Devlin-McGregor is the monopoly producer of Provasic which is composed of a mixture of electrolytes and Soma. If e units of electrolytes and s units of Soma are combined they generate min{e, 2s} units of Provasic. Devlin-McGregor can purchase any amount of electrolytes for $2 a unit. Soma, however, is produced by a monopoly supplier, the Umbrella Corp. The Umbrella Corp.'s cost of producing y units of Soma is C(y) = 0.5y 2 . Page 2 The Umbrella Corp. sets a wholesale price of w per unit of Soma to Devlin-McGregor. DevlinMcGregor in turn sets the downstream price of Provasic to end users. Downstream demand is characterized by an inverse demand curve of 100 q.

1. Determine Devlin-McGregor's minimum cost to produce q units as a function of q and w.

2. Determine the profit maximizing quantity of Provasic that Devlin-McGregor will sell as a function of w.

3. What is Umbrella Corp.'s profit maximizing choice of w?

4. What is the most that Devlin-McGgegor should pay to acquire Umbrella Corp. (this means control of their Soma production technology)?