Question

Victoria has $2000 to put toward consumption this month. She believes there is a 40% chance she will have a bike accident this month, in which case she will incur medical costs of $1500 (leaving her with $500 to put toward consumption). Victoria's utility over consumption is given by where c is consumption (in dollars). In the absence of any insurance, the expected value of Victoria's consumption this month is $ utility Victoria receives from her consumption this month is numbers in the blanks, and please round to the nearest whole number if necessary) In the absence of any insurance, the expected utils (enter only Question 3 2 pts Consider Victoria from the previous question. What is the actuarially fair premium for $1500 worth of insurance coverage to be paid in the event she has a bike accident this month? (enter only a number in the blank, and please round to the nearest whole number if necessary). Hint: This question is asking for the actuarially fair premium amount in dollars, not the actuarially fair premium share of the insurance coverage (i.e., $bX from class, not b). Question 4 4 pts Consider Victoria from the previous questions. The expected value of Victoria's consumption should she purchase $1500 worth of insurance at the actuarially fair premium is $ Victoria's expected utility should she purchase $1500 worth of insurance at the actuarially fair premium i:s nearest whole number if necessary). utils (enter only numbers in the blanks, and please round to the

Answer 1

Q.2.

Probability of bike accident = 40% = 0.4

Consumption = 2000 -1500 = 500

Utility = c^0.8 = 500^0.8 = 144.23

Probability of being safe = 60% = 0.6

Consumption = 2000

Utility = c^0.8 = 2000^0.8 = 437.34

In the absence of any insurance, expected value of Victoria's consumption

$\small = p_1c_1 + p_2c_2 = 0.4*500 + 0.6*2000 = 1400$

In the absence of any insurance, expected utility of Victoria's consumption

$\small = p_1u(c_1) + p_2u(c_2) = 0.4*144.23 + 0.6*437.34 = 320.1$