Some Additional Cost Concepts

The author suggests that a good function to represent total cost has the general form

TC = f + aQ + bQ^2 + cQ^3,

Where the key ^ means raise to power,

f represents fixed cost,

Q represents the level of output that can vary, and

a, b, and c are numbers, sometimes called constants.

The average cost (AC OR ATC) = TC/Q = f/Q + a + bQ + cQ^2, the average variable cost is a + bQ + cQ^2, the average fixed cost is f/Q and the marginal cost = a + 2bQ + 3Q^2.

Sometimes firms make more than one type of good and one type of cost function to represent the total cost of making both goods would be

TC = f + aQ1Q2 + Q1^2 + Q2^2.

The marginal cost with respect to Q1 would be

MC1 = aQ2 + 2Q1, and with respect to Q2

MC2 = aQ1 + 2Q2.

Economies of Scope.

This is when you buy Scope in a really big bottle.

Economies of scope are present whenever it is less costly to produce a set of different goods in one firm than it is to produce that set in two or more firms.

Example of two goods in the set. Add up the cost of good 1 in one firm and the cost of good 2 in another firm then subtract the cost from making both in one firm.

In notation form we have

TC(Q1, 0) + TC(0, Q2) – TC(Q1, Q2).

If this expression > 0 we have economies of scope,

If < 0 we have diseconomies of scope, and

If = 0 we do not have economies of scope.

The degree of scope economies is

Sc = {TC(Q1, 0) + TC(0, Q2) – TC(Q1, Q2)} / TC(Q1, Q2).

Why do scope economies exist?

Particular outputs share common inputs. Example: advertising diet coke with lemon twist also helps classic coke because the brand names are the same.

Cost complementarities – when increasing the production one good it lowers the marginal cost of producing the other good.

Example: Say a multiproduct firm has

TC = 100 -0.5Q1Q2 + Q1^2 + Q2^2

In terms of scope economies

If Q2 = 0 TC1 = 100 + Q1^2 and if Q1 = 0 TC2 = 100 +Q2^2,

Then TC1 + TC2 – TC = 100 + .5Q1Q2 which >0 for Q1 and Q2 greater than 0. So economies of scope exist.

In terms of cost complementarities

MC1 = -.5Q2 + 2Q1 so if Q2 goes up MC1 goes down, and

MC2 = -.5Q1 + 2Q2 so if Q1 goes up MC2 goes down. Thus there are cost complementarities.

If in the example on the previous screen if the firm divested itself of product 2 its cost would become

TC = 100 +Q1^2 and its MC would be 2Q1. This MC is more than under the case of cost complementarity.