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 Dps(pB, pS) = 80 - Ps + pB/2. Meanwhile, teenagers do not demand bikes at all but have a demand for skateboards given by Dt(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"—although it sells skateboards too) 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!"). If you do this, what prices will you charge in each store? Is it worth it to pay the additional rent? Why?
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 Dps(pB, pS) = 80 - Ps + pB/2. Meanwhile, teenagers do not demand bikes at all but have a demand for skateboards given by Dt(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"—although it sells skateboards too) 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!"). If you do this, what prices will you charge in each store? Is it worth it to pay the additional rent? Why?
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