Question 4

Question 4 Devlin-McGregor is the monopoly producer of Provasic which is composed of a mixture of elec- trolytes 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) = 0.5y2. Page 2 Not For Distribution Beyond the Class The Umbrella Corp. sets a wholesale price of w per unit of Soma to Devlin-McGregor. Devlin- McGregor 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)