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