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Im sure you are all familiar with the Lagrange method of solving production functions and the classic shortcut to MPL/MPK. I've done it a million times.
My question is this: what happens when the production function does not have any exponents? The Lagrange method falls apart:
If we say Y(L,K)=8L2+2K2 w=10, and r=15 (divisble numbers for simplicity), then we get 16L/4K = 10/15, which we can easily solve for.
However, if we say Y(L,K)=8L+2K with the same w and r, Lagrange is "broken" in effect: 8/2 = 10/15. Clearly 4 != 2/3...
Am I missing something or is this Econ formula just totally stupid?
My question is this: what happens when the production function does not have any exponents? The Lagrange method falls apart:
If we say Y(L,K)=8L2+2K2 w=10, and r=15 (divisble numbers for simplicity), then we get 16L/4K = 10/15, which we can easily solve for.
However, if we say Y(L,K)=8L+2K with the same w and r, Lagrange is "broken" in effect: 8/2 = 10/15. Clearly 4 != 2/3...
Am I missing something or is this Econ formula just totally stupid?
