## What are first and second order conditions?

Profit maximization arises when the derivative of the profit function with respect to an input is zero. This property is known as a first-order condition. A second characteristic of a maximum is that the second derivative is negative (or nonpositive). This property is known as the second-order condition.

## What is a first order condition in economics?

First Order Condition • For a function of one variable to attain. its maximum value at some point, the. derivative at that point must be zero. 0.

What is the second order condition in economics?

Second-order condition (SOC) If the first-order condition is satisfied at x = x0, f(x0) is a local maximum if f”(x0) < 0. f(x0) is a local minimum if f”(x0) > 0.

### What is FOC and SOC?

FOC and SOC are conditions that determine whether a solution maximizes or minimizes a given function. At the undergrad level, what is usually the case is that you need to choose x∗ such that the derivative of f is equal to zero: f′(x∗)=0. This is the FOC.

### What are the second order conditions?

For a minimum the second order condition is that H be a positive definite matrix. The conditon for a matrix to be positive definite is that its principal minors all be positive. For a maximum, H must be a negative definite matrix which will be the case if the pincipal minors alternate in sign.

What is an example of second order conditioning?

For example, an animal might first learn to associate a bell with food (first-order conditioning), but then learn to associate a light with the bell (second-order conditioning). Honeybees show second-order conditioning during proboscis extension reflex conditioning.

#### What is first order necessary?

1st-order necessary conditions Let A(x) = E∪{i ∈ I : ci(x) = 0} be the set of all active. constraints at a point x. Assume that at a point x∗, the active constraints gradients ∇ci(x∗), i ∈ A(x∗) are linearly independent.

#### What does it mean if second order condition is zero?

If it is zero it could be a maximum or minimum depending upon the value of the fourth derivative at the critical point. It might appear that the precise second order conditions for a maximum could be formulated in terms of the next nonzero derivative.

What does FOC stand for?

FOC

Acronym Definition
FOC Free of Cost
FOC Faint Object Camera (Hubble Telescope)
FOC Finance and Operations Committee (various organizations)
FOC Freedom of Choice

## What is second order sufficient condition?

Second-order sufficient optimality conditions (SSC) are derived for an optimal control problem subject to mixed control-state and pure state constraints of order one. The proof is based on a Hamilton-Jacobi inequality and it exploits the regularity of the control function as well as the associated Lagrange multipliers.

## What is the second order condition for minimization?

How is the second order condition different from the first order condition?

But, unlike the first-order condition, it requires to be and not just . Another difference with the first-order condition is that the second-order condition distinguishes minima from maxima: at a local maximum, the Hessian must be negative semidefinite, while the first-order condition applies to any extremum (a minimum or a maximum).

### What are the second order conditions for a maximum?

If it is zero it could be a maximum or minimum depending upon the value of the fourth derivative at the critical point. It might appear that the precise second order conditions for a maximum could be formulated in terms of the next nonzero derivative.

### Which is the first order condition for minimum?

As in the one and two variable unconstrained case the first order terms vanish and the conditions for a minimum is the positive definiteness of H and similarly negative definiteness for the maximum. Those conditions in turn can be stated in terms of the signs of the principal minors of H.

Which is the first order condition in FOC?

This is the FOC (first order condition). This is called the SOC (second order condition). The target is to find a local maximum (or minimum) of a function. The first derivative test will tell you if it’s an local extremum.