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1 vote

Optimisation problem and KKT conditions (unsatisfied?)

Indeed, I think the problem is that the Jacobian of the (active) constraints is not of maximal rank at $(0,0)$. One solution is to rephrase your set of constraints. $$ \begin{align*} &x^3 \le - y\\...
tdm's user avatar
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1 vote

Cost function from a weighted CES production function

I'll use $(w_1, w_2)$ to denote the factor prices instead of $(p_1, p_2)$ as the latter is traditionally used for output prices. $c(w_1, w_2, y)$ solves the maximization problem: $$\max_{x_1, x_2 \ \...
uninterestedacademic's user avatar
1 vote

Why this optimisation problem cannot be solved with "usual" KT conditions?

The generalized Lagrangian function is: $$L(x,y,\lambda) = 2xy+yz+\lambda (1-x-y-2z)$$ The Kuhn-Tucker conditions for maximum: $$\begin{cases} L_x=2y-\lambda \le0, \quad \quad \quad \quad x\ge 0, \...
farruhota's user avatar
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