1. States of the World In this section we introduce the notion that in the future the outcome in the world is not certain. Plus we introduce some related concepts.

2. Possibilities We will assume in our analysis in this chapter that tomorrow either one of two things will happen, and wealth (or income) might be different depending on what does occur. So, wealth depends on which state of the world occurs. An example of this notion might be that tomorrow it either rains or shines. Wealth may depend on which results. On the next screen let’s see a graph we will use to do some analysis in this area.

3. States and wealth Wealth at state 1 Wealth at state 2 What is being measured in the graph is the wealth that would occur at each state of the world. Only one state occurs, but we plot the wealth that would occur in each state as an ordered pair.

4. example Wealth at No fire Wealth at fire If there is no fire your wealth will be 100, but if there is a fire your wealth will be reduced to 40 (60 damage and assuming you have no insurance.) Maybe you buy insurance for 20 – no fire wealth is 80, fire wealth is 100-60-20 +60 = 80. (40, 100) (80, 80)

5. Ex ante preferences When we view the points on the previous slide we might say one option is preferred to the other. But we will only make this type of statement in the context of before the state of the world is known. Ex ante means before.

6. Expected value Recall in the example we had a “basket” of wealth = 40 if a fire occurred and wealth = 100 if no fire occurred. The expected value of this point or basket is the average value of the wealth outcomes, with wealth weighted by the probability of occurrence of each state. To continue with the example, say the probability of a fire is.25 and the probability of no fire is.75. The expected value of the basket (40, 100) is.25(40) +.75(100) = 10 + 75 = 85. Each basket or point in the graph has an expected value.

7. Iso-expected value lines The expected value, EV, of a point in the graph is EV = p1w1 + p2w2, where the p’s are the probabilities in each state and the w’s are the wealth values in those states. We could rewrite this equation as w2 = (EV/p2) – (p1/p2)w1. This is a line. If there are many points that have the same expected value, then all the points would be on the line. We would call the line an iso-expected value line (iso means same in Latin, I believe.) On the next screen we see a bunch of iso-expected value lines, with lines farther out from the original having a greater expected value. Notice the slope of a line is the ratio of probabilities.

8. Iso-expected value lines Wealth, state 2 Wealth, state 1 45 degree line Each downward sloping line has the same expected value all along the curve.

9. Riskiness On the previous screen we put in a 45 degree line. The significance of this line can be thought of by considering a point on the line. The individual would have the same wealth which ever state of the world occurs. This point is then one where the individual knows with certainty what wealth they will have next period. Moving away from the 45 degree line along an iso-expected value curve would mean those points are more risky relative to the 45 degree line point because the variation between the two wealth values at those points gets larger.

10. example You have a dollar. A game of chance is available. If heads comes up you get 50 cents ( and then you have 1.50), but if tails comes up you lose 50 cents (and then you have.50). Heads will come up 50 % of the time and thus so will tails. If you do not bet, EV =.5(1) +.5(1) = 1. If you accept the bet EV =.5(1.50) +.5 (.5) = 1. The same expected value occurs here. The no bet has the same wealth in either state and would thus be on the 45 degree line. If the bet is accepted there is a greater amount of variation between the two wealth possibilities.