Bidding on a painting worth a uniform amount

A painting's true worth $V$ is uniformly distributed on $[0, 100{,}000]$ dollars, and you do not know $V$. You submit a single bid $b$; if $b > V$ you buy the painting for $b$ and immediately resell it to a museum for $1.5V$, otherwise nothing happens. What bid maximises your expected profit? (Answer $\text{\char36}0$ if no bid gives a positive expected profit.)

Bid $\text{\char36}0$. Winning with bid $b$ tells you $V<b$, so conditionally $V$ is uniform on $[0,b]$ with mean $b/2$ and the resale is worth $0.75b$ on average. You always pay more than you expect to recoup, so any positive bid has negative expected profit (winner's curse).