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### Course: Microeconomics>Unit 5

Lesson 2: Utility maximization using marginal utility per dollar spent

# Marginal utility free response example

In this video, walk through the solution to a question on the 2012 AP Microeconomics exam applying the concepts of marginal utility and utility maximization.

## Want to join the conversation?

• I thought total utility was the culmination of all individual units of utility because the marginal utility shows the incremental increase/decrease. So why isnt it 10+18+24=32?
• From the author:You are right that total utility is the sum of all units of utility, but I think you are misunderstanding marginal utility here. When she consumes one train, she gets 10 units from that. When she increases consumption to two trains, she gets 8 units from the second train, not 18. Her total utility from two trains is 18 because she gets 10 from the first, and an additional 8 from the second. Similarly, when she increases her consumption to three trains, she gets 10 from the first, 8 from the second, and 6 from the third.
It might be helpful to think of it incrementally. For example, "ok, I am consuming one toy train. What happens to my total utility if I increase to two trains? Well, the second train will provide me with 8 more utils, so that brings me up to a total of 18."
• When Sal comes to a point where the marginal utility per dollar of both goods are equal, he says that you can choose either at random. I may be overthinking this, but because a bagel is worth \$2 (and I'm assuming you can't buy half a bagel), shouldn't you take the next 2 dollars into consideration? For example, when he gets to the point where marginal utility per dollar of both equals 4, he says that you could get either the toy car or the bagel. But if you choose the bagel, you get 4 utils per dollar for your next 2 dollars, whereas for the toy car, you would get 4 utils only for the first dollar, and 3 utils for the next one. So your marginal utility for the next 2 dollars would be 8 for the bagel, but only 7 for the toy car. In this situation, wouldn't you choose the bagel?

The final answer comes out the same, so I'm wondering if this matters at all, or if I'm just overcomplicating things for myself.
• I understand how Sal figured out that Theresa spent 5\$ on toys with the table, but I need someone to breakdown how he used the table to conclude she spent 6\$ on Bagels.
• When Theresa actually buys a bagel she spends \$2 so 2x3(bagels)=\$6. The table just shows the MU per \$1 (basically the MU per half a bagel).
(1 vote)
• What happens when Theresa's income can't be split perfectly by the price of two products? For example, if she has \$12, what will she do about that extra \$1? Does she buy one more toy (affordable but has a lower MU/price than the MU/price of the next bagel)? Or does she saves the money?
• Theresa consumes toy cars? How come she doesn't have a tummy ache?

I get the bagel part, but who would eat CARS!?
• In second question, if Theresa had a weekly income of \$13, then she would have bought 5 toy cars and 8 bagels. In that situation MU per unit price would not be equal for the two. How to understand it?
• I thought it was asking for total utility. If MU= change in TU/change in Q, then wouldn't you use that to find TU, instead of simply adding the MUs
(1 vote)
• You could make a different table for TU, then your answer would be the value corresponding to the number of toy cars.
When she consumes one toy car, she gets 10 units from that. When she increases consumption to two toy cars, she gets 8 units from the second toy, not 18. Her total utility from two toys is 18 because she gets 10 from the first, and an additional 8 from the second.
So you see, you can do it both ways.
(1 vote)
• Why isn't the answer to this question 4 bagels and 3 cars?
(1 vote)
• I think the confusion here is looking at total utility vs the (marginal) utility per dollar, which is what is used when calculating maximized utility given a certain budget, in this case \$11. When we consider the price of bagels (\$2), the utility per dollar is half of what their total utility is. Sal shows this new table at about .
(1 vote)
• If lets say the question doesn't give a number that works out like \$11, and she has left over money (because let's say if she buys the item that gives her greatest marginal benefit makes her go over her budget, will she just not spend the money, or will she use that money to buy an item even if it doesn't give her the most (MU/P)/Bang for her buck. Thanks
(1 vote)
• How can we incorporate the remaining budget and the possible choices? i.e. how can we explain the following?
A @2\$: mu/p -> 7 - 6
B @1\$: mu/p -> 7 - 5
budget=2\$
in all of the videos, we never incorporated the remaining budget and the possible choices when mu/p is the same.
(1 vote)