Modeling Insurance Supply

While I covered the demand side pretty well in class yesterday, demonstrating the fundamental result that if insurance is priced in an actuarially fair manner then then insured demands full coverage for loss, I glossed over the supply side.  So here is a bit on that.

We would like to consider both the case of perfect competition in the long run and the case of pure monopoly.  Perfect competition in the long run means firms make zero economic profits.   The mental picture of this is that there are many firms, each one small relative to the size of the market.

If there are many small insurance companies one needs to ask are they nonetheless large enough to get the full benefits from diversification so they can be taken to be risk neutral.  In other words, there is some tension between having insurance companies get the full diversification benefit but assuming no individual firm has market power.  The waving hands I did in class was meant to assume away this particular difficulty.  In reality, there are several insurance companies that are name brands (you know their TV commercials....like a good neighbor) and they do have some market power but they also do compete with one another.  The oligopoly case then is more realistic, but it is harder to model, so we won't do that in our class.

For the most part, we will then make another highly simplifying assumption - the only costs the insurance companies have is the payout of coverage in the event of loss.  In the perfectly competitive case this means the premiums just cover the expect payout of coverage.   That is how we will model perfectly competitive supply.  It can be interpreted as saying there are no fixed loads and the variable load equals the probability of loss.  This makes the math of supply very simple.

One can extent this a little bit if there are administrative costs per policy that the insurance companies need to cover.  Then in perfect competition there would be a fixed load, to cover those administrative costs, but the variable load would still equal the probability of loss.  In either case, we will then assume that supply is perfectly elastic at that price, which is what a long run supply curve looks like in a constant cost industry.  That keeps things quite simple, which is good, because the interesting issues are on the demand side.