Question

Vinay and Arjun each book trips to Thailand costing $5000.   Vinay has a 10% probability of cancelling his trip due to illness and Arjun has a 5% probability of cancelling his trip due to illness. Both wish to buy cancellation insurance, and are each willing to pay $10 above the expected value of that insurance to remove their risk.

a) Suppose the insurance company does not know Vinay and Arjun’s probability of cancellation and assumes an average probability of cancellation of 7.5% based on previous data. The company decides to offer one cancellation policy at a cost of $380. Will Vinay and/or Arjun buy the insurance?

b) Given your answer in (a), and assuming Arjun and Vinay are the only potential customers, what is the insurance company’s expected profit from offering cancellation insurance at a cost of $380 per policy?

c) Based only on the information given in this question (on the previous page) is there adverse selection and/or moral hazard present in this market?   Explain.

d) Suggest two specific ways the insurance company could change its premiums or offerings to increase the profits calculated in (b). Explain carefully why/how your suggestions would increase profits.

Answer 1

Vinay probability of cancelling =10%

Expected value from insurance= 0.1*5000+0.9*0=500

As 90% chance he won't use it so 0.9*0.

Vinay is willing to pay 10 extra so for him price=500+10=510

Arjun probability of cancelling =5%

Expected value from insurance= 0.05*5000+0.95*0=250

As 95% chance he won't use it so 0.95*0.

Arjun is willing to pay 10 extra so for him price=250+10=260

(a) The company is offering insurance for 380

380<510, so Vinay will buy it

380>260, so Arjun won't buy it.

(b) Expected value for company= 0.075*5000+0.925*0=375

Company selling at 380, so already making a profit of 5

If only Arjun and Vinay are their only customer,

Arjun won't buy, Vinay will buy

Profit from Arjun =0

Profit from Vinay=5

Total Profit = 5

Expected profit or loss= 0.1*-5000+0.9*5=-495.5, as Vinay has more chances of cancelling than they thought so they will incur a expected loss.

(c) Yes, Adverse selection is there in the market as each individual has their own probability of cancelling, which the insurance firm don't know about so they use their historic average to calculate the cost of policy. IF the firm would knew how much each is willing to pay above expected value firm could make a profit of 20.

(d) Two ways

(1) Firm could use the medical history of individual patient and then accordingly offer the policy. In this way firm can earn upto 20 profit from both.

(2) Firm could ask the customers how much they will be willing to pay and then accordingly sell the policy. In this way firm will not agree for Arjun price and Vinay if quote and price above 380, will be additional benefit for the firm. As he is willing to pay 510, so will surely quote a price above 380.