Deepti and Sanjay are neighbours. Each owns a car valued at $$10,000.$

Neither has comprehensive insurance $($which covers losses due to theft$).$ Deepti$$s wealth,

including the value of her car, is $$80,000.$ Sanjay$$s wealth, including the value of his car, is

$$20,000.$ Deepti and Sanjay have identical utility of wealth functions, $()=..$ Deepti

and Sanjay can park their cars on the street or in a garage. In their neighbourhood, a street$-$

parked car has a $50\%$ probability of being stolen during the year. A garage$-$parked car will not

be stolen.

a$.$ What is the largest amount that Deepti is willing to pay to build a garage to park her car?

What is the maximum amount that Sanjay is willing to pay?

b$.$ Compare Deepti$$s willingness$-$to$-$pay to Sanjay$$s$.$ Why do they differ? Include a comparison

of their Arrow$-$Pratt measures of risk aversion