# Bonus Assignment: Marginal Propensity to Consume

There were two unanswered questions in the problems we covered in class (one in slide#20 of the lecture – this was not a typo – and the other in slide#21). I will rewrite them here. The first person to answer both correctly, gets a half-point bonus. Please write all steps clearly.

1. If C0 = \$500, Cy = 0.8 and t = 0.2, what is the value of income Y, for which household saving SH equals zero?

2. If C0 = \$400, Cy = 0.75 and t = 0.15 and national income changes from \$10,000 million to \$11,000 million, what is the change in YD and C? Calculate these changes without using the consumption function.

You must answer both questions correctly, and show clearly how you got the answer. The first person to do that will get the half-point bonus.

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## 5 comments for “Bonus Assignment: Marginal Propensity to Consume”

1. David Lefebvre
February 26, 2008 at 9:03 pm

1. If C0 = \$500, Cy = 0.8 and t = 0.2, what is the value of income Y, for which household saving SH equals zero?

Households spend all of their income on one of three things: (1) Consumption; (2) Savings and; (3) Taxes. So Y = C + S + T.

In this case S equals zero, so Y = C + T.

Today we learned that C = C0 + CyYD, where YD is the disposable (or after-tax) income, and YD = (1-t)Y. Taxes “T” are simply Y times the tax rate t. Plugging these into the above equation, Y = C0 + Cy(1-t)Y + t(Y)

Plugging in the numbers, we get Y = 500 + 0.8(1-0.2)Y + (0.2)Y.

Solving,
Y = 500 + (0.64)Y + (0.2)Y
Y = 500 + (0.84)Y
(0.16)Y = 500
Y = 3125

2. If C0 = \$400, Cy = 0.75 and t = 0.15 and national income changes from \$10,000 million to \$11,000 million, what is the change in YD and C? Calculate these changes without using the consumption function.

YD = (1-t)Y.

YD = (1-0.15)10,000
YD = 8,500

YD = (1-0.15)11,000
YD = 9,350

YD increases from \$9,350 million to \$8,500 million when national income changes from \$10,000 million to \$11,000 million.

Savings is what’s not consumed or paid in taxes times disposable income, or S = (1-Cy)YD

Y = C + S + T –> C = Y – S – T –> C = Y – (1-Cy)YD – (t)Y

C = 10,000 – (1-0.75)(8,500) – (0.15)(10,000)
C = 6,375

C = 11,000 – (1-0.75)(9,350) – (0.15)(11,000)
C = 7,012.5

C increases from \$6,375 million to \$7,012.5 million when national income changes from \$10,000 million to \$11,000 million.

2. David Lefebvre
February 26, 2008 at 9:07 pm

Oops, the answer to question 1 above should say “YD increases from \$8,500 million to \$9,350 million when national income changes from \$10,000 million to \$11,000 million.”

3. Minna Howell
February 26, 2008 at 9:41 pm

I am not sure if this is correct but its worth a try.
1.) C=Y^D-S^H but since S^h is zero in this case C=Y^D
Y^D=(1-t)Y
=(1-.2)Y
=.8Y

C=Co+CyY^D
but C=Y^D in this case so substituting in:
Y^D=Co+CyY^D
substituting in from above:
.8Y=500+.8(.8Y)
.8Y=500+.64Y
.16Y=500
Y=3125 (Looking above I got the same answer as David but I think I did it a little differently. I got a different answer for number 2:

2.) for Y=10 mill
Y^D=(1-t)Y=(1-.15)(10 mill)=8,500,000
for Y=11 mill
Y^D=.85(11mill)=9,350,000
so the change in Y^D=9350,000-8,500,000=850,000

MPC= the change in C/ change in Y^D
so substituting in:
.75=change in C/850,000
multiply both sides by 850,000 and you get:
change in C=850,000 times .75= 637,500

change in Y^D=850,000
change in C= 637,500

4. David Lefebvre
February 27, 2008 at 2:47 pm

We actually got the same answers, except that you forgot some zeros in problem 2 (Y was \$10,000 million, not \$10 million in the problem). I’ll admit that your method for 2b was simpler though

5. Arnav
February 27, 2008 at 5:41 pm

minna: as david already pointed out, your mistake was in taking \$10m instead of \$10,000m. but i liked the fact that you took your own approach though. so i’ll give you a .25 bonus.

david: you get the full half-point.

good job, guys.