[maister]

Anyone had a look at those questions?

> Question 2: In a country where everyone is identical, 100 people wait in line each day to buy raspberries at a controlled price. The government has decided to hand out free coffee to the people standing in line. The coffee costs the government $1 per cup, but the people in line value that coffee at only 75 cents per cup. What is the social cost of providing the coffee?

> Grading Remarks: This answer completely misses the key fact that free coffee will cause the line to get longer (in fact it must cause the line to get longer, given the stated assumption that everyone is identical, hence initially indifferent between standing in line and not standing in line). In fact (unless one assumes a very small population), the line must grow until the extra waiting time completely dissipates the value of the free coffee; thus the social cost of providing the coffee is $100.

Wait what? So the line must get longer, *given the stated assumption that everyone is identical*. Well what about the given stated assumption *that 100 people wait in line each day*? One of the stated assumptions can be dropped just like that, while the other is treated like a law of nature? Also where is the logic in "everyone is identical, hence initially indifferent between standing in line and not standing in line"? Am I missing something?

[DuckFeathers]

I fed the question and the grading remark to GPT-4 and here's what I got:

"""

The problems with the question and grading remark are as follows:

1. The question assumes that everyone is identical, which is an unrealistic and oversimplified assumption. In reality, people have different preferences, time constraints, and valuations of goods and services. This assumption may limit the applicability of the conclusions drawn from the model.

2. The grading remark assumes that the provision of free coffee will cause the line to get longer. While this may be true in some cases, it is not necessarily true in all cases. The increased utility from receiving free coffee may not be enough to incentivize more people to join the line, especially if the waiting time is already long, or if there are alternative sources of coffee or raspberries available.

3. The grading remark also assumes that the waiting time will increase until the value of the coffee is completely dissipated. This is a strong assumption and may not hold in all cases. The increase in waiting time may be limited by factors such as the opening hours of the store or the availability of raspberries.

4. The grading remark calculates the social cost of providing the coffee as $100, which may be an oversimplification. The actual social cost may depend on factors such as the opportunity cost of the time spent waiting in line, the environmental impact of producing and distributing the coffee, and any externalities associated with coffee consumption.

5. The question does not specify whether the government's cost of $1 per cup includes the opportunity cost of the resources used to provide the coffee or only the direct monetary cost. This may lead to an underestimation of the true social cost of providing the coffee.

In conclusion, the question and grading remark are based on a simplified model that may not accurately capture the complexities of the real world. The assumptions made in the question and grading remark may limit the applicability of the conclusions drawn from the model.

"""

Maybe it's not a failure of GPT-4 but a failure of a system which regards "professors of economics" as competent people.

[hgsgm]

Landsburg is a famous economist with an "unusual" interpretation.

It's reasonable that GPT, like most economists it is trained on, would not give satisfactory answers to his tests.

His students call attention to his idiosyncratic theory and logic. (Some like it; some don't.)

https://www.ratemyprofessors.com/professor/71418

[fabbari]

Think about it these terms: originally there are 100 people in the line because the 101st will not queue since the time to get to the beginning of the line is more valuable than the raspberries at the controlled price. If nothing changes there will not be more people in that queue.

When the government gives free coffee to the people in line now the perceived value is the value of the raspberries at the controlled price plus the $ .75 of the coffee, making it worth to queue more - until the queue gets to the length at which the waiting time exceeds the value of the added coffee.

[skeaker]

If your first paragraph was actually in the question then I would agree, but in the actual question, the reason there are exactly 100 people in line is that the question says there are 100 people in line. Phrasing certain parameters in your question as though they are absolutes and then expecting the person answering the question to change those parameters is like the worst kind of trick question. It's like when a toddler asks you if a ninja or a pirate would win in a fight, then says the pirate would win because he secretly has super strength. It's cute when a toddler does it because they innocently don't understand why their question wouldn't logically convey that hidden parameter to the listener, but inexcusable for a professor.

[SilverBirch]

I think you're just reading an ambiguous sentence in a way that obviously wouldn't make sense in context. The question is in a very familiar form: describe a scenario with some assumptions, describe a peturbation, ask what impact the peturbation has. If the context was some annoying internet quiz, the answer might have been a gotcha that the number of people in the queue stay the same.... but this is an econ question it's going to involve how people respond to economic incentives.

[hgsgm]

This is like those LeetCode questions in job interviews, or the interviewer wants a complicated O(n) solution when the problem as stated would be better solved with a simple O(n^2) solution because the maximum problem size is tiny.

It's a mind-reading game of which assumptions the professor/interviewer wants to keep solid which ones are open to change.

[foxyv]

Instructions weren't clear, ended up with a free cafe in front of raspberry store.

[mumrik]

Before the coffee, the equilibrium was for the line to be 100 persons long.

After the introduction of the coffee, the equilibrium changes so that people are willing to wait in a longer line than 100 people, although the individuals themselves don't have any preferences (like A only standing in line if it's less than 20 people and so on).

I think not much thought was given to explain the answers in depth since the main point was to show where GPTs reasoning was lacking.

[adrianmonk]

The point is that it's a badly-worded question because there are two ways to interpret it.

It's clear (after reading the score's explanation) what the intended interpretation is, which is the one you're describing.

The other interpretation is that the length of the line is set by the government based on how many people they choose to to allow to buy raspberries at a controlled price. Once 100 people are in line, they won't let a 101st person get in line, so it is always 100 people. In this interpretation, a cup of coffee that would normally be worth $1.00 is only valued at $0.75 because what the people are there for is raspberries, not coffee. Some of them may not even like coffee that much.

[usaar333]

I definitely agree on the vagueness. You have to understand that the 100 is caused by emerging phenomenon, not a population limit or government restrictions - it's really not obvious. You also have to understand that for some reason you actually have to enqueue before the raspberries are distributed (also not obvious).

That said, it doesn't fundamentally help GPT-4. It's too complex for it to get.

PROMPT:

In a country with thousands of people where everyone has identical preferences, the government sells raspberries at a controlled price. To obtain the raspberries, people must line up before the raspberries are sold and the market will process people's orders one at a time. Once the market opens up, additional people are not allowed to enqueue.

Currently, 100 people wait in line every day to buy raspberries.

The government additionally decides to hand out free coffee to a raspberry purchaser (after the raspberries are bought). The coffee costs the government $1 per cup, but the people in line value that coffee at only 75 cents per cup. What is the social cost of providing the coffee?

ANSWER: To calculate the social cost of providing the coffee, we need to consider the value of the coffee to the people and the cost of providing the coffee to the government.

There are 100 people in line who receive free coffee after purchasing raspberries. The cost of providing the coffee to the government is $1 per cup, totaling $100 for all 100 people ($1 * 100).

The people in line, however, value the coffee at only 75 cents per cup. So, the total value of the coffee for the 100 people in line is $75 (0.75 * 100).

The social cost of providing the coffee can be found by subtracting the total value of the coffee to the people from the cost of providing the coffee to the government:

Social cost = Cost to government - Value to people Social cost = $100 - $75 Social cost = $25

Therefore, the social cost of providing the coffee is $25.

I tried pushing GPT-4 a bit:

PROMPT: "Why are you assuming the line stays the same size?"

ANSWER: You're right, I made an incorrect assumption that the line would stay the same size. With the introduction of free coffee, it's possible that more people would be attracted to join the line to buy raspberries and receive the free coffee.

Let's analyze the potential change in the line size.

The value of the free coffee to the people is 75 cents per cup. Assuming people are rational and will join the queue if the value of the free coffee is higher than the cost of waiting in line, we can expect the line to grow until the marginal person values waiting in line at exactly 75 cents.

The social cost of providing the coffee can then be calculated by considering the additional waiting time for the people in line and the cost of providing the coffee to the government.

Unfortunately, without more information about how many new people would join the line and the cost of waiting in line, it is not possible to accurately calculate the social cost of providing the coffee.

Hardly a "0" answer with the hint and in fact GPT-4 comes close, but it isn't able to make the connection to what the equilibrium point must be.

[Imnimo]

I think with any test there's an element of general test-taking ability required to interpret the question. From context, I think it's clear what the intended interpretation is, and I'd be surprised if any student read the question as saying that the size of the line was fixed by the government.

[maister]

> I think not much thought was given to explain the answers in depth since the main point was to show where GPTs reasoning was lacking.

Funnily enough it seems as if the prof has also fallen for a reasoning error then. How can both be equally true? The line gets longer than 100 people and the social cost of the coffee is exactly 100 dollar (1 Dollar for every person).

[JoshuaDavid]

Maybe it cancels out somehow?

Let's put in some concrete numbers to see if it does. Specifically, let's say that people value the ability to buy raspberries at $1.00, which means that they value their time at $0.01 per place-in-line (so waiting in a line of 100 people costs $1.00 of their time, and as such joining a line of 100 people would involve a $1.00 benefit (buying raspberries) for a $1.00 cost (waiting in line) and so 100 people long is the point where anyone is indifferent to joining the line.

Before the coffee is introduced, the first person in line receives $1.00 in value, the second receives $0.99, and the hundredth receives $0.01, and the 101st does not join at all, for a total of $50.50.

Now add in the coffee which costs $1.00 and is valued at $0.75. This causes the line to get longer by 75 people. The first person in line receives $1.75 in value, the second receives $1.74, the 175th receives $0.01, and the 176th does not join at all. This is a total of $154.00, which is $103.50 more than the total value of the line before the coffee was added (at the cost of the government spending $175.00 on coffee). Which yields a social cost of $71.50. Which is not $100. Hm.

If I replace $1.00 as the value of buying raspberries with $5.00 (and so the cost of waiting one place in line is $0.05), the numbers work out as line length 100 -> 115, total value $252.50 -> $333.50, cost of coffee $0.00 -> $115.00, which yields a social cost of $34.00. Which is not only "not $100" but also isn't even the same as the last value.

Maybe the assumption is that, say, at 6:00 every morning, every person has a choice of "wait in line until 9:00 am for raspberries" or "don't". But then if everyone who waits gets raspberries, then you'd expect either everybody or nobody to join the line. Or maybe the coffee is only given to the first 100 people in line? Or only given to the people who join the line after the first 100?

Yeah I got nothin. Maybe I'm missing something though.

Edit: maybe if you include the cost of providing the raspberry subsidy, the numbers line up? In the first case, that would be $1.00 x 75 more people, so the cost would go up to $146.50, while in the second case that would be $5.00 x 15 more people, bringing the social cost to $109.00. So yeah, still not sure what's going on. There's probably some configuration of assumptions which yields a social cost of exactly $100 without needing magic numbers, but I'm sure not finding it.

[carlmr]

>After the introduction of the coffee, the equilibrium changes so that people are willing to wait in a longer line than 100 people

I do agree with OP that this has to be stated as part of the question. Otherwise you can't expect anyone to give the stated answer.

Basically any answer is correct.

[icedistilled]

The line doesn't have to get longer. The grader is incorrect under their own logic. Raspberries could be an unimaginable luxury, say on a moon colony or a very poor country unsuited to berry or fruit growth. Without knowing the value of raspberries, the value and cost of coffee is meaningless funny money.

Coffee keeps well and could be dirt cheap and it could be bad instant coffee that people don't really like. It may feasibly not be worth a single extra person standing in line for the bad coffee worth 0.75 zimbabwean dollars or 0.75 weimar marks.

This is pedantic and stuffy answer, but that is also what the "correct" answer is.

[yunwal]

The second thing is that even if students magically guessed that the line can grow after the government offers coffee, the answer is still wrong (or at least, makes unreasonable assumptions). The line will grow until the last person in line values coffee + berries as equivalent to the time to wait in line. This means everyone in front of that person still benefits from the coffee. How much social cost is created depends on the cost function of waiting in line, which is unstated.

[sideshowb]

For question 3, not being an economist, I'd like to know why gpt is wrong to say there's not enough information. If people have less money after spending more on groceries, how do we know they will reduce spend on housing specifically? Couldn't they instead reduce spend on something else, like car mileage or whatever?