Pricing and Price Discrimination at Twin Pines Mall You sell skateboards and bikes at Twin Pines Mall.

You have two types of customers: Parents of small children, who may have some preference but will generally buy either a skateboard or a bike, and teenagers, who insist on being "cool" and buying a skateboard. You estimate that the demand by parents for bikes is Dpb (pb,ps) = 80 - pb + ps/2 , where pb is the price you charge for bikes and ps is the price you charge for skateboards; the demand by parents for skateboards is given by Dpb (pb,ps) = 80 - ps + pb/2. Meanwhile, teenagers do not demand bikes at all but have a demand for skateboards given by Dts (pb,ps) = 80 - ps/4 . The wholesale price (i.e., your cost) is $60 for a bike and is $40 for a skateboard.

a) What prices will you charge for bikes and skateboards? Why is it optimal to charge the same price for skateboards that you do for bikes, even though bikes cost you more?

b) Now suppose you can open a second store in the mall for $1000 and can give each store a theme such that only parents will enter the first ("McFly's Bikes for Tykes") and only teenagers will enter the second ("Tannen's Danger Zone," which has the tagline "If you don't shop here, you're a chicken!"). what prices will you charge in each store? Is it worth it to pay the additional rent? Why?

Decision Tree and Risk problem

You are Mr. Boddy, the principal for a small family investment fund specializing in information technology investments, Boddy Ltd. The current value of the fund is $16M, and your utility over your final wealth w is -1/w . You could invest in Mustard Mechanical, who is designing new flight stabilization software for military helicopters. You estimate that there is a two-in-five chance that the firm will be successful; if so, you expect to obtain a return of twice your investment plus your principal back (so if you invested $1M, your final wealth would be $18M). But there is a three-in-five chance that the firm will fail, and you will not see any return (so if you invested $1M, your final wealth would be $15M).

a) Suppose that your only choice is whether to invest $1M: Do you invest? Why or why not? What if you must invest $2M or nothing: Will you invest then? Why did your answer change?

b) Suppose that you must indeed invest $2M or nothing. However, if you do invest, you will have the chance to invest in a follow-up second round an amount of your choice if your initial investment was successful. If you invest in this follow-up round, you expect that Mustard may be bought by Peacock Armamentsin which case you will make three times your investment including the return of your principal (so for a second-round investment of $1M you will end up $2M richer); you estimate the probability of this outcome at one-half. You expect a one in-nine chance that the firm will fail at this stage (so you lose any money you invested in the second round, but still enjoy the benefits of your first-round success). Finally, there is a remaining seven-in-eighteen chance that Mustard will not fail but also not be purchased, in which case you will just get your second-round investment back (and so your wealth will not change). Suppose you invested the requisite $2M in the first round and Mustard was successful: How much will you invest in the second round? (Please consider that your wealth has changed since the first round was successful.) Given this follow-up opportunity, should you change your decision about whether to invest in the initial round at $2M? Why?