Question

A person with the following utility function, u(x) In(x) faces a world where with probability 0.1 will suffer of identity theft which will reduce their wealth from $250000 to $100000. This means that we can write: Eu(.0.91n(x)+0.1n(y) where would be the wealth under no identity theft and y the wealth under identity theft This means that the marginal utilities are: MU0.9 MUy = 0.1 Using this information answer the following questions 1) What is this persons attitude towards risk? explain your answer? 2) What is the certainty equivalent and risk premium? find your answer algebraically and graph to represent them use a 3) What is the optimal purchase of insurance if the person faces an insurance premium of 15%? 4) What is the optimal purchase of insurance if the person faces an insurance premium of 10%?

Answer 1

Sol function Given uCx) hCx) $250000 to alth theia which oil the Pt peduce x$2S000o In Ly) o9lnlx)+ o E uC ai sk Pessons owaads attitude because * The peasan attitude touoads is isk avease Pe san i's u Incx) uti bity unction wheoe, identity theft X Wealth ndeg no that oil ake the of thelb urcestin situation Pesson less happy hove Su'sk .to we quivalent Ceafanty ond have heft and o thef Cy utilitte in Case o Iny) 0.9In) Inc) u) ECu) o.9 ucx) + .1 (n(o0000) inCa500e) 0.q 12.429)+Col11.512)

Euc 186 15 A 12. 32 7 2.34 Theafooe Risk Prenum is the expected bss due to theft Penu Ex Pected doss Faio PEneniunWealh ndes ni theft - expecled wealth EoJ Fai Foemu 2S000O Faj Pemn25000o Co.(10D)+)coo00) - (oo00 +225000) Fai Poemum = Soooo Fai Penium 2500oo - 23 Soo o untwaed n Maximum pemiun = Sooo ECuC CECO 12.30) e12.34 xpC12.34) C 22866 2

3 2Soooo --- 223 66 2 21338 Premum o5,. ofinsuoance Case amount as The pe sen should pay the maximum eu $2133 Calcalated 8 loy 4Jn in suoance Case anwacd fai poeiun The peason shou ld Pay The pesrson should Pay $1sooO 14