Help on this econ problem...

[The Hype]

Is it possible for a production function F(L,K) (not necessarily constant returns to scale) to have a marginal product of labor formula which is scale invariant, but a marginal product of capital formula which is not scale invariant? If so, give an example. If not, explain why not.


Thanks in advance.

[phk]

I'm pretty sure this is possible.

I assume your teacher uses L and K to define Labor and Capital?

It would have to be a perfect substitutes production function where capital and labor were easily substituted from each other.

Y = 6L + K^(3)

MPL = 6. Which is scale invariant obviously. This formula is totally scale invariant with respect to any variable.

MPK = 3K^2. Which as we scale up, actually does scale up really fast (exponentially) and is obviously not scale invariant.

MPK(1) = 3(1^2) = 3
MPK(2) = 3(2^2) = 12

By scaling capital up by 2, we end up scaling MPK by 4.

I think this is somewhat impossible for a Leontief (perfect substitutes) function or a Cobb-Douglass, but I could be wrong.

Where do you go to school btw?

[The Hype]

I'm pretty sure this is possible.

I assume your teacher uses L and K to define Labor and Capital?

Yes sir.

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Thank you very much!

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ITT Tech

[phk]

I'm pretty sure this is possible.

I assume your teacher uses L and K to define Labor and Capital?

Yes sir.

You must be logged in to read this quote.

Thank you very much!

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ITT Tech

Really... they teach Micro there?

[The Hype]

I'm pretty sure this is possible.

I assume your teacher uses L and K to define Labor and Capital?

Yes sir.

You must be logged in to read this quote.

Thank you very much!

You must be logged in to read this quote.

ITT Tech

Really... they teach Micro there?

If you want to call it that.