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.

Briefly explain which of the quantified costs are sunk.

Answer 1

a) Marginal Cost is the change in total cost that is caused due to production of one more unit.

Average cost is total cost divided by total number of units.

MC = Change in TC/ Change in Units

AC= Total cost/ No. of units

Marginal cost and Average cost curves, both are "U" shaped.

Relation between Average cost and Marginal cost:

• When average cost falls as a result of an increase in output, marginal cost is less than average cost.
• when average cost rises as a result of increase in output, marginal cost is more than average cost.
• when average cost is minimum, marginal cost is equal to the average cost. In other words, marginal cost cuve cuts average cost curve at it's minimum point ( optimum point).

In the figure provided, you can clearly see that both the cuves are "U" shaped and MC and AC are cutting each other at point "P", which is the minimum point of AC, and after that point, MC and Ac both rises, but MC> AC.

(b) U shaped LAC arises due to returns to scale. When the firm expands, returns to scale increases. After a range od constant returns to scale, the returns to scale finally decreases.

On the same lines LAC curve first declines and then finally rises.

Increasing returns to scale cause fall in the long run average cost and decreasing returns to scale results in rise in long run average cost curve.

Falling long run average cost and increasing economies to scale result from internal and external economies of scale and rising long run average cost and diminishing returns to scale result from internal and external diseconomies of scale.

The long run average cost curve initially falls with increase in output and after a certain point, it rises making a boat shape (u). The long run average cost curve is also known as Planning curve of the firm.

(c) Sunk costs are those costs which once incurred cannot be recovered.

So, in the above question following are the sunk costs.

(i) Past purchase of a metal pole for inventory- This is a sunk cost because since they have already purchases the metal pole for inventory in the past and now they cannot return it or recover their money from where they purchased it.

(v) Selling an uninstalled metal pole for scrap- Since once they've sold an uninstalled metal pole for scrap, they cannot recover the material back. Once sold, cannot be recovered.