Math Skills Prerequisite to ECON 2030

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