1. Vincent van Gogh can produce paintings at constant marginal cost cV V G = 1. The population of buyers of VVG paintings is grouped into two categories: Serious Art Collectors (SAC) and Casual Art Collectors (CAC). The SAC to CAC population ratio is 1 : 4. Assume that the utilities of these two types of buyers is given as follows,

uSAC (x, t) = 3?x ? t; uCAC (x, t) = ?x ? t

Assuming VVG charges a fixed price for every painting, find the profit maximizing fixed price.

2. Now assume that VVG offers bundles {(x1 , t1 ); (x2 , t2 )}. Compute VVG's (expected) profit from this strategy if he offers the following bundles, i.e. in each case compute his expected profit:

• (x1,t1)=(1,3),(x2,t2)=(1/4,1/2).
• (x1,t1)=(9/4,7/2),(x2,t2)=(1/4,1/2). • (x1,t1)=(9/4,9/2),(x2,t2)=(1/4.1/2).