In discussions of the concept of economies of scale, it is commonly believed that the more a firm produces, the lower the unit costs. This is not always true, as depicted in Figure 4.1.

The cost equations of a hypothetical small motor industrial manufacturer are as follows.

TC = 300 + 8Q2 (1)

AC = 300/Q + 8Q (2)

Here, TC is the total cost of production in dollars, Q is the number of units, and AC is the average cost per unit in dollars.

(a) What are the total costs to the firm when 4 units are produced? Hint: Substitute 4 for Q in Equation (1).

(b) What is the average cost per unit when 4 units are produced? Hint: Substitute 4 for Q in Equation (2).

(c) Do the same for TC and AC for quantities of 1 and 2. What pattern do we observe?

(d) Put in a large number for Q, say Q = 55. What are the values for TC and AC? Comment on the value of AC.

(e) Explain why AC has increased. (Hint: Consider the operating environment of the manufacturer)

(f) Assume the manufacturer wishes to stop production when the average cost is at its lowest. What is the number of units that the firm should produce? (Hint: Calculate AC progressively, starting from Q = 1. You will not have to go beyond Q = 10.)