Incentive Considerations in Allocating a Scarce Resource The Brantford Corporation has 500 units of capacity available for production during the upcoming period. This capacity is to be distributed between the two major divisions in the company: the Commercial Controls Division and the Computer Division. Each division uses one unit of capacity to make one unit of output.

The managers of each division view the demand for the products of the two divisions.

Only the division's manager knows the demand facing that division.

The contribution margin provided by each Commercial Controls Division product is

$250,000, and the division manager believes that the total demand for the Commercial Controls Division products will be somewhere between 500 and 800 units, with each value on this interval equally likely.

The contribution margin provided by each Computer Division product is $320,000, and the division manager believes that the total demand for the Computer Division products will be somewhere between O and 500 units, with each value on this interval equally likely. Because of production line setups and tooling, once the capacity is assigned to one division at the start of the production period, it cannot be transferred for the other division to use if the demand on the facility turns out to be less than the amount allocated. The managers of the two divisions have been asked to submit their requirements for use of the capacity during the upcoming period.

Required

( 1 ) What level of capacity will each manager request if each manager's bonus is based solely on the manager's ability to meet the production plan for the allocated capacity?

What is the expected contribution margin associated with this assignment of capacity?

(2) What level of capacity will each manager request if each manager's bonus is based on the contribution margin generated by the capacity allocated to that manager's division and the managers are not assigned a charge for the capacity allocated to their respective divisions? What is the expected contribution margin associated with this assigrunent of capacity?

(3) What level of capacity will each manager request if each manager's bonus is based on the contribution margin associated with the capacity that is earned by the company?

What is the expected contribution margin associated with this assignment of capacity?

(4) What do the results to Requirements 1 , 2, and 3 imply about the design of incentive schemes in decentralized organizations? Why might these results be misleading?