Why are you willing to pay up to 5 shells for 1 crab? From my perspective, this would imply that you perceive that crabs are in short supply. You perceive that crabs are relatively scarce.
It is not because something is relatively scarce that it has a fixed value.
Imagine this: you’re going to the supermarket to buy a pizza for tonight. The normal price is $10. But when you arrive at the store, it appears the price has gone up. Will you still buy it? Well that depends on the new price. If it’s say $12 (your WTP), you will, but if it’s $20 or $30? Probably not. Does that mean that you’d always happily pay $12 for a pizza that normally costs $10? Well I don’t know about you, but I wouldn’t. The WTP is not a fixed quantity. You’re probably familiar with the Richard Thaler story about the beer on the beach: https://www.psychologytoday.com/blog/one-among-many/201612/beer-the-beach-and-other-priceless-tales. This illustrates what I mean. If I am really hungry, or very keen on pizza, or I am tired and don’t fancy thinking about an alternative, I’d be willing to pay more. If there is a straightforward substitute that is still $10, and my preference for pizza is weak, I’ll quickly switch to something else.
But now imagine this: you arrive at the supermarket, the pizzas are on offer — buy two for $14. By using the $2 you saved last time by paying only $10 for a pizza that was worth $12 to you, you can now get two pizzas! Maybe the thought alone makes you hungry, or maybe you can freeze one for next week. The point is: by getting your pizza for less than your WTP you can increase your utility.
So in the real world, WTP is an upper limit, but we’ll be looking to pay well below that amount, so we can maximize our overall utility by adding things to our bundle we can afford if we do so.
So… which one is it? Do you perceive that crabs are relatively scarce? Or do you perceive that crabs are relatively abundant?
Both! Abundance and scarcity are indeed relative concepts, and so anything is always scarce or abundant relative to something else.
I think the problem we have here is that we map a ‘macro’ concept (scarcity or abundance) on a ‘micro’ level (an individual’s preferences). Abundance or scarcity is a feature of aggregate supply and demand, and cannot really be derived from the WTP (or WTA) of an individual agent.
Does it matter what you perceive? Well yeah! How else could we efficiently allocate the island’s very limited supply of labor?
All we can go by is how much I am paying for the crab, and how much you’re selling it for. Say my WTP is three shells for one crab, and your WTA is one shell for two crabs. How would the allocation of labour be better if we moved to either extreme, rather than stick with the one shell for one crab transaction? In the first case I’d have two fewer shells, and you’d have two more. That means I can buy less ship spotting (or I’d need to work more to get more shells), but you can buy more of it (or you can simply do less work. In the latter case I’d have twice as much crab as now, so I’d have an extra shell tomorrow to spend on ship spotting (or I could do less work); in contrast, you’d have only half the amount of shells and so you could buy less ship spotting, or you’d need to sell more crabs (and work harder).
Would either of these be better than the status quo?