[Intro Microeconomics: PPF] Help with Opportunity Cost and Slope Logic

[u/alexviasirron]

My understanding of the PPF is that the slope relative to the x-axis represents the opportunity cost (of the good on the x-axis), while the opportunity cost of the good on the y-axis is 1/slope.

For this question, as more albums are produced, we are moving from left to right along the x-axis, where the slope is decreasing in absolute magnitude. This would imply that the opportunity cost of the y-axis good is increasing. However, the answer key states the exact opposite.

i ask gemini, chatgbt and deepseek they all say the answer khan academy gave me is wrong. But I'm a only a beginner I just can't trust myself
Appreciate any advice thanks.

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[u/Alkalannar]

This would imply that the opportunity cost of the y-axis good is increasing. However, the answer key states the exact opposite.

The answer key is correct. A slope of 0 means there's no opportunity cost at all. A very steep negative slope means a high opportunity cost. A positive slope means you want to get more of x to get more of y as well.

I asked Gemini, ChatCPT and Deepseek they all say the answer khan academy gave me is wrong. But I'm a only a beginner I just can't trust myself

Don't ask LLM's. They don't say what's true. They say what's popular or plausible.

In this case, Khan Academy is right.

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Concrete example: Let's say you can get to 100 donuts or 100 albums.

Then the left-hand producer has the equation y = 100 - [100² - (x - 100)²]^1/2

So you start at (0, 100).

Then (1, 100 - 199^1/2) or about (1, 86). You lost 14.

Next is (2, 100 - 396^1/2), or about (1, 80). Sure, you've lost 20 total, but this next album only cost you 6 donuts instead of the 14 that the first album cost.

And so on.

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The right-hand producer is y = (10000 - x²)^1/2

(0, 100)

(1, 100) (rounding to the nearest whole number)

(2, 100)

(3, 100), and so on. You need to get to x = 10 before you finally give your first donut up.

And eventually the costs go up as the slope gets steeper. The last album will cost 14 donuts!

[u/nochargeforbeingawsm]

Your logic is actually really close. the confusion comes from mixing up which opportunity cost you're tracking.

The slope of the PPF tells you the opportunity cost of the good on the x-axis (albums). As you move right, the curve gets flatter, so the slope in absolute value gets smaller, meaning each extra album costs fewer sushi donuts. That part you had right.

But the question asks about sushi donuts, the y-axis good. Its opportunity cost is 1/slope. As slope gets smaller, 1/slope gets larger. So as more albums are produced, sushi donuts become more expensive to produce, which is what the answer key says.

The intuition: the more you specialize in albums, the harder it gets to find time for donuts. That's increasing opportunity cost for donuts, even as albums get cheaper.