Question

Consider the following five lottery tickets: l1 = ($100, .5; $10, .5); l2 = ($110, .5; $10, .5); l3 = ($55, 1); l4 = ($110, .5; $0, .5); l5 = ($100, .7; $10, .3). Refer to the list of lotteries in the question above. Draw two coordinate diagrams where one could draw some of those two-outcome lotteries when we consider fixed probabilities and varying prizes. In one diagram you can draw all but one of the lotteries, in the other you can draw exactly two lotteries.

(a) In each diagram specify the probability of each state and which lotteries correspond to which points in the diagram.

(b) Draw in dashed indifference curves through the lotteries for individuals who are risk neutral.

(c) Draw dotted indifference curves for a risk averse individual.

Answer 1

The diagrams below shows possible lotteries.

a. 4 possible points are marked. Here,

1. l1 is equivalent to ($110, 0.45; $10, 0.55)

2. l3 is equivalent to ($110, 0.45 ; $10, 0.55)

3. l4 is equivalent to ( $110, 0.45; $10, 0.55)

All having expected prize of $55.

2 possible points are marked.

Note : x- axis shows the probability of getting $100 and y-axis shows probability of getting $10. The line segment shows the maximum line of probability i.e. 1 ( where probability becomes certainty)

b. In the diagrams below the straight line ( indifference curve) represents lotteries for individuals who are risk neutral.

c. The diagram shows indifference curve depicting lotteries for individuals who are risk averse.