Question

Consider cost theory.

a. Prove that marginal cost and average cost are equal where average cost is minimized.

b. Respecting the standard U-shaped long-run average cost curve, briefly provide two distinct explanations for the downward sloping part of the curve, and an explanation for the upward sloping part.

c. Suppose an electricity distribution firm purchases a number of metal poles for inventory at a price of ?? per pole. Sometime later, metal poles become obsolete in the industry in favour of fiberglass poles, and command a price of ?? per pole in the scrap metal market. By the time the firm switches to fiberglass poles, some of the metal poles previously purchased remain in the firm’s inventory. The price of a fiberglass pole is ??. Assume that 0 < ?? < ?? < ??. In terms of these variables, quantify the accounting and economic costs of each of the following activities:

i. Past purchase of a metal pole for inventory.

ii. Current purchase of a fiberglass pole for inventory.

iii. Keeping a fiberglass pole in inventory.

iv. Keeping a metal pole in inventory.

v. Selling an uninstalled metal pole for scrap. Briefly explain which of the quantified costs are sunk.

Answer 1

Answer (a)

Output -- Total Cost -- Average Cost --- Marginal Cost

0 10

1 20 20 10

2 28 14     8

3 34 11.3333 6

4 38 9.5     4

5 42 8.4 4

6 48 8    6

7 56 8 8

8 72    9 16

As, we can see that average total cost is decreasing initially, and at output equal to 7 units, marginal cost is equal to average total cost.At this point the average total cost is at its minimum.

Answer (b)

The downward sloping average total cost curve means that as the production increases, the total cost decreases.It simply means that the prodution process is smooth and the resources are being utilized efficiently.In other words, this phase is called economies of scale.

The upward sloping average total cost curve means that as the production increases, the total cost also increases.It simply means that the prodution process is not smooth and the resources are not being utilized efficiently.In other words, this phase is called diseconomies of scale.