Problem 1:
Given: | C = 750 + 0.90Y | |
I = 350 | ||
G = 400 | ||
Find: | the values of Y and C that satisfy the equation: Y = C + I + G |
Y = C + I + G | ||
Y = 750 + 0.90Y + 350 + 400 | ||
Y - 0.90Y = 1,500 | ||
0.1Y = 1,500 | ||
Answer: | Y = 15,000 | |
C = 750 + 0.90Y | ||
C = 750 + 0.90(15,000) | ||
C = 750 + 13,500 | ||
Answer: | C = 14,250 | |
Alaternatively: | Y = C + I + G | |
C = Y - I - G | ||
C = 15,000 - 350 - 400 | ||
Answer: | C = 14,250 |
Problem 2:
Given: | DY = [-b/(1-b)] DT | |
b = 2/3 | ||
Find: | the value of DT that yields a DY of 200 | |
Note:: | The Greek letter "D"
(Delta) means "change." The equation indicates that the change in Y is
-b/(1-b) times the change in T.
You need not (and should not) convert the fraction 2/3 to 0.666666666666666666666666666666666666666666666666666. |
DY = [-b/(1-b)] DT | ||
200 = [-(2/3)/(1-2/3)] DT | ||
200 = [-(2/3)/(1/3)] DT | ||
200 = -2 DT | ||
Answer: | DT = -100 |
Problem 3:
Given: | M = C + D | |
D = R/r | ||
C = 600 | ||
R = 400 | ||
Find: | the value of r that yields an M of 2,600 |
M = C + D | ||
M = C + R/r | ||
2,600 = 600 + 400/r | ||
2,000 = 400/r | ||
r = 400/2000 | ||
Answer: | r = 0.20 |
Problem 4:
Given: | C = a + bY, where a and b are known parameters | |
Y = C + I | ||
Find: | the equation that describes how C depends upon I | |
Hint: | You're looking for an equation
in the form C = h + jI,
where h and j are expressions in a and/or b. |
|
Application: | Suppose that a = 400 and b = 0.75. | |
Find: | the corresponding values of h and j. | |
Write C = h + jI, using the these numerical values. | ||
When I = 600, how much is C? |
If C = a + bY, and we know that Y = C + I, | ||
then, C = a + b(C + I) | ||
C = a + bC + bI | ||
C - bC = a + bI | ||
(1 - b)C = a + bI | ||
C = a/(1-b) + b/(1-b) I | ||
If a = 400 and b = 0.75, | ||
then C = 400/(1-0.75) + 0.75/(1-0.75) I | ||
C = 400/(0.25) + 0.75/(0.25) I | ||
C = 1600 + 3I (which means that h = 1600 and j = 3) | ||
If I = 600, | ||
then C = 1600 + 3(600) | ||
C = 1600 + 1800 | ||
C = 3400 |