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6 votes

Cost Minimization and Karush-Kuhn-Tucker

Here is the cost minimisation problem that we need to solve: \begin{eqnarray*} \min_{x_1,x_2} & w_1x_1+w_2x_2 \\ \text{s.t. } & \sqrt{x_1x_2}=\overline{y} \\ \text{and } & x_1\geq 1, x_2\...
Amit's user avatar
  • 8,881
5 votes

Cost Minimization and Karush-Kuhn-Tucker

Let's setup the optimization problem first, $$min_{\{x_1,x_2\}} \omega_1x_1+\omega_2x_2 $$ $$ s.t \hspace{5 mm} (\bar{y}=x_1^{\frac{1}{2}}x_2^{\frac{1}{2}}) \wedge(x_1 \ge 1)\wedge (x_2 \ge 0)$$ ...
SGP's user avatar
  • 171
9 votes
Accepted

Cost Minimization and Karush-Kuhn-Tucker

The term $\lambda_2(x_1-1)$ in your Lagrangian is incorrect; it treats the second constraint as an equality rather than an inequality. To allow for the constraint being an inequality you can include a ...
Adam Bailey's user avatar
  • 8,519
0 votes

To find optimal number of customers in fully competitive market with both MC and AC increasing?

I think that at the point that Price=MC, we obtain optimal customers.
Murat Yazıcı's user avatar

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