Choice With Uncertainty Review

The green line reflects an interest rate increase or decrease? Increase This is the formula for present or future value? Present value Will the optimal bundle change? Spend less today! Yes How? Will this person be happier or less happy with the change in interest rates? Happier! If you earn $4,000 this month and $5,000 next month what is the present and future values of your total two-month income with a 4.5% interest rate?

If M1 = $200 and M2 = 300 and the interest rate is 5% what are the budget intercepts? /1.05 = (1.05) = 510 If you have a inter-temporal rate of substitution of 1.1 at your endowment bundle, does this bundle maximize your utility? 1.1 ≠ 1.05 so no. Should you save more or spend more today to maximize your utility? Spend more today to lower the slope of indifference curve. If interest rates increase to 8%, what are your new budget intercepts? Will you be happier or less happy with the interest rate increase? Note: this graph is for illustration and does not depict the question! /1.08 = (1.08) = 516 Happier – draw the graph and prove it to yourself. B Which is the endowment bundle? Optimal bundle? A is optimal; B is endowment Does the graph at right accurately depict the numbers given? NO!

Given the following graph with U=sqrt(M): What is the utility of the expected value of a chance of A and C? 7.07 What is the expected utility of a chance of A and C? 6.71 expresses what statistical principal? Jensen’s inequality What is this curve? Utility function What probability of winning would make you take the gamble? p(8.94) + (1-p)( 4.47) = 7.07 p = 58.17% What would be your expected value of the gamble you would take? 61.2

You face the following probabilities of losses: a 5% chance of a $100 loss; a 50% chance of a $40 loss; and a 25% chance of a $20 loss. What is your expected loss? If you start with $100 and have a utility function U=sqrt(M), how much would you pay for insurance against these losses? (note: there is no probability of any gain) If insurance against these losses cost $50, what is the highest probability of total loss ($100) you would need to justify this price, assuming the probabilities of $40 and $20 losses stayed the same? Test yourself: Come up with a story (or two!) that matches these numbers.

Good Luck! Quiz reminders: 1.You can start the quiz as early as 8am and must end at the end of class at 10:10. 2.You need a calculator that does square root that is NOT attached to a networked device (phone, tablet) 3.Please use PENCIL! 4.You can have one (1) page of notes 5.Behavioral Economics Next Week! – No Math!!