2. Alex plays football for a local club in Kumasi. If he does not suffer any injury b y the end of the season, he will get a professional contract with Kotoko, which is worth $10,000. If he is injured though, he will get a contract as a fitness coa ch worth $100. The probability of the injury is 10%. Describe the lottery What is the expected value of this lottery? What is the expected utility of this lottery if u(x) = √X Assume he could buy insurance at price P that could pay $9,900 in case of inj ury. What is the highest value of P that makes it worthwhile for Alex to purcha se insurance? What is the certainty equivalence for this lottery?

4. Consider the situation in which player 1 knows what game is played (the first or the second). But player 2 only knows that the first game is played with probability 1/3 and the second game is played with probability 2/3. Player 1 Player 1 Player 2 S B S 1,1 0,0 B 0,0 0,0 Player 2 S B S 0,0 0,0 B 0,0 2,2 (a) Describe the game as a Bayesian game. (b) Find the Bayesian Nash equilibria.

A. From the graph below explain how an insurance plan which provides the buyer a $15,000 wealth level, regardless of any uncertain event, is a good deal for the buyer? In other words, what does the distance between points D’ and C’ represent? Note we are referring to D prime, not D.   B. Considering the graph below, can you explain the difference between expected utility and certainty utility?

2. Christiaan can go hiking, or he can stay at home. Hiking would be fun if nothing bad happens, but there is a risk if he goes hiking that he will meet a bear (not fun) or get bitten by a snake (very not fun). Christiaan decides that if there is a 5% chance of meeting a bear and a 1% chance of getting bitten by a snake, he would prefer to go hiking rather than stay at home. However, if the chance of meeting a bear is 10% and the chance of a snake bite is 5%, he definitely would rather stay at home. then (a) Consider the utility function: U (stay home) = 25, U (hike no event) = 100, U (hike & snake) -1000, U (hike & bear) = -200. Does this utility function represent Christiaan's pref- erences? Explain. (b) Suppose that the utility function in (a) does represent Christiaan's preferences. Would Christiaan prefer to hike or stay home if the probability of meeting a bear is 6% and the probability of being bitten by a snake is 4%? Show your work.