The Alpha Division of the XYZ Company manufactures product X at a variable cost of $40 per unit. Alpha Division's fixed costs, which are sunk, are $20 per unit. The market price of X is $70 per unit. Beta Division of XYZ Company uses product X to make Y. The variable costs to convert X to Y are $20 per unit and the fixed costs, which are sunk, are $10 per unit. The product Y sells for $80 per unit.

a. What transfer price of X causes divisional managers to make decentralized decisions that maximize XYZ Company's profit if each division is treated as a profit center?

b. Given the transfer price from part (a), what should the manager of the Beta Division do?

c. Suppose there is no market price for product X. What transfer price should be used for decentralized decision-making?

d. If there is no market for product X, is the operations of the Beta Division profitable?