Problem:
An online retailer mails out catalogs. You might browse through one and decide to order. You call a toll free number and place your order and it will arrive in several days by post or UPS. However, what you probably don't know (since you only live at one post office address) is that the merchant sends out multiple catalogs at the same time. And the prices in the catalogs can differ substantially for the same item. Since they know the address of the mailing and the buying habits of the customer, they can set prices differently based on demographics (the address tells them that) and past preferences of customers (your purchase record with them tells them that). In addition, other factors, e.g., climate, may influence the demand curve.
Suppose that the merchant estimates that the demand for their wool sweaters is
PNY = 140 - 4QNY
where QNY is the quantity of the merchants wool sweaters demanded in New York (in units of 10) when the price of a wool sweater is PNY and that the demand for their wool sweaters in North Dakota is
PND = 50 - 2QND
where QND is the quantity of wool sweaters demanded in North Dakota (in units of 10) when the price of a wool sweater is PND.
It costs 5 to produce a wool sweater and the shipping cost from their distribution center is a constant 3 per sweater to either destination.
Should they charge the same price for a wool sweater in New York and North Dakota to maximize profit? Or should they charge different prices in New York or North Dakota? Show their profits under each method.
The merchant (Should, Should Not) charge the same price in New York as in North Dakota for a wool sweater.
Their profit if they charge the same price is: ______________
Their profit if they charge different prices is: ______________
Suppose that it costs Land's End 300 more to produce two different catalogs as opposed to just one catalog. Would that change your answer in the (Should, Should Not) question? If so, why and if not, why not?
It (Would, Would Not) change my answer because
Show detailed work for each problem.