microeconomics-risk aversion

Microeconomics- Risk Aversion

Q3 (a ) According to the expected utility model , does a risk averter

Always choose to be fully insured if offered an actuarially fair insurance premium . Thus the optimization problem is

max U (w , c ? su (wA C - ? C (1- ? s )u (wN - ? C

Now , if insurance is "fair , i .e . if ? s , then this reduces to

u (wN - ? C /u (wA C - ? C 1

so the marginal utility of a bad state is equal to that of a good state This implies that (with state-independent

utility , wA C - ? C wN - ? C , which implies , in turn , that C wN - wA , i .e . the agent takes full coverage so that the entire income loss from an accident is recovered The optimal coverage is shown in Figure 4 by the allocation c (wN- wA ) where the highest indifference curve U (c ) is tangent to the fair insurance line F on the 45 ? certainty line Figure illustrating Optimal Insurance source : HYPERLINK "http /cepa .newschool .edu /het /essays /uncert /statepref .htm http /cepa .newschool .edu /het /essays /uncert /statepref .htm ? s . As we know in case of fair insurance any risk averse agent insures completely . And since both are risk averse and losses are the same , we can conclude that both will purchase the same amount of insurance , equal to the value of losses , as it is shown in below figure Demand of the two risk averse individuals (with different preferences but the same initial endowment ) for fair insurance Source : HYPERLINK "http /www .icef .ru /study /materials /micro3 /Micro .doc http /www .icef .ru /study /materials /micro3 /Micro .doc (ii )Never pay an actuarially unfair insurance premium to avoid taking risk

It is wrong to say that that an risk averter shall never pay an actuarially unfair insurance premium to avoid taking risk . When the insurance premium normally exceeds the expected value of the insured loss , it is referred as an actuarially unfair insurance premium . Thus in unfair insurance , we consider the situation when price of insurance exceeds the probability of accident (otherwise insurance company will have negative expected profit . In this case , risk-averse individuals may choose only partial insurance .eg use of a "deductible " if there 's a fixed cost of any claim (to avoid paying premium to cover small losses which the individual would prefer to bear , rather than insure at actuarially "unfair "rates . Thus , depending on the piece of insurance and degree of risk aversion agents will purchase partial insurance or will stay with their initial endowments , the tangency of the unfair insurance line G with the highest indifference curve source : HYPERLINK "http /cepa .newschool .edu /het /essays /uncert /statepref .htm http /cepa .newschool .edu /het /essays /uncert /statepref .htm . As we know in case of unfair Source : HYPERLINK "http /www .icef .ru /study /materials /micro3 /Micro .doci http /www .icef .ru /study /materials /micro3 /Micro .doci insurance risk averse agents will purchase less than full insurance if insurance is unfair . But since...