Question

A firm is planning to manufacture a new product. As the selling price is increased, the quantity that can be sold decreases. Numerically the sales department estimates:

P = $350 - 0.2Q where
P = selling price per unit
Q = quantity sold per year
On the other hand, management estimates that the average unit cost of manufacturing and selling the product will decrease as the quantity sold increases. They estimate
C = $40Q + $20,000
where C = cost to produce and sell Q per year

Answer 1

The firm experiences losses when producing five units due to the price being less than the average cost. The marginal unit is subtracting from profits, indicating a need to reduce quantity produced.

Step-by-step explanation:

Total revenues in this example will be a quantity of five units multiplied by the price of $25/unit, which equals $125. Total costs when producing five units are $130. Thus, at this level of quantity and output the firm experiences losses (or negative profits) of $5.

If price is less than average cost, the firm is not making a profit. At an output of five units, the average cost is $26/unit. Thus, at a glance you can see the firm is making losses. At a second glance, you can see that it must be losing $1 for each unit produced (that is, average cost of $26/unit minus the price of $25/unit). With five units produced, this observation implies total losses of $5.

When producing five units, marginal costs are $30/unit. Price is $25/unit. Thus, the marginal unit is not adding to profits, but is actually subtracting from profits, which suggests that the firm should reduce its quantity produced.