Harold has wealth of 10 (thousands) and faces a risk of losing 4 (thousands) with probability 25%. He can buy an insurance policy and is free to decide how much coverage to purchase but for each dollar of coverage he has to pay 25 cents to the insurer as a premium.

a. (2 marks) Derive Harolds budget constraint that links his consumption in the case he has a loss to his consumption in the case he does not have a loss.

b. (1 mark) Draw the budget constraint you derived in a) plotting consumption in case of no loss on X axis and consumption in case of the loss on Y axis. Make sure you provide the numerical values for the points where the budget constraint intersects with the axes. Plot Harolds endowment point (his consumption in case he does not purchase any insurance) on this graph. Is it on the budget constraint? .

(1 mark) Explain what fair insurance is. From Harolds point of view is the insurance that he can purchase fair?

d. (2 marks) Suppose Harold is risk averse. What combination of consumptions in the cases with the loss and without it does he choose? How much coverage does he purchase? e. (2 marks) Now suppose Harold is risk neutral and the probability of his loss is 50%. This means that his indifference curves are straight lines with the slope of 1 (negative 1). What combination of consumptions in the cases with the loss and without it does he choose now? Show this point on the graph above.

f. (2 marks) How is he planning to achieve the combination of consumption in

e). How much coverage does he buy? Explain Harolds choice. In your explanation relate Harolds choice to his risk attitude, propensity to have accidents and insurance contracts available.