Zoe Goggles is a deep sea underwater photographer. Her camera and lenses are valued at $4,000. There is a chance of 1/20 that she will lose her equipment on a dive over the course of the year. Her wealth, including the value of her equipment, is $30,000. Zoe's utility function is?U (w) ??ln w . Zoe wishes to purchase insurance against the risk of losing her equipment on a
dive. The price per dollar of coverage is γ.
a. Write an equation to represent Zoe's net wealth in the state of the world where she does not lose her equipment and she has purchased K dollars of coverage. Call this w1.
b. Write an equation to represent Zoe's net wealth in the state of the world where she does lose her equipment and she has purchased K dollars of coverage. Call this w2.
c. Combine your equations from parts (a) and (b) to write her budget constraint. What is the price of a claim on one dollar of wealth in state of the world 1? What is the price of a claim on one dollar of wealth in state of the world 2? What is the slope of her budget constraint, if w2 is on the vertical axis and w1 on the horizontal axis?
d. Provide an expression for Zoe's marginal rate of substitution, MRS = - dw2 / dw1 .
e. If γ = 0.10, how much insurance coverage K will Zoe buy? What is her total premium γK in that case?
f. If, instead, the price of insurance is actuarially fair, show that Zoe will purchase full insurance: K = $4,000.
g. Draw a diagram depicting Zoe's budget constraint and her optimal choice of w1 and w2.