question archive A property developer is selling new villas in Spain
A property developer is selling new villas in Spain
Subject:BusinessPrice: Bought3
A property developer is selling new villas in Spain. The cost of building each villa is 100,000 euros. There are two types of potential buyers. Type 1 buyers are willing to pay up to P1 = 250,000 - 10,000M1, where M1 is the number of months that they would have to wait before taking possession of the villa. Type 2 buyers are willing to pay up to P2 = 200,000 - 1,000M2, where M2 is the number of months that they would have to wait. Let us assume for simplicity that the developer could supply all villas immediately if she wanted. Assume further that there are 10 impatient (i.e. type 1) buyers and 10 patient (i.e. type 2) buyers. Each buyer buys at most one villa. The developer cannot tell the different types of buyers apart. Moreover, administrative fees are high enough to prevent any reselling between buyers.
(a) Suppose that the developer can choose the number of months M a buyer has to wait as well as the price P a buyer has to pay for a villa. The developer offers two options. In the first option, the villa costs 240,000 and is available immediately. In the second option, the villa costs 190,000 and is available in 6 months. Which option will a type 1 buyer choose? Which option will a type 2 buyer choose? How much profit will the developer make?
(b) Can the developer do even better than in part (a)? How? In particular, let (P1, M1) denote the price/waiting time package aimed at impatient (type 1) buyers and (P2, M2) the package aimed at patient (type 2) buyers.
