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ANSWERS EXTRA PROBLEM FOR HOMEWORK SET 3

# To investigatefurtherset 0inthesystemabovewe

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Unformatted text preview: ifferentiate them totally: Likewise, for the other conditions We are asked in the first question about the derivative . To investigate further, set 0 in the system above. We then have the matrix system of equations: 1 0 0 Let Δ . Because the function is strictly concave, we know its Hessian is negative semidefinite. Further, to apply the implicit function theorem, we must assume Δ 0, so we know this determinant is negative (recall, the 3rd principle minor will be non‐positive, and we are assuming Δ 0, so Δ 0. Now, solving for The first term of numerator of this expression is positive due to the strict concavity assumption. The second term is negative. How can we make sense out of this expression, intuitively? The factor price is connected to the factor . The terms tell us how the productivity of the alternative factors (or , potential substitutes in the production process) change when we add additional amounts of those factors. By the productivity, we mean, for , , and for z, . But as we add more of , it changes the productivity o...
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