Question

In prospect theory, the interplay of overweighting of small probabilities and concavityconvexity of the value function leads to the so-called fourfold pattern of risk attitudes. Each quadrant shows an individual’s choice between two prospects (x; p) in the first row and the individual’s risk attitude in the second row.

	Gains	Losses
High probability	Choose (949) over (1000, 0.95) Risk averse	Choose (-1000,0.95) over (-949) Risk seeking
Low probability	Choose (1000, 0.05) over (51) Risk seeking	Choose (-1000,0.95) over (-949) Risk seeking

For each quadrant, explain the individual’s risk attitude with reference to the choice between the two prospects. Show your calculations clearly.

Answer 1

1.

Choosing 949 over (1000,0.95)

Expected value for (1000,0.95) is 1000*0.95 = 950

So, choosing 949 over (1000,0.95) means choosing 949 over expected value of 950.

So, it can be said that individual is risk averse and would be happy to choose a confirm 949 over an expected 950.

2.

Choosing (1000,0.05) over (51)

Expected value for (1000,0.05) is 1000*0.05 = 50

So, choosing (1000,0.95) over 51 means choosing expected value of 50 over 51.

So, it can be said that individual is risk seeking and would be happy to choose expected 50 over confirm 51. As taking risk carries 5% chance that the individual may get payoff of 1000.

3.

Choosing (-1000, 0.95) over (-949)

Expected Value of (-1000, 0.95) is -1000*0.95 = -950

So, choosing (-1000, 0.95) over (-949) means choosing expected value of -950 over confirmed -949.

So, it can be said that individual is risk seeking and would be happy to choose expected -950 over confirm -949. As taking risk carries 5% chance that the individual may get payoff of 0 (i.e. no loss).

4.

Same as case 3.