The purchasing department of Ball Brothers purchases raw materials and supplies for the various divisions in the firm. Most of the purchasing department’s costs are labor costs. The costs of the purchasing department depend on the number of items purchased. The manager of the purchasing department estimates how her department’s costs will vary with different levels of demand by the divisions. The following table provides her estimates of how the costs of purchasing vary with the aggregate number of items purchased by all divisions.

Number of Items Purchased per Week Total Cost per Week
100– 199 ................ $ 1,000
200– 299 ................ 1,100
300– 399 ................ 1,200
400– 499 ................ 1,400
500– 599 ................ 1,700
600– 699 ................ 2,100
700– 799 ................ 2,600
800– 999 ................ 3,200
In deriving this table, the manager of purchasing projects expanding the size of the department in order to keep roughly constant the time to purchase an item and the quality of the purchasing department’s services at all levels of demand placed on the department. That is, if the department is processing 750 items per week, it will provide the same quality of services given a budget of $ 2,600 as it would processing 250 items per week given a budget of $ 1,100.

Required:
a. Suppose the purchasing department is currently purchasing 610 items per week. Should the department’s costs of $ 2,100 per week be allocated back to the divisions, making the purchases at a charge of $ 3.44 per item purchased ($ 2,100 610)? Explain why or why not.
b. Suppose the purchasing department is currently purchasing 210 items per week. Should the department’s costs of $ 1,100 per week be allocated back to the divisions, making the purchases at a charge of $ 5.23 per item purchased ($ 1,100 210)? Explain why or why not.
c. Reconcile (explain) why your answers to ( a ) and ( b ) are either the same or different.