Deducing the Right Prices

You are in charge of determining prices for Marple Insurance, a small insurance firm that operates in

southwest England. You offer home insurance in the villages of St$.$ Mary Mead, King$$s Abbot, and

Styles St$.$ Mary $($all of which are the same size$).$ A resident of any of these villages has a net worth of

$2520$ including the value of their home, which is half of their net worth, i$.$e$.,1260.$ The utility of

an individual for a wealth $($including the value of their home$)$ is given by $!"$

# $.$

However, the chance of a catastrophic event destroying a home varies by village: it is $"$

$ in Styles St$.$

Mary, $"$

$\%$ in King$$s Abbot, and $"$

& in St$.$ Mary Mead over the relevant time period. You are required by

law, however, to offer the same price to consumers in all three villages.

a$)$ What price will you charge for insurance? Which villages do you expect to serve? What are

your expected profits? $(15$ points$)$

b$)$ Regulators have come to realize that St$.$ Mary$$s Mead is a uniquely dangerous place. For this

reason, they have decided that you may charge residents of St$.$ Mary$$s Mead a different price

than residents of other villages. What price will you now charge residents of St$.$ Mary$$s

Mead? Residents of other villages? Why did your pricing for villagers outside of St$.$ Mary$$s

Mead change? $(15$ points