CAN YOU PLEASE CHECK IF MY WORK IS CORRECT

a.When Sofia buys a computer for $1,000, she knows that there is a 10% chance that it will break within the first year if she treats it with care.She is risk averse and would therefore pay up to $120 for a warranty that will replace the computer if it breaks for any reason during this period.If a risk-neutral firm offered her a warranty at this price, what would its expected profits be if it sold her a warranty at this price?Assume that she treats the computer with care.

= (90% X 120) + (10% X (120 - 1000))= $20

c.Alejandro is less careful than Sofia.There is a 20% change the $1,000 computer will break within the first year if he treats it with care.He is also risk averse and would pay up to $220 for a similar warranty.If a risk-neutral firm sold him a warranty for $220, what would its expected profits be?Assume that he treats the computer with care.

= (80% X 220) + (20% X (220 - 1000))= $20

d.Suppose that the firm cannot work out how is careful and who is not.Who will buy the warranty at a price of $120 (Sofia's reservation price)?What would the firm's profits be if it offered to sell its warranty to anyone who wants it at this price?Assume that the customers will treat the computer with care.

Expected payoff of company= (1000 X 10%) + (0 X 90%)= 100

Profit of firm= $120- 100= $20

Sofia will buy the warranty at $120

e. Suppose that the firm cannot work out how is careful and who is not.Who will buy the warranty at a price of $170 (the average of Alejandro and Sofia's reservation prices)?What would the firm's profits be if it offered to sell its warranty to anyone who wants it at this price? Assume that the customers will treat the computer with care.

Expected payoff of company= (1000 X 20%) + (0 X 80%)= 200

Profit of firm= $170- 200= -$30

Alejandro will buy the warranty at $170

f. Suppose that the firm cannot work out how is careful and who is not.Who will buy the warranty at a price of $220 (Alejandro's reservation price)?What would the firm's profits be if it offered to sell its warranty to anyone who wants it at this price?Assume that the customers will treat the computer with care.

Expected payoff of company= (1000 X 20%) + (0 X 80%)= 200

Profit of firm= $220- 200= $20

Alejandro will buy the warranty at $220