This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Your name: Econ 420K Midterm Exam II Fall 2009 Svetlana Boyarchenko Solutions 1. (25 points) Alices utility of wealth is u ( w ) = w . Alices only asset is a valuable violin which is worth $400. There is a 48 percent chance that the violin will be damaged during the next year. If the violin is damaged, it will only be worth $100. Alice can buy insurance for her violin. If she pays $ K to an insurance company, the insurance company will pay Alice back $ K if the violin is damaged. (a) (5 points) Determine the value of the premium rate, , if the in surance company makes zero profit on average. The insurance company gets K and with probability 0.48 it pays Alice back K . Therefore the expected profit is K . 48 K = 0 = 0 . 48 . (b) (5 points) What is Alices expected wealth if she buys the insur ance? E [ w ] = 0 . 48 (100 . 48 K + K ) + 0 . 52 (400 . 48 K ) = 0 . 48 (100 + 0 . 52 K ) + 0 . 52 (400 . 48 K ) . (c) (5 points) What is Alices expected utility of wealth if she buys the insurance? E [ u ( w )] = 0 . 48 100 + 0 . 52 K + 0 . 52 400 . 48 K. (d) (10 points) What is the value of coverage, K , that maximizes Alices expected utility? We need to find K which solves the following problem: max K . 48 100 + 0 . 52 K + 0 . 52 400 . 48 K. The first order condition is . 48 . 52 2 100 + 0 . 52 K . 48 . 52 2 400 . 48 K = 0 , 2 equivalently, 1 100 + 0 . 52 K 1 400 . 48 K = 0 , equivalently, 400 . 48 K = 100 + 0 . 52 K 400 . 48 K = 100 + 0 . 52 K, whence, K =$300. Hence Alice completely covers her potential loss.=$300....
View
Full
Document
This note was uploaded on 06/15/2011 for the course ECO 420K taught by Professor D during the Fall '10 term at University of Texas at Austin.
 Fall '10
 d
 Utility

Click to edit the document details