Question

6. 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.

Answer 1

Solution

A property developer is selling new villas in Spain. The cost of building each villa

a) Buyer 1 is willing to pay , P1 = 250,000 - 10,000M1

If Buyer 1 chooses 1st option he has to pay 240,000

If Buyer 1 chooses 2nd option he has to pay - 250,000 -( 10000*6)

= 250,000 - 60,000 = 190,000 euros.

Buyer 1 will choose 2nd option.

Buyer 2 is willing to pay 200,000 - 1000M2

If Buyer 2 chooses 1st option he has to pay 240,000

If Buyer 2 chooses 2nd option he has to pay - 200,000 - (1000*6)= 194,000 euros.

Thus , Buyer 2 will choose 1st option.

b) In case of Buyer 1 most profitable option for Developer is P1= 239,000 and M1 =1

In case of buyer 2 most profitable option for developer is P2 = 198,000 and M2 =1