Transcript Definitions of Costs  It is important to differentiate between accounting cost and economic cost – – the accountant’s view of cost stresses out-ofpocket expenses, historical.

Definitions of Costs

It is important to differentiate between
accounting cost and economic cost
–
–
the accountant’s view of cost stresses out-ofpocket expenses, historical costs, depreciation,
and other bookkeeping entries
economists focus more on opportunity cost
Definitions of Costs

Labor Costs
–
–
to accountants, expenditures on labor are
current expenses and hence costs of
production
to economists, labor is an explicit cost

labor services are contracted at some hourly wage
(w) and it is assumed that this is also what the labor
could earn in alternative employment
Definitions of Costs

Capital Costs
–
–
accountants use the historical price of the capital
and apply some depreciation rule to determine
current costs
economists refer to the capital’s original price as
a “sunk cost” and instead regard the implicit cost
of the capital to be what someone else would be
willing to pay for its use

we will use r to denote the rental rate for capital
Economic Cost

The economic cost of any input is the
payment required to keep that input in its
present employment
–
the remuneration the input would receive in its
best alternative employment
Two Simplifying Assumptions

There are only two inputs
–
–
homogeneous labor (L), measured in laborhours
homogeneous capital (K), measured in machinehours


entrepreneurial costs are included in capital costs
Inputs are hired in perfectly competitive
markets
–
firms are price takers in input markets
Economic Profits

Total costs for the firm are given by
total costs = TC = wL + rK

Total revenue for the firm is given by
total revenue = Pq = Pf(K,L)

Economic profits () are equal to
 = total revenue - total cost
 = Pq - wL - rK
 = Pf(K,L) - wL - rK
Economic Profits

Economic profits are a function of the
amount of capital and labor employed
–

we could examine how a firm would choose K
and L to maximize profit
But for now we will assume that the firm has
already chosen its output level (q0) and
wants to minimize its costs
Cost-Minimizing Input Choices

To minimize the cost of producing a given
level of output, a firm should choose a
point on the isoquant at which the MRTS
is equal to the ratio w/r
–
it should equate the rate at which K can be
traded for L in the productive process to the
rate at which they can be traded in the
marketplace
Cost-Minimizing Input Choices
K per period
TC1
TC3
Costs are represented by
parallel lines with a slope
of -w/r
TC2
TC1 < TC2 < TC3
q0
L per period
Cost-Minimizing Input Choices
K per period
The minimum cost of
producing q0 is TC2
TC1
TC3
TC2
K*
q0
The optimal
choice is L*, K*
L per period
L*
The Firm’s Expansion Path


The firm can determine the costminimizing combinations of K and L for
every level of output
If input costs remain constant for all
amounts of K and L the firm may demand,
we can trace the locus of cost-minimizing
choices
–
called the firm’s expansion path
The Firm’s Expansion Path
The expansion path is
the locus of costminimizing tangencies
K per period
E
q1
q0
q00
The curve shows
how inputs increase
as output increases
L per period
Total Cost Function

The total cost function shows that for any
set of input costs and for any output level,
the minimum cost incurred by the firm is
TC = TC(r,w,q)

As output increases, total costs increase
Average Cost Function

The average cost function (AC) is found by
computing total costs per unit of output
TC (r , w, q)
average cost  AC (r , w, q) 
q
Marginal Cost Function

The marginal cost function (MC) is found by
computing the change in total costs for a
change in output produced
TC (r , w, q)
marginal cost  MC (r , w, q) 
q
Graphical Analysis of
Total Costs

Suppose instead that total costs start out as
concave and then becomes convex as output
increases
–
–
one possible explanation for this is that there is
another factor of production that is fixed as capital
and labor usage expands
total costs begin rising rapidly after diminishing
returns set in
Graphical Analysis of
Total Costs
Total
costs
TC
Total costs rise
dramatically as
output rises
after diminishing
returns set in
Output
Graphical Analysis of
Total Costs
AC
MC
MC is the slope of the TC curve
MC
AC
min AC
If AC > MC,
AC must be
falling
If AC < MC,
AC must be
rising
Output
Shifts in Cost Curves

The cost curves are drawn under the
assumption that input prices and the level of
technology are held constant
–
any change in these factors will cause the cost
curves to shift
Short-Run, Long-Run Distinction



In the short run, economic actors have only
limited flexibility in their actions
Assume that the capital input is held constant
at K1 and the firm is free to vary only its labor
input
The production function becomes
q = f(K1,L)
Short-Run Total Costs


Short-run total cost for the firm is
STC = rK1 + wL
There are two types of short-run costs:
–
–
short-run fixed costs (SFC) are costs associated
with fixed inputs
short-run variable costs (SVC) are costs
associated with variable inputs
Short-Run Marginal and Average
Costs

The short-run average total cost (SATC)
function is
SATC = total costs/total output = STC/q

The short-run marginal cost (SMC) function is
SMC = change in STC/change in output = STC/q
Short-Run Average Fixed and
Variable Costs

Short-run average fixed costs (SAFC)
are
SAFC = total fixed costs/total output = SFC/q

Short-run average variable costs are
SAVC = total variable costs/total output = SVC/q
Relationship between Short-Run
and Long-Run Costs
STC (K2)
Total
costs
STC (K1)
TC
The long-run
TC curve can
be derived by
varying the
level of K
STC (K0)
q0
q1
q2
Output
Relationship between Short-Run
and Long-Run Costs
Costs
SMC (K0)
SATC (K0)
MC
AC
SMC (K1)
q0
q1
SATC (K1)
The geometric
relationship
between shortrun and long-run
AC and MC can
also be shown
Output