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September 22, 2014

Homework Help: Economics, Marginal Utilities

Posted by Ed on Monday, June 11, 2007 at 9:57pm.

Help Economyst....

1) I think I get this one but maybe n
not?

Bridget has a limited income and comsumes only wine and cheese, her current consumption is four bottles of wine and 10 pounds of cheese. The price of the wine is $10 per bottle and the price of the cheese is $4 per pound. The last bottle of wine added 50 units to Bridget's utility, while the last pound of cheese added 40 units.
a) Is Bridget making the utility-
maximizing choice? Why or why not?
Answer:
X= Wine Y=Cheese
$4 at 10 bottles of wine = $40
$4 per pound of cheese at 10 pounds = $40
(50 x 40) + (40 x $40) = $3600 income
spent
MUx/Px = MUy/Py
50/$40 = 40/$40 = 1.25>1
The marginal utility per dollar spent on the wine is greater than the marginal utility of cheese. The comsumer takes dollars away from the cheese to buy additional bottles of wine.
b) If not what should Bridget do instead? Why?
ANSWER:
Bridget should continue to substitute cheese for wine until equity holds.
MUx/Px = MUy/Py

2) I am lost here with this one, not sure what to do....

Suppose Bill is on a low-carb diet. he can eat only three foods: Rice Krispies, cottage cheese, and popcorn. The marginal utilities for each food are tabualted below. Bill is allowed only 167 grams of carbs daily. Rice Krispies, cottage cheese, and popcorn provide 25, 6, and 10 grams of carbs per cup, respectively. Rferring to the accompanying table, respond to the questions below:
Units of MU MU MU
food Rice cott pop
(cups/day) Krisp Cheese corn
1 175 72 90
2 150 66 80
3 125 60 70
4 100 54 60
5 75 48 50
6 50 36 40
7 25 30 30
8 25 18 20

a) Given that Bill can consume 167
grams of carbs, how many cups of
each food willhe consume daily?

b) Suppose Bill's doctor tells him to
further reduce his carb intake to
126 grams per day. What combination
will he consume?

I think I am thrown my the verbage but I am not sure the formual set up is the same? Help?!?!?!

Thanks,
EY

Problem 1)
first, Bridget spent $40 on wine, $40 on cheese. Total income is, ergo, $80.
Second, the price and MARGINAL utility of wine are $10 and 50. So, MUx/Px is 50/10 = 5. MUy/Py is 40/4 = 10. As the marginal utility per dollar of cheese is greater than for wine, she should substitute cheese for wine (as you originally concluded).

2) instead of dollars, the "budget" constraint is grams of carbs. Instead of price in dollars, price is carbs per cup. analysis is the same. So, first step, divide each of the MU values by the price.
1) 7 12 9
2) 6 11 8
3) 5 10 7
4) 4 9 6
5) 3 8 5
6) 2 6 4
7) 1 5 3
8) 1 3 2

Now, march down the table picking the highest MU/P values untill you run out of money. Bill will first eat 3 cheeses (cost=18), then he is indifferent between eating another cheese or his first corn. He takes both cost=18+16=34. He is now indifferent between eating his 5th cheese or his second corn. He takes both, total cost now is 50. Next, he eats a Krips, cost=75.

Take it from here.

Geez, looks like I don't have and I thought I did, this is frustrating! Okay, I thought that the units at the end of problem one was telling me something but I didn't get it, now I think I do....the last unit cost (50 and 40) is divided by the unit cost ($10 and $4). I haev one question though, economyst, you mentioned "total income is,ergo, 80" what is that? I did not see it in the book I see where the 80 came from but they mention a formula for income as follows: Suppose a customer with an income of $140 is spending it all on 20 units of X priced at $4 each and 30 units of Y priced at $2 each:
($4 x 20) + ($2 x 30) = $140. I applied this in the following manner even though I did not have an income spent because I thought it would give me one:
X= Wine Y=Cheese
$4 at 10 bottles of wine = $40
$4 per/pound of cheese at 10 pounds = $40
(50 x 40) + (40 x $40) = $3600 income
spent

I'm a little confused as to what I did and didn't do here, can you explain?

Thanks,
EY


In your original problem, Bridget, who only consumes cheese and wine, consumed 4 bottles of wine at $10 each and 10 lbs of cheese at $4 per lb. So, (4*$10) + (10*$4)=80 -- her total income and total spending. It is not $3600 as you state.

Now then, AT THE MARGIN (i.e., with her last bottle of wine, Bridget got 50 "utils" or "units of satisfaction." (In this problem, we are implicitly assuming we can measure "happiness" and can assign a numerical value to that happiness, and that the measure has normal counting properties (2 units of satisfaction is twice as good as 1 unit)).
Now then, we do not know Bridget's TOTAL satisfaction. We can say that with the first bottle of wine, she got more than 50 utits, because MARGINAL utility declines the more we consume of something.

As economists examining the behavior of consumers, we assume that people will try to maximize their happiness subject to a budget constraint. And How do they do that? Without knowing what a person's total satisfaction, I can confidently assert that satisfaction will be maximized when (MUx/Px) = (MUy/Py) = (MUz/Pz) .......
Since Bridget is in a two-good world, you can ignore the z good and the the "......" Note that Px is the price of obtaining the next (marginal) unit of good x.

So, now im trying to understand your follow up question. A person with income of $140, buying 20 units of x at $4 each and 30 units of y at 2 each. Since you did not provide any information about utility, there is not much you can say. Except, if this is a rational consumer, you can say that (MUx/$4) = (MUy/$2), therefore MUx/2 = MUy

I hope this helps.

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