SOLVED

17) A do-it-yourself homeowner is installing a new toilet. While installing the toilet he must decide on what kind of connecting pipe he will install to the water supply. There are two available options, one that has a shut-off valve in case of a leak and a cheaper one without the shut-off valve. Suppose that the shut-off valve pipe costs an extra ten dollars and that the homeowner must buy one of the two. a.Draw a decision tree for this scenario, labeling the cost of a leak as X and the chance of a leak as P. b.If the chance of a leak causing household damage is 1%, at what $ amount of household damage is the owner neutral on which pipe to buy? c.If the cost of a leak would be $10,000 what is the maximum % chance to leak at which the homeowner would prefer to buy the cheaper pipe? d.If the cost of a leak is $1,000 and the chance to flood .1% which pipe should the homeowner buy? 18) A poker player is considering three different options after his opponent bet 200 before him. If the player folds, he will lose instantly. If the player calls, he figures he will win half the time. If he raises, he figures that the opposing player will not re-raise him, but rather will either call or fold. He figures the opposing player will call only ¼ of the time, folding the other ¾ of the time. If the opposing player calls his raise, he figures he will never win. The pot size is 1,000 (including the opposing player’s bet). a. Draw a decision tree for this scenario including the information provided in part b. b. Suppose that the player is thinking of raising to $400 (he will put in 200 to match the opponent’s bet and another 200 as a raise, his opponent would then have to put in 200 more to call the raise). Is this the best option or should he instead call or fold? c. At what raise size is the player’s EMV of a raise equivalent to simply calling? a. b. EMV of a fold is 0, EMV of a call is .5(1000) – .5(200) = 400, EMV of the raise is .75(1000) – .25 (400) = 650. The player should raise, not call or fold. c. EMV of a call is 400 from above, EMV of a raise is .75(1000) – .25(Raise Size). Setting these equal so 400 = .75(1000) – .25(Raise size) the raise size comes out to 1400.