How to determine value from willingness to pay? I use the British pounds symbol instead of dollars because $ conflicts with Mathjax.
Source: p 296, The Legal Analyst, Ward Farnsworth

"... one time in a thousand we
  do lose the film; if you’re willing to pay an extra ten dollars, I can have
  it delivered by armored car and guarantee that it won’t be lost.” ... In that case we
  have another way to think of the value she put on the film. If we consider
  the £10 a premium for a kind of insurance, we can reason backwards
  to the value that the owner of the film put on it for these purposes. You
  wouldn’t spend £10 to insure against a 1/1,000 chance of a misfortune
  that would cost you only £10 or £100—at least not if you were being
  economically rational. It wouldn’t be worth it. In the long run you would
  end up paying more in insurance premiums than you ever would collect
  when the dreaded event occurs. Imagine paying £10 a day for 1,000 days,
  then collecting £100 on the day when the bad thing happens: it would be
  a bad deal. But if the loss were worth £1 million to you, the £10 payment
  to avoid the 1/1,000 chance of it would be a bargain. So to return to our
  case, if we assume £10 is the most you would pay to accept the $\color{green}{1/1,000}$
  risk of lost film, the implication is that you value the film at £10,000.

I know that $ \dfrac{10}{ \color{green}{ \dfrac{1}{1000} } } = 10,000$, but would someone please explain how and why this is how to determine the value of the film? What's the intuition? I don't perceive the 'implication'; this isn't a math book so am I missing something easy and trivial here? Another example from p 316, supra,

...willingness
  to pay” studies...  begin by trying to determine how much people
  value their lives by looking at how much they are willing to spend to
  reduce small risks of death. Suppose, for example, that an airbag for
  an automobile costs £300, and suppose it is known that every 10,000
  purchases of an airbag saves a life. In effect that means £3 million will
  be spent (by 10,000 consumers) to save that life. Put differently, each
  purchaser evidently is willing to spend £300 to obtain the benefit of the
  1/10,000 chance that it will save his life—and this suggests that each
  values his own life at £3 million.

 A: The intuition is that your payment $x$ should be the same as the expected loss $E(L)$. With $p$ = probability of loss $l_0$, and a $(1-p)$ probability of losing nothing, this gives
$$ x = E(L) = pl_0 + (1-p)0 = pl_0$$
Solving for $l_0$ leads to your formula $$l_0=\frac{x}{p}$$
Of course insurance doesn't really work like that because there are lots of administrative costs, profits to be made, etc, so the premium is typically more than the expectation of loss. 
More importantly, people don't value insurance on expected loss; rather they value it on utility. When I was a student, I paid to insure my possessions. But now I've been in employment for some years, I don't insure my possessions, even though they're worth more and they're less at risk (so I could get a better deal), because I judge that I could afford to replace them. I still insure the building I live in, because regardless of the value of the insurance, I couldn't bear the loss.
A: The text you quote does not seem to discuss the reasoning of an actual human being.
Expected value of gain is often not what we want to optimize.
At least this is the case for myself.
About the film example:
If I was a film retailer that bought and sold a great number of films, then I would look at expected values and the reasoning is correct.
But as a single person I might want to order a film and be sure that it is there for my date next weekend.
Then I do not care about expected values, but only the probability of something going awry in this one case.
About the airbag example:
People want protection not only from death, but also from injury.
And they also want to feel safe, even if there is no actual safety.
I guess my point is that humans cannot always be modeled in such a trivial way.
Sometimes it does work, but sometimes not.
The implications are implications within a model of human thought and behaviour.
A: The rationale behind this is as described: If you value the film at some value $x$ and get the offer for an insurance as described, you start calculating: I expect the loss of $x$ to happen with probability $\frac1{1000}$, so on average I suffer from $\frac x{1000}$ (or more visually: During $1000$ repeated experiments I expect to suffer once from $x$, so again on average I suffer $\frac x{1000}$ per event). Now if $x>\$10000$ you notice that paying that extra fee of $\$10$ gets rid of that expeccted loss $\frac x{10000}>\$10$, hence ist would be profitable for you to accept the insurance. Similarly, if $x<\$10000$, definitely paying $\$10$ instead of only expecting to lose $\frac x{1000}$ looks like a bad idea and you won't buy the insurance. Hence form the fact that someone buys such an insurance (and is assumed to act rationally) we can conclude that his $x$ is $\ge\$10000$.
However, this model is not perfect. It assumes that the value of a random amount of money is its expected value. The key point to answer the question is to consider risk aversion. 
Assume I suggest a game to you: Throw a coin and if you win, you get \$5, if you lose nothing happens. Will you play the game? Of course, you will - you have nothing to lose and the expected value is $E[X]=\$2.5$! What if I suggest this: If you win, you get \$10,000,005 and if you lose you must pay \$10,000,000 (I also accept cars, houses, spouses, and kidneys as payment). While the expected value of the second game is the same as for the first, if you lose the second game you are more or less doomed to spend the rest of your life in poverty - or not even have a rest of your life. Therefore, you will not wish to play the second game. Well, maybe you do - but probably only if you are very, very rich and can easily afford a loss (even if you had \$11,000,000 you won't be as happy with a possible raise to \$21,000,005 as you'd be unhappy with dropping to a mere \$1,000,000, so you'd still not like to play). Some model this by taking logarithms: If your capital grows from \$500 to \$1000 or from \$1000 to \$2000, in both cases it doubles, hence is considered the same "personal gain", effectively. And, voíla, the logartithm of your capital grows by the same amount in both cases. This refelcts that a rich man will not be as happy about finding a $10 note as a poor man will be about finding a nickel. 
The simple model as in the first paragraph therefore holds only for things that are small compared to your total capital. Especially when talking about the person's life itself, this assumption is not valid.
