As of May 31, 2023, we have updated our Code of Conduct.

# Tag Info

Accepted

### Why do we need Complementary Slackness Condition for Karush-Kuhn-Tucker Conditions

Solving a non-linear programming (with inequality constraints) is about trial and error. You don't know a priori if a constraint is active. You consider all the possible cases satisfying your ...
Accepted

### Use of zero profit condition in determining unique solution

If the technology is CRS, and the parameters are such that 0 profit is both maximal and attainable with nonzero production, then the optimal solution is not unique, any multiple of it will also be ...
Accepted

### The formula for expansion path

The answer depends on what you mean by "computing the expansion path". Variant (i): For fixed $p_2$ and $M$, you want to compute the optimal points $\boldsymbol{x}=(x_1,x_2)$ as a function ...
Accepted

### Bellman Equation & Envelope Theorem

The key thing to note here is that in the optimum, $c_t$ will depend on $k_t$. Thus, the value function is \begin{align} V(k_t, t) &= \max\{u(c_t) + \beta V(f(k_t) - c_t, t + 1)\}\\ &= u(c_t(...
Accepted

### Quasiconvex Constraints in Maximisation

Consider the maximisation problem : $$\max_x f(x) \text{ s.t. } g(x) \leq c$$ Note that If $f$ is quasi-concave and $g$ is quasi-convex, then the set of solutions to the above problem is either an ...
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 $\mathbb{R}^n$ ...