Question: Millner Inc. has two divisions, Apples and Bananas. The price elasticity of demand for apples is -5 and the price elasticity of demand for bananas is -2.5. The average variable cost of a bag of apples is $3 and the average variable cost of a bunch of bananas is $2. Both average variable costs are constant across all levels of output. Fixed cost at Apples is $100 and it is $200 at Bananas. Apples and bananas are substitutes. Millner Inc operates both divisions as independent profit centers and each division manager receives 10% of the profit earned at his or her division; the compensation to the division manager for Apples is 10% of the profit at Apples and the compensation to the division manager for Bananas is 10% of the profit at Bananas. Millner Inc has strong financial controls to prevent the manager from using accounting devices to inflate profit and to insure that all revenues and costs are recorded properly.

Which product has the more elastic demand: apples or bananas?

b. Does the pair of prices set by independent profit centers (each division maximizes its individual profit) maximize profit for Millner Inc. If so, explain how you know. If not, what type(s) of change(s) would increase profit for Millner Inc and explain why this (these) change(s) would increase profit for Millner Inc.

c. Describe the advantages and disadvantages of paying each division manager 5% of the profit earned by Millner Inc instead of 10% of their respective profits? Assume thatwhen both divisions maximize their respective profit, the profit at Apples equals the profit at Bananas. The assumption implies that changing the compensation scheme would not affect the compensation to either manager if total profit remains constant.