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 C_{0} = $500, C_{y} = 0.8 and t = 0.2, what is the value of income Y, for which household saving S^{H} equals zero?

2. If C_{0} = $400, C_{y} = 0.75 and t = 0.15 and national income changes from $10,000 million to $11,000 million, what is the change in Y^{D} 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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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.

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.”

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

So the answer:

change in Y^D=850,000

change in C= 637,500

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

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.