + 715 + 600
C = 1,330
Finally, to calculate S (saving), we use the equation:
S = Y - C
Substituting the values, we have:
S = 1,430 - 1,330
S = 100
So, the values of equilibrium Y (income/output), C (consumption), and S (saving) are:
Y = 1,430
C = 1,330
S = 100