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Results tagged with cost-functions
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user 11824
3
votes
Accepted
Quasi-convex constraints using monotonic functions
Real-valued Monotonic functions defined on real line or subset of real line are both quasi-concave and quasi-convex, but that is not necessarily the case if the function is defined on $\mathbb{R}^n$ o …
- 9,842
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\geq 0 \end{eq …
- 9,842
5
votes
Accepted
Prove all cost functions are concave in input prices and demand for inputs is downward
Let $x(w, q)$ denote the solution to the cost minimization problem :
\begin{eqnarray*} \min_{x} & \ w\cdot x \\ \text{s.t.} & \ \ f(x) \geq q \end{eqnarray*}
where $f$ is the production function.
Sin …
- 9,842