The remaining questions in this section are based on the following diagram 45o l
ID: 1124407 • Letter: T
Question
The remaining questions in this section are based on the following diagram 45o line Indifference Curve 50 20 WCE 50 00 W terms They states of nature. Describe exactly what the two variables mcan. If the given a tangent line at point B. The (a) The variables on the axes in this diagram are mcasured in money probability of state of nature l is and of state of nature 2 is 1-1 write out the prospects the individual faces at point E and at point A. The indifference curve drawn on the diagram is slope of this tangent is parallel to the line AE. Using this information, calculate the value of t, and show that the individual's expected wealth is equal to £50 (b) averse or not? Explain your answer. Also, give the meaning of Wcr on the diagram and explain why the location of this term is consistent with the answer you give (c) Define precisely what is meant by risk aversion. Is the individual in the diagram riskExplanation / Answer
a.
The variables on the axes in the diagram are measures in money terms and it refers to states of nature. Suppose the variables are two lotteries A and E on the consumption W1 and W2 where Point A refers to Lottery A and point E refers to lottery E.
In the diagram, the 45 degree line represents line of lotteries without risk.
Given, lottery A: get £50 for sure independently of illness state and expected value =£50
This is a lottery without risk.
Lottery E: win £100 with probability and win £20 with probability 1-
Expected value also £50
b.
The slope of the tangent lie is parallel to the line AE.
The indifference curve is the curve that gives us the combinations of consumption (i.e. W1 and W2) that provide the same level of Expected Utility
Lottery A is on an indifference curve that is to the right of the indifference curve on which Lottery E lies.
Therefore we can write,
(100) + 1- (20) = 50
Solve for , we get
100 + 20 -20 =50
80 = 30
= 3/8 = 0.375
1 – = 1 – 0.375 = 0.625
Decreasing line with slope = - /(1- ) = -0.375/0.625 = 0.6
Expected value of the wealth = p1x1 + p2x2 = (100) + 1- (20) = 0.375 (100) + 0.625 (20)
By solving, we get
Expected value of the wealth = 0.375 (100) + 0.625 (20) =50
c.
Risk aversion: risk aversion is the behavior of humans especially customers and investors where they are willing to earn less money rather than taking risk and earn money.
An agent is risk–averse if, at any wealth level W, he or she dislikes every lottery with an expected payoff of zero, i.e., E[U(W + x)] < U(W) for all W and every zero-mean random variable x.
if the individual was risk averse, he will prefer Lottery A to Lottery E.
These indifference curves belong to a risk adverse individual as the Lottery A is on an indifference curve that is to the right of the indifference curve on which Lottery E lies.
Lottery A and Lottery E have the same expected value but the individual prefers A because he is risk averse and A does not involve risk. Therefore, Iif the indifference curves are convex then the individual is risk averse.
Point B lies on the same indifference curve where point E lies.
It represents that Expected utility at point B will be less than expected utility at point A as indifference curves are convex and Expected utility on the IC closest to origin will be lowest than any other IC.
point WCE represents the amount of W1 a consumer will use to get the expected value as WCE as it lies on the 45 degree line and this is a lottery without risk.