An genius artist sells oil paintings of colorful dots and circles. It costs 0 to produce each painting. There are 1 unit of buyers, indexed by i [0,1]. Buyers do not hold any intrinsic value for the paintings. However, the paintings are trendy and rare. Owning one of these paintings gives a feeling of exclusivity and pleasure of showing off wealth. Formally, if B 1 people have paintings, the reservation price of buyer i [0,1] is given by i**(1B) where 1 is a positive constant capturing preferences for exclusivity.

a. For a given B 1, determine how many units of buyers buy paintings at a given price p

b. What is the demand for paintings for a given price p larger than ?

c. Show that if p> 1/2( - 1/2), the demand is increasing in , and if p<1>