# DMP Search Model - Terminology

In the most basic Diamond-Mortensen-Pissarides (DMP) model we have the variable $$V$$ which represents the present discounted value of expected profits from a vacant job. The corresponding Bellman equation is

$$rV = -pc + q(\theta)(J-V)$$

Where $$pc$$ is the cost of a vacant job per unit of time, $$q(\theta)$$ is the rate at which vacancies are filled and $$J$$ is the present discounted value of expected profits from an occupied job. If I think of a vacancy as an asset for the firm the Bellman equation makes sense but how can a vacancy be an asset?

What I don't understand is the intuitive meaning of $$V$$. How can a vacant job result in profits for the hiring firm? Furthermore, my textbook says

In equilibrium all profit opportunities from new jobs are exploited, driving rents from vacant jobs to zero. Therefore the equilibrium condition for the supply of vacant jobs is $$V=0$$

Again, how are there 'rents' from having a vacant job?

A vacant job is an asset if we consider that the firm can match with a worker and get a positive expected profit. Firms post vacancies up to a point where $$V=0$$. If $$V$$ were positive, more firms would enter, would post additional vacancies, and would get a $$`$$rent' (by matching with worker).
• That clarifies things a bit. However, we said that $J$ was the expected profits from an occupied job. And it is only then that the firm will realise the profits. So $V$ is simply a hypothetical? Clearly the vacancy in and of itself cannot generate any profits, it is only when they match with an unemployed worker that profits are realised. I feel like I am overcomplicating things but the idea of a vacancy being an asset is just too strange for me. – BenBernke Apr 4 '19 at 11:19