# can you explain opportunity costs

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```							Opportunity Cost                                                      06/11/2005

The Opportunity Cost of an Action (or Item) is the value of the next best alternative
foregone.

The maximum price a buyer is willing to pay is called the Buyer’s Reservation Price.
The Direct Opportunity Costs of an alternative, say A, are e.g. direct net payments that
have to be made in order to obtain A. Typically, the direct opportunity costs are simply
the nominal price plus other direct (out-of-pocket) expenses of the alternative. (The
direct opportunity costs are also called Accounting Costs, because these are the costs that
accountants use in regular bookkeeping.) The Net Benefit of an alternative is the benefit
of the alternative minus its opportunity costs. The Consumer Surplus of an alternative is
the benefit of the alternative minus the direct opportunity costs. The Indirect Opportunity
Costs of an alternative is the benefit minus the direct costs of the next best alternative –
i.e. the indirect opportunity cost is the consumer surplus of the next best alternative.
Finally, (Total) Opportunity Costs of an alternative is the sum of its direct and indirect
opportunity costs. (The indirect opportunity cost are not included in accounting costs!)

Notation.

Benefit of A = B(A), Direct Opportunity Costs of A = DOC(A), Reservation Price of A =
RP(A) = B(A), Net Benefit of A = NB(A), Opportunity Cost of A = OC(A) and
Consumer Surplus CS(A).

Definitions.

(1) RP(A) = B(A)

(2) CS(A) = B(A) – DOC(A)

The Consumer Surplus on the nth unit purchased in a market is illustrated here. The
direct opportunity costs is simply the price paid!

S
(3) OC(A) = DOC(A) + B(B) - DOC(B)

(4) NB(A) = B(A) - OC(A)

In the above definitions, if we substitute (3) into (4) then we get:

NB(A) = B(A) -DOC(A) - [B(B) - DOC(B)]

or      NB(A) = CS(A) – CS(B).

In other words, in this example where there are only two alternatives, the Net
Benefit of alternative A is the Consumer Surplus of A minus the Consumer Surplus
of B!

Similarly, we have that

NB(B) = CS(B) – CS(A).

Consequently,             NB(A) = - NB(B).

It now follows that, whichever alternative has a positive Net Benefit is the preferred
alternative.

Numerical Examples

Example 1

Suppose a secretary has to decide between two alternative ways of spending the next
8 hours. She can:

(A) take the bus to work, which will cost \$2, take 1.5 hour and then she can work for
6.5 hours at a rate of \$25 per hour.

(B) take a taxi to work, which will cost \$20, take .5 hour and then she can work for
7.5 hour at a rate of \$25 per hour.

Then the Consumer Surplus of A is

CS(A) = (8 – 1.5) x \$25 - \$2 = \$162.50 - \$2 = 160.50
and the Consumer Surplus of B is

CS(B) = (8 - .5) x \$25 - \$20 = \$187.50 - \$20 = \$167.50.

From above we have

NB(A) = CS(A) – CS(B) = - \$7

and

NB(B) = CS(B) – CS(A) = \$7.

Therefore, alternative B is the better of the two!

Example 2

This example is the same as example 1 except there are now three (3) alternatives!

Suppose a secretary has to decide between three alternative ways of spending the next 8
hours. She can:

(A) take the bus to work, which will cost \$4, take 0.5 hour and then she can work for
7.5 hours at a rate of \$25 per hour.

(B) take a taxi to work, which will cost \$20, take 0.25 hour and then she can work
for 7.75 hour at a rate of \$25 per hour.

(C) ride her bicycle to work which will cost her nothing, take 1 hour and then she can
work for 7 hours at a rate of \$25 per hour.

Calculate the Consumer Surplus and Net Benefit for each alternative and explain how
your calculations can be used to decide which alternative is the best from an economic
point of view.

The Consumer Surpluses are as follows.

CS(A) = 7.5 x 25 – 4 = 187.50 – 4 = 183.50

CS(B) = 7.75 x 25 – 20 = 193.75 – 20 = 173.75

CS(C) = 7 x 25 = 175
Since there are three (3) alternatives the determination of the Net Benefit of an alternative
requires that we calculate the differences between the alternative’s Consumer Surplus and
those of the other two. For example, to determine the Net Benefit of A we need to
subtract the Consumer Surplus of the “Next Best Alternative.” However, we don’t know
which of the other two alternatives is the “Next Best Alternative” compared to alternative
A. A simple way to solve this is to calculate the differences between the Consumer
Surplus of each alternative and the Consumer Surpluses of the other two alternatives.

CS(B) = 183.50 – 173.75 = 9.75

NB(A) = CS(A) -

CS(C) = 183.50 – 175 = 8.50

CS(A) = 173.75 – 183.50 = - 9.75

NB(B) = CS(B) -

CS(C) = 173.75 – 175 = - 1.25

CS(A) = 175 – 183.50 = - 8.50

NB(C) = CS(C) -

CS(B) = 175 – 173.75 = 1.25

It follows that alternative A is the best. (You should notice that the best alternative is
always the alternative with the largest Consumer Surplus. Moreover, the “Next Best”
alternative for a given alternative is always the “other” alternative with the largest
Consumer Surplus.)

By doing it the way illustrated here we avoid getting into circular reasoning. For
example, it could be argued that the indirect opportunity costs of an alternative should be
defined as the net benefit of the next best alternative foregone (and not as above where
the indirect opportunity costs are defined as the consumer surplus of the next best
alternative!) The difference is critical. The following shows, that if indirect opportunity
cost are defined as the net benefit of the next best alternative then it leads to circular
reasoning and is therefore not valid.

What follows is only intended to explain the problem to those who are curious to
know. It involves mathematical reasoning and is not material you are expected to
know for econ 101/102.

Here, instead of defining OC(A) = DOC(A) + CS(B), as we did above, we define it as
OC(A) = DOC(A) + NB(B). Then for alternatives A and B we would have

(5)   NB(A) = B(A) – OC(A)

= B(A) – DOC(A) – NB(B)

and

(6)    NB(B) = B(B) – OC(B)

= B(B) – DOC(B) – NB(A)

Substituting (6) into (5) we get

(7)    NB(A) = B(A) – DOC(A) - B(B) +DOC(B) + NB(A)

and, therefore, canceling NB(A) and re-arranging the terms we have

(8)    B(A) – DOC(A) = B(B) – DOC(B)

or

(9)    CS(A) = CS(B)

Which, in general, is NOT correct. (See the above numerical examples.) In other words,
the alternative definition of OC leads to circular reasoning.

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Shared by: Richard Cataman
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