# What is the “bequest condition” in a finite-horizon discrete optimization problem?

For a finite-horizon discrete time optimization problem, my textbook provides a condition called the "bequest condition", which I'm not familiar with. Specifically, where the state at time $$t$$ is denoted $$x_t$$, the bequest condition states that at the final state, $$x_T$$, it must hold that $$x_T\geq \bar x$$. What does this mean?

## 1 Answer

It is simply the terminal condition of the model. You do not specify the variable that x represents, but if it were, for example, capital, this would simply state that in the last period (since horizon is finite) there is a condition that states that capital must be greater or equal to some given amount (bequest --> legacy, you might find some sense in that word). Again, you do not specify the model, but normally these types of conditions relate to either a simplifying assumption that allows you to solve models using certain methods (for example undetermined coefficient, iterative solution methods, etc.), or to some logical notion.