Consider a firm that sells red pens and blue pens. Each pen costs $0.15 in labour and raw materials.In addition, each pen must be run through a machine that costs $1000 a day to use, regardless of how many pens it processes. The total capacity of the machine is 8000 pens per day (red or blue).The first 5000 red pens are sold for $0.30 each; additional red pens can be sold at $0.20 each.Blue pens, in contrast, are sold for $0.25 per pen regardless of quantity.

The firm was selling 5000 red pens and 3000 blue pens for a daily profit of $50 (5000 red pens at a $0.15 margin plus 3000 blue pens at a $0.10 margin minus $1000 of fixed cost).

At this point, an accounting consultant was hired to generate a system of cost allocation across product lines. The consultant decided to allocated shared overheads (fixed costs) on the basis of output (5000/8000 = red and 3000/8000 = blue pens' share of output). Thus the $1000 running costs of the machine were allocated as $625 to the red-pen production line and $375 to the blue-pen production line.

Based on this new accounting system, the blue-pen production line showed a loss of $75 per day (3000 pens at a $0.10 margin minus a fixed cost of $375). Accordingly, the firm decided to shut down the blue-pen production line and increase the output of red pens to 8000 per day. Revenues were now 5000 pens at $0.30 plus 3000 pens at $0.20, or $2100. However, total costs were 8000 times $0.15 (labour and raw materials) plus $1000 (to run the machine), implying a loss of $100 per day. The firm thus decided to shut down the red-pen production line.

In summary, the firm started with a profit of $50 per day and ended up with a profit of zero. Explain clearly what