McPeak
Lecture 8
PPA 723
Costs.
We are leaving selling price /
revenue out of the picture for the moment, but we are adding in the issue of
input costs.
Economic cost. Includes both the explicit and the implicit
cost. Full accounting of cost to society.
There are counterfactual, competing
allocations that underlie this concept.
“
What you could have done with that
time – the cost of leisure includes the foregone income if you could have had
if you worked instead; the cost of staying home to care for children includes
the foregone wages you could have gotten; the cost of studying includes the
foregone income you could have gotten…
These costs plus the explicit costs
(leisure the cost of the gas and bait and dock fees for your fishing trip;
child care the strollers, slings, toys for home; the studying the books,
tuition, fees,…) lead to the full cost.
Coming to study here for a year has
both an explicit cost of what you pay to attend and an implicit cost in terms
of the foregone earnings opportunity of the year you spend here.
You bought that year from yourself
in a sense.
[This gets us towards thinking about
zero economic profit. The next best
alternative is another form of investment that earns a positive rate of return
(more on this later).]
If you own a piece of land and
choose to build a house on it, the full cost of building the house are the
material, labor,…costs plus the current value of the land (by building you are not
selling the land).
In a perfectly competitive market
with no externalities and no dynamic implications, market price reflects
economic cost.
If this is not the case, economic
cost can deviate from market prices.
Historical cost is not important,
but actual cost is.
Concept of sunk cost – an
expenditure that can not be recovered but for scrap value.
486 computers.
Soviet economic planning details.
The value of these is what the
market will bear currently, not what it cost when you obtained it.
Short run costs.
Fixed cost- the production expenses
of the firm that do not vary with output.
Costs of inputs the firm can not
feasibly vary in the short term.
Variable cost- production expenses that change with the quantity of output produced.
Total cost is variable cost plus
fixed cost.
Three average cost measures are
derived from the fact that:
TC=VC+FC.
Divide through by q.
(TC)/q is average cost. Total cost divided by units of output
produced.
(VC)/q is average variable
cost. Variable cost divided by units of
output produced.
(FC)/q is average fixed cost. Fixed cost divided by units of output
produce.
AC=AVC+AFC
In addition, we can add in one more
cost concept. Marginal cost is the amount
by which the firm’s cost changes in order to produce one more unit of
output.
WARNING - FOR
THE FIRST TIME, WE ARE PUTTING CHANGE IN Q or Q IN THE DENOMINATOR. THIS IS IMPORTANT TO KEEP TRACK OF.
Example from the book
|
Output |
Fixed Cost |
Variable Cost |
Total Cost |
Marginal Cost |
AFC |
AVC |
AC |
|
0 |
48 |
0 |
48 |
NA |
NA |
NA |
NA |
|
1 |
48 |
25 |
73 |
25 |
48 |
25 |
73 |
|
2 |
48 |
46 |
94 |
21 |
24 |
23 |
47 |
|
3 |
48 |
66 |
114 |
20 |
16 |
22 |
38 |
|
4 |
48 |
82 |
130 |
16 |
12 |
20.5 |
32.5 |
|
5 |
48 |
100 |
148 |
18 |
9.6 |
20 |
29.6 |
|
6 |
48 |
120 |
168 |
20 |
8 |
20 |
28 |
|
7 |
48 |
141 |
189 |
21 |
6.9 |
20.1 |
27 |
|
8 |
48 |
168 |
216 |
27 |
6 |
21 |
27 |
|
9 |
48 |
198 |
246 |
30 |
5.3 |
22 |
27.3 |
|
|
|
|
|
|
|
|
|
The average cost curve is the
vertical sum of the average variable cost curve and the average fixed cost
curve (look back at numbers in table and this graph).
The minimum of the average cost
curve is where the AC curve is crossed by the MC curve (look back at numbers in
table and this graph).
AVC and AC fall when MC is below
them, and rise when it is above them.
[if the cost of producing one more unit of output is below the current
average, the average calculated at the next point will be lower, if higher,
then higher].
[can recall example of marginal
person entering the room and changing average height in the room]
Return to the production function
idea, and recall diminishing marginal returns to production.
Show production function.
X-axis is input level. Multiply by cost of the input.
Then we have output as a function of
input cost.
Tip it over, and we have cost as a
function of output.
Given input prices, the shape of the
cost curve is determined by the production function.
The shape of the production function
is determined by marginal returns, with the possibility of increasing returns
to scale over low range of output and decreasing returns to scale over high
ranges of output.
[show graphs]
This relationship between the production function and the marginal cost curve
leads to the following relationship.
MC=change in cost / change in
quantity.
[Cost is VC or C]
MC= cost of input times change in
input / change in quantity.
Remembering marginal product is
change in quantity divided by change in input, we can state:
MC= cost of input / MP
A similar process holds for the
Average Variable Cost, so that we can say:
AVC=VC/q or cost of input *input level / output level. This means AVC= input cost / AP.
Summary:
7 short run cost concepts.
Total cost.
Fixed cost.
Variable cost.
Average cost.
Average fixed cost.
Average variable cost.
Marginal cost.
Long run costs.
What is the value of fixed cost F in
the long run when there are no fixed inputs?
Zero, since all inputs can be adjusted.
[Note idea of avoidable cost. There may be costs in the long run that do
not vary with output except in the binary sense].
Three long run cost concepts:
Total cost.
Average cost.
Marginal cost.
An isocost line. A line tracing out different combinations of
inputs with given input prices that can be obtained at identical total
cost.
The maximum amount of inputs that
can be bought given input prices at a given total cost level.
Draw example for C=10, w=2,
r=1. Then C=20.
Again, note that we are saying it is
long run cost since two variable inputs, but could also have two variable
inputs in short run if a third is fixed.
The key here is that we assume there are two inputs to production and
both of them are variable (K and L).
The slope is determined by the
negative of the relative price ratio.
Discussion here of deriving the
slope of the budget line from the cost function, and why the expression depends
on whether you put K or L on the y-axis.
An isoquant is like an indifference
curve.
An isocost is like a budget line.
However, there is a difference in
how we treat a budget line and an isocost line.
Remember the consumer had fixed income Y in the consumer theory
section. Here there is nothing exogenous
to cost, so we have to think about it differently. Firms are choosing cost level, while the
consumer was not able to choose income level.
Producing in a way that is
technically efficient (meaning?) and in a way that is cost minimizing is
economically efficient.
We are technically efficient on the
isoquant curve remember.
Draw isoquant / isocost and contrast
points.
3 ways of conceptualizing how we
arrive at an economically efficient, cost minimizing point.
1)
Lowest isocost rule. Minimum cost subject to producing a given
output level efficiently (being on an isoquant).
2)
Tangency rule. The point where the isoquant is tangent to
the isocost line. Where the slope of the
isoquant (MRTS) is equal to the negative of the input price ratio.
3)
Last dollar rule. Pick input bundle so that the last dollar
spent on one input adds as much output as the last dollar spent on the other
input.
The expansion path traces out the
cost minimizing combination of inputs for each output level. If we look at the line traced out by the
tangency points, we trace out a line of economic efficiency.
We can take the information from the
expansion path to trace out a long run cost curve (note the use of the isocost
and isoquant labels, which differs from what we did for the demand curve
derivation).
[show derivation]