Consider the following model and again answer related questions. 1. Y = C + I +
ID: 1211305 • Letter: C
Question
Consider the following model and again answer related questions.
1. Y = C + I + G + X - M
2. C = 100 + 0.50Y
3. I = 400 - 1000r
4. G = 400
5. X = 300
6. M = 100 + 0.25Y
How much is equilibrium level of income or output if Fed decides to set the rate
of interest at 10 percent (r=0.10).
In an effort to cool down the economy, the Fed raises the rate of interest to r
=0.15. By how much will Y change?
To coordinate the fiscal and monetary policies, assume government decides to
balance the budget by cutting its spending by 100 and at the same time Fed
decides to counter the contractionary effect of cutting spending and lowers the
rate of interest to r = 0.05. Can you predict the change in Y?
Explanation / Answer
Y = C + I + G + X – M
= 100 + 0.50Y + 400 -1000r + 400 + 300 – (100 + 0.25Y)
= 100 + 0.50Y + 400 -1000r + 400 + 300 – 100 -0.25Y
Y = 1100 + 0.25Y – 1000r
0.75Y = 1100 – 1000r
Y = 1466.67 -1333.33r
a.
Output (r = 0.10) Y = 1466.67 – 1333.33 * 0.10 = 1333.337
b.
Y = 1466.67 – 1333.33r
dy / dr = - 1333.33
dy = -1333.33*dr
dr = 0.15, dy = -1333.33*0.15 = -199.9995
c.
GDP = Y = C + I + G + (X-M)
Cutting spending 100
Y = 100 + 0.50Y + 400 -1000r + 300 + 300 – (100 + 0.25Y)
= 100 + 0.50Y + 400 -1000r + 300 + 300 – 100 -0.25Y
Y = 1000 + 0.25Y – 1000r
0.75Y = 1000 – 1000r
Y = 1333.33 – 1333.33r
If r= 0.05
Y = 1333.33 – 1333.33*0.05 = 1266.66