# Tag Info

2

You can use Karush-Kuhn-Tucker conditions. As you are considering a minmisation problem, this gives: $$\frac{\partial F'}{\partial L_i} \ge \lambda \text{ with equality if L_i > 0}\\ \frac{\partial F'}{\partial C_i} \ge \mu \text{ with equality if C_i > 0}$$ where $\lambda$ and $\mu$ are the Lagrange multipliers for the adding up constraintes. ...

5

Maybe the following is useful: Sato (1970), The Estimation of Biased Technical Progress and the Production Function, International Economic Review, 11, 179-208 JSTOR link

3

Your eq (2.10) is not more general than (2.9), but corresponds to an alternative specification. A more general version would be: $$C_i(Q_i)=FC_i+a_{1,i}Q_i+a_{2,i}Q^2_i.$$ This specification allows marginal cost to be constant as in (2.9) if $a_{2,i}=0$ or nonconstant as in (2.10) for $a_{1,i}=0,a_{2,i} \neq 0.$ It is more general because it is compatible ...

Top 50 recent answers are included