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8/14/2019 Cost Function.ppt
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Cost Accounting
ofFactor Inputs
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Introduction
In the supply process, households first offer thefactors of production they control to the factormarket.
The factors are then transformed by firms into
goods that consumers want.
Productionis the name given to thattransformation of factors into goods.
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The Role of the Firm
A key concept in production is the firm.
Thefirmis an economic institution that
transformsfactors of production(inputs) into
consumer goods (output, quantity supplied).
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The Role of the Firm
A firm: Organizes factors of production.
Produces goods and/or services.
Sells goods it produces to individuals.
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The Role of the Firm
When the firm only organizesproduction it is
called a virtual firm.
Virtual firmssubcontractout all work.
While most firms are not virtual, more and
more of the organizational structure of businessis being separated from production.
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The Firm and the Market
Whether an activity is organized through the
market depends on transaction costs.
Transaction costscosts of undertaking
trades through the market.
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The Firm and the Market
The various forms that businesses organize
themselves include
sole proprietorships,
partnerships, corporations,
for-profit firm,
nonprofit firms, and
cooperatives.
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Firms That Maximize Profit
Profitis the difference between total revenue and
total cost.
Profit = total revenue total cost
= TR TC
= P*Q (TC/Q)*Q
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Firms Maximize Profit
For an economist, total costis explicit payments to
factors of productionplusthe opportunity cost of the
factors provided by the owners.
Total Costs = accounting costs + opportunity costs. Accounting costs = expenses that appear on the
books.
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Firms Maximize Profit
Total revenueis the amount a firm receives
for selling its good or service plus any increase
in the value of the assets owned by firms.
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Firms Maximize Profit
Economists and accountants measure profit
differently.
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Firms Maximize Profit
For accountants, total revenue is total sales
times price.
Profit is explicit revenue less explicit cost.
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Firms Maximize Profit
For economists, revenue includes any increase or
decrease in the value of any assets the firm owns.
They count implicit costs which include the
opportunity costs of owner-provided factorsof production.
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Firms Maximize Profit
For economists:
Economic profit =
(explicit and implicit revenue)(explicit and implicit cost)
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Output
Diminishingmarginal
returns
Diminishingabsolute
returns
323028
262422201816141210
86420
1 2 3 4 5 6 7 8 9 10
Increasingmarginal
returns
Number of workers
TP
Outputperworker
1 2 3 4 5 6 7 8 9 10Number of workers
7
6
5
4
3
2
1
0
MP
Diminishingmarginal
returns
Diminishingabsolute
returns
(a) Total product (b) Marginal and average product
AP
A Production Function
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For factors hired or employedby a firm:
The costs are (the value of) the highest-
valued alternative use of the money spentin
hir ing them.They are called explicit costsas they
involve a transfer of money.
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For factors ownedby a firm:
The costs of usingthese factors are (the value
of) the highest-valuedalternative uses of the
factors.
They are called implicit costs()
or imputed costs, as they do
not involve a transfer
of money.
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Classif ication of costs of different factor inputs
Sunk cost (historical cost)
The cost of a past act.
As past options are not available at present, sunk costcannot be avoided now. Sunk cost is not a (present or
future) cost.
Bygone is bygone.It should have no effect onanypresent or future decisions.
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Fixed cost
The cost of employing fixed factors.
It does not change with output.
It is a present cost paid for the use of fixed factorsand hence it affects the net receipt.
It has no effect on MC & no effect onthe determination
of the wealth-maximizing output level.
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Variable costThe cost of employing variable factors.
It changes with output.
It is a present cost paid for the use of variable factors
& hence it affects the net receipt.
It affects marginal cost & hence it affects the wealth-maximizing output.
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Q8.6:
A restaurant is making a short run decision for its production
next month. Identify if the following costs are sunk costs (SC),
fixed costs (FC) or variable costs (VC).
(a) Rent of the restaurant under a 2-year contract ( )
(b) Wage payments ( )
(c) Expenditure on meat and vegetables ( )
(d) Water charges ( )
(e) Electricity charges ( )
(f) Acquisition cost of machines ( )
(g) Continuing possession cost of machines ( )
(h) Operating cost of machines ( )
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Cost Function
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Cost function() describes the
relationship between output and cost.
Output
= ???
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Short-run Cost Curves
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Measure of costsOutput changesCost changes
Total cost (TC)
Change in cost can be expressed in three ways:
Marginal cost (MC)
Average cost (AC)
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Total cost
is the whole amount of payments to al l factorsused
in producing a given amount of output (Q), composed of:
Total fixed cost(TFC): is the whole amount ofpayments to f ixed factors.
Totalvariable cost(TVC): is the whole amount ofpayments to variable factors.
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Totalcost
$400
350
300
250
200
150
10050
0
FC
2 4
M
6 8 10 20 30Quantity of earrings
VCTC
L
Total Cost Curves
O
TC = (VC + FC)
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TVC = w xLtotal variable cost:
Formula:
TC = TFC +TVCTotal Cost:
Assume two factors only:
Capital(fixed factor) and labour(variable factor)
Lunits of labour are employed at a wage rate of w.
a constant independent of outputtotal f ixed cost:
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Average cost/average total cost (ATC)
is the cost per unit of output, composed of :
average f ixed cost(AFC):the f ixed costper unit of output.
average variable cost(AVC):
the var iable costper unit of output.
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Formula:
AVCAFCQ
TVCTFC
Q
TCATC
Average Total Cost:
QTFCAFCaverage f ixed cost:
AP
w
L
Q
w
L
QL
Lw
Q
Lw
Q
TVCAVC
average variable cost:
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ATC curve and AVCcurve will come closer and closer as
the amount of output increases (ATC = AFC + AVC and
AFC drops continuously).
AVCcurve is U-
shaped. (AVC =
w/AP and AP is
inverted-U shaped.)
AFCcurve drops
continuously. (AFC
= TFC/Q)
Features:
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The turning point of ATC curve (b)occurs at a larger
output than the turning point of AVC curve (a). Why?
(b)(a)
At (a), the fall in AFC is >the rise in AVC initially
but at (b), the fall in AFC is
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Marginal Cost
is the change in total cost for producing an additional
unit of output, composed of :
The marginal cost curve goes through the minimum
point of the average total cost curve and average variable
cost curve.
Each of these curves is U-shaped.
marginal f ixed cost(MFC): is the change in f ixed costfor producing an additional unit of output
marginal variable cost(MVC): is the change in variable cost
for producing an additional unit of output.
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The law of diminishing marginal productivity sets
in as more and more of a variable input is added
to a fixed input.
Marginal and average productivities fall and marginal costs
rise.
And when average productivity of the variable input falls,
average variable cost rise.
The average total cost curve is the vertical summation of
the average fixed cost curve and the average variable cost
curve, so it is always higher than both of them.
The U Shape of the Average and
Marginal Cost Curves
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Formula:
0
QTFCMFCmarginal f ixed cost:
MVCMFCQ
TVCTFC
Q
TCMC
Marginal cost:
marginal var iable cost:
MP
w
L
Q
w
L
QL
Lw
Q
Lw
Q
TVCMVC
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MCcurve passes through the minimum points of AVCcurve
and ATCcurve.
MC or MVC
curve is
U-shaped
As TFC is a constant, MFC = 0. So MC = MVC.
MC = MVC = w/MP. As MP curve is inverted-U shaped, MC
or MVC curve is U-shaped.
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MC curve(= MVC
curve) =Slope of TC
curve& TVC curve.
Derivation of total cost
curves:
Notice the points
where MC = mini.;
MC = AVCand MC
= ATC.
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Q8.7: The following table is composed of product items and cost
items of a firm. Suppose the unit cost of capital and labour are $10 and
$20 respectively. Fill in the missing columns..
Units
of
capital
Units
of
labour
TP AP MP TFC TVC TC ATC
4
4
4
4
4
4
1
2
3
4
5
6
2
5
10
14
14
12
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Q8.8(a) When output increases, if AP of a variable factor rises,
what will happen to AVC and ATC?
(b) When output increases, if AP of a variable factor falls,
what wi ll happen to AVC and ATC?
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Long-run Cost Curves
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The firm enjoyseconomies of
scaleat the beginning
LRAC & LRMC
As the scale of production
further, the firm suffers
diseconomies of scale
LRAC & LRMC
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The production scale (combination of factors) with
the lowest LRAC.
Optimum scale
LRAC curve with
a horizontal region
U-shaped LRAC curve
Optimum scale
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LRMC = slope of LRTC
Slope
=LRMC
=LRAC
Derivation of total
cost curves:
Notice the points
where LRMC = mini.and LRMC = LRAC.
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The Relationship Between Productivity
and Costs
The shapes of the cost curves are mirror-
image reflections of the shapes of the
corresponding productivity curves.
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The Relationship Between Productivity
and Costs
When one is increasing, the other is decreasing.
When one is at a maximum, the other is at aminimum.
h l h d
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Costsperunit
Productiv
ityofworkersatt
hisoutput
$1816
141210
86
42
0 4 8 12 16 20 24
98
76543
21
0 4 8 12 16 20 24
AVC
MC
Output Output
A
AP ofworkers
MPof workers
The Relationship Between Productivity
and Costs
l i hi i l d
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Relationship Between Marginal and
Average Costs
The marginal cost and average cost curves are
related.
When marginal cost exceeds average cost, average
cost must be rising.
When marginal cost is less than average cost,
average cost must be falling.
R l i hi B M i l d
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Relationship Between Marginal and
Average Costs
This relationship explains why marginal cost
curves always intersect average cost curves at
the minimum of the average cost curve.
R l i hi B M i l d
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Relationship Between Marginal and
Average Costs
The position of the marginal cost relative to
average total cost tells us whether average
total cost is rising or falling.
R l i hi B M i l d
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Relationship Between Marginal and
Average Costs
To summarize:
If MC > ATC, then ATC is rising.
If MC = ATC, then ATC is at its low point.
If MC < ATC, then ATC is falling.
R l ti hi B t M i l d
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Relationship Between Marginal and
Average Costs
Marginal and average total cost reflect a general
relationship that also holds for marginal cost and
average variable cost.
If MC > AVC, then AVC is rising.
If MC = AVC, then AVC is at its low point.If MC < AVC, then AVC is falling.
R l ti hi B t M i l d
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Relationship Between Marginal and
Average Costs
Average total cost will fall when marginal cost
is above average variable cost, so long as
average variable cost does not rise by more
than average fixed cost falls.
R l ti hi B t M i l d
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Relationship Between Marginal and
Average Costs
$90
80
70
6050
4030
2010
0
Quantity of output
Area B
Area A Area CMC
ATC
AVC
1 2 3 4 5 6 7 8 9
Q1
B
AVC
ATC
MCQ0A
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Economies of scalerefer to the property whereby long-run
average total cost falls as the quantity of output increases.
Diseconomies of scalerefer to the property whereby long-runaverage total cost rises as the quantity of output increases.
Constant returns to scalerefers to the property whereby long-run
average total cost stays the same as the quantity of output
increases.
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The goal of firms is to maximize profit, which
equals total revenue minus total cost.
When analyzing a firms behavior, it is
important to include all the opportunity costs
of production.
Some opportunity costs are explicit while
other opportunity costs are implicit.
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A firms costs reflect its production process.
A typical firms production function gets flatter as
the quantity of input increases, displaying the
property of diminishing marginal product. A firms total costs are divided between fixed and
variable costs. Fixed costs do not change when the
firm alters the quantity of output produced;
variable costs do change as the firm alters
quantity of output produced.
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Average total cost is total cost divided by thequantity of output.
Marginal cost is the amount by which total
cost would rise if output were increased byone unit.
The marginal cost always rises with thequantity of output.
Average cost first falls as output increases andthen rises.
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The average-total-cost curve is U-shaped.
The marginal-cost curve always crosses the
average-total-cost curve at the minimum of
ATC.
A firms costs often depend on the time
horizon being considered.
In particular, many costs are fixed in the short
run but variable in the long run.