Transcript The Cost Side of The Market - Ka

Perfectly Competitive Supply:
The Cost Side of The Market
Ka-fu Wong
University of Hong Kong
1
Example 6.1. How should Leroy divide
his time between…
…picking apples…
…and writing pulp fiction?
Note: Pulp magazines (or pulp fiction; often referred to as “the pulps”) were inexpensive fiction
magazines. They were widely published from the 1920s through the 1950s. The term pulp fiction can
also refer to mass market paperbacks since the 1950s. (from Wikipedia)
2
Example 6.1. How should Leroy divide
his time between…
 A men's magazine will pay Leroy 10 cents per word to write fiction
articles.
 He must decide how to divide his time between writing fiction,
which he can do at a constant rate of 200 words per hour, and
harvesting apples from the trees growing on his land, a task only
he can perform.
 His return from harvesting apples depends on both the price of
apples and the quantity of apples he harvests.
 For each hour Leroy spends picking apples, he loses the $20 he
could have earned writing pulp fiction.
 He should thus spend an additional hour picking as long as he will
add at least $20 worth of apples to his total harvest.
3
Example 6.1. How should Leroy divide
his time between…
 Earnings aside, Leroy is indifferent between the two
tasks.
 The amount of apples he can harvest depends on the
number of hours he devotes to this activity:
Hours
Total bushels
Additional bushels
1
8
8
2
12
4
3
15
3
4
17
2
5
18
1
4
Example 6.1. How should Leroy divide
his time between…
 For example, if apples sell for $2.50 per bushel:
Hours
Total bushels
Additional bushels
$ for the additional hour
1
8
8
20 = 8x2.5
2
12
4
10 = 4x2.5
3
15
3
7.5 = 3x2.5
4
17
2
5 = 2x2.5
5
18
1
2.5 = 1x2.5
 Leroy would earn $20 for the first hour he spent picking apples, but
would earn only an additional $10 if he spent a second hour.
 Leroy will devote only the first hour to picking apples. That is, a
total of 8 apples.
5
Example 6.1. How should Leroy divide
his time between…
 If the price of apples then rose to $5 per bushel:
Hours
Total bushels
Additional bushels
$ for the additional hour
1
8
8
40 = 8x5
2
12
4
20 = 4x5
3
15
3
15 = 3x5
4
17
2
10 = 2x5
5
18
1
5 = 1x5
 It would pay Leroy to devote a second hour to picking, which would
mean a total of 12 bushels of apples.
6
Example 6.1. How should Leroy divide
his time between…
 Once the price of apples reached $6.67 per bushel
Hours
Total bushels
Additional bushels
$ for the additional hour
1
8
8
53.36 = 8x6.67
2
12
4
26.68 = 4x6.67
3
15
3
20.00 = 3x6.67
4
17
2
13.34 = 2x6.67
5
18
1
6.67 = 1x6.67
 Leroy would devote a third hour to picking apples, for a total of 15
bushels.
7
Example 6.1. How should Leroy divide
his time between…
 If the price rose to $10 per bushel
Hours
Total bushels
Additional bushels
$ for the additional hour
1
8
8
80 = 8x10
2
12
4
40 = 4x10
3
15
3
30 = 3x10
4
17
2
20 = 2x10
5
18
1
10 = 1x10
 Leroy would devote a fourth hour to picking apples, for a total of 17
bushels.
8
Example 6.1. How should Leroy divide
his time between…
 If the price rose to $20 per bushel
Hours
Total bushels
Additional bushels
$ for the additional hour
1
8
8
160 = 8x20
2
12
4
80 = 4x20
3
15
3
60 = 3x20
4
17
2
40 = 2x20
5
18
1
20 = 1x20
 Leroy would devote a fifth hour to picking apples, for a total of 18
bushels.
9
Example 6.1. How should Leroy divide
his time between…
Leroy's individual supply curve for apples relates the amount
of apples he is willing to supply at various prices.
P ($/bu)
Leroy's supply curve
for apples
20.00
10.00
6.67
5.00
2.50
8
12 15
18
17
Q (bu/day)
10
Example 6.1. How should Leroy divide
his time between…
 Marginal cost can be computed:
Hours
Total
bushels
Additional
bushels
Marginal cost
(of an additional bushel)
1
8
8
$2.5=$20/8
2
12
4
5=20/4
3
15
3
6.67=20/3
4
17
2
10=20/2
5
18
1
20=20/1
The perfectly competitive firm’s supply curve is its marginal cost curve.
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Market Supply
 The quantity that corresponds to any given price on the
market supply curve is the sum of the quantities
supplied at that price by all individual sellers in the
market.
12
Example 6.2.
 If the supply side of the apple market consisted of 100 suppliers
just like Leroy, what would the market supply curve for apples look
like?
P ($/bu)
Market supply curve
for apples
20.00
10.00
6.67
5.00
2.50
8
12 15
18
17
Q (100s of bu/day)
13
Reasons for upward sloping supply
1. The Fruit Picker's Rule (Always pick the low-hanging fruit first).
 When fruit prices are low, it might pay to harvest the lowhanging fruit but not the fruit growing higher up the tree,
which takes more effort to get to.
 But if fruit prices rise sufficiently, it will pay to harvest not only
the low-hanging fruit, but also the fruit on higher branches.
2. Differences among suppliers in opportunity cost
 People facing unattractive employment opportunities in other
occupations may be willing to pick apples even when the price
of apples is low.
 Those with more attractive options will pick apples only if the
price of apples is relatively high.
14
Supply and opportunity cost
At what price would Andy Lau consider it
worth his while to pick apples?
15
Profit-Maximizing Firms and Perfectly
Competitive Markets
 Definition. The profit earned by a firm is the total
revenue it receives from the sale of its product minus all
costs—explicit and implicit—incurred in producing it.
 Definition. A profit-maximizing firm is one whose
primary goal is to maximize the difference between its
total revenues and total costs.
 Definition. A perfectly competitive market is one
in which no individual supplier has significant influence
on the market price of the product.
16
Profit-Maximizing Firms and Perfectly
Competitive Markets
 Definition. A price taker is a firm that has no
influence over the price at which it sells its product.
Laundry
Art reproduction
17
Price setters
Microsoft operating systems
Intel microprocessors
18
Price setter vs. price taker
Generic USB MP3 player:
price taker
Apple iPod: Price setter
19
Factor of production
 Definition. A factor of production is an input used
in the production of a good or service.
20
Fixed factor of production
 Definition. A fixed factor of production is an input
whose quantity cannot be altered in the short run.
Example: Transmission tower
for a student radio station.
21
Variable factor of production
 Definition. A variable factor of production is an
input whose quantity can be altered in the short run.
Example: Music library
for a student radio station.
22
Example 6.3. Louisville Slugger uses two inputs:
labor (e.g., woodworkers)…
and
capital (e.g., lathes, tools, buildings)
A lathe is a tool which spins a block of material to perform
various operations such as cutting, sanding, knurling, or
deformation with tools that are applied to the workpiece to
create an object which has symmetry about an axis of
rotation.
… to transform raw materials (e.g., lumber)
…into finished output (baseball bats).
23
The short-run production function
Total number of
Total number
employees per day of bats per day
0
0
1
40
2
100
3
130
4
150
5
165
6
175
7
181
Note that output gains begin
to diminish with the third
employee.
Economists refer to this
pattern as the law of
diminishing returns,
and it always refers to
situations in which at least
some factors of production
are fixed.
24
Some Important Cost Concepts
 Suppose the lease payment for the Louisville Slugger’s
lathe and factory is $80 per day.
 This payment is both a fixed cost (since it does not
depend on the number of bats per day the firm makes)
and, for the duration of the lease, a sunk cost.
FC = rK
25
Some Important Cost Concepts
 The company’s payment to its employees is called
variable cost, because unlike fixed cost, it varies with
the number of bats the company produces.
VC = wL
26
Some Important Cost Concepts
 The firm’s total cost is the sum of its fixed and variable
costs:
Total cost = Fixed Cost + Variable Cost
TC = FC + VC
TC = rK + wL
27
Some Important Cost Concepts
 The firm’s marginal cost is the change in total cost
divided by the corresponding change in output.
MC = DTC/DQ
MC = DVC/DQ
28
Example 6.4.
 If Louisville slugger pays a fixed cost of $80 per day,
and to each employee a wage of $24/day, calculate the
company’s output, variable cost, total cost and marginal
cost for each level of employment.
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Example 6.4.
Employees
per day
Bats per
day
Fixed Cost
Variable
($ per day) Cost ($/day)
Total Cost
($/day)
Marginal
Cost ($/bat)
0
0
80
0
80
1
40
80
24
104
0.6
2
100
80
48
128
0.4
3
130
80
72
152
0.8
4
150
80
96
176
1.2
5
165
80
120
200
1.6
6
175
80
144
224
2.4
7
181
80
168
248
4.0
30
Choosing Output to Maximize Profit
 If a company’s goal is to maximize its profit, it should
continue to expand its output as long as the marginal
benefit from expanding is at least as great as the
marginal cost.
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Example 6.5.
 Suppose the wholesale price of each bat (net of lumber
and other materials costs) is $2.50.
 How many bats should Louisville Slugger produce?
32
Example 6.5.
 If we compare this marginal benefit ($2.50 per bat) with the marginal
cost entries shown in table, we see that the firm should keep
expanding until it reaches 175 bats per day (6 employees per day).
Employees
per day
Bats per day
Fixed Cost
($ per day)
Variable
Cost ($/day)
Total Cost
($/day)
Marginal
Cost ($/bat)
0
0
80
0
80
1
40
80
24
104
0.6
2
100
80
48
128
0.4
3
130
80
72
152
0.8
4
150
80
96
176
1.2
5
165
80
120
200
1.6
6
175
80
144
224
2.4
7
181
80
168
248
4.0
33
Example 6.5.
 To confirm that the cost-benefit principle thus applied identifies
the profit-maximizing number of bottles to produce, we can
calculate profit levels directly:
Employees per
day
Output
(bats/day)
Total revenue
($/day)
Total cost
($/day)
Profit
($/day)
0
0
0
80
-80
1
40
100
104
-4
2
100
250
128
122
3
130
325
152
173
4
150
375
176
199
5
165
412.50
200
212.50
6
175
437.50
224
213.50
7
181
452.50
248
204.50
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Choosing Output to Maximize Profit
 When the law of diminishing returns applies (that is,
when some factors of production are fixed), marginal
cost goes up as the firm expands production beyond
some point.
 Under these circumstances, the firm's best option is to
keep expanding output as long as marginal cost is less
than price.
 The profit maximizing output level for the perfectly
competitive firm:
P = MC
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Note on Example 6.5.
 Note in Example 6.5 that if the company's fixed cost had been
any more than $293.50 per day (say, 300), it would have made a
loss at every possible level of output.
Employees per
day
Output
(bats/day)
Total revenue
($/day)
Total cost
($/day)
Profit
($/day)
0
0
0
300
-300
1
40
100
324
-224
2
100
250
348
-98
3
130
325
372
-47
4
150
375
396
-21
5
165
412.50
420
-7.5
6
175
437.50
444
-6.5
7
181
452.50
468
-15.6
36
Note on Example 6.5.
 As long as it still had to pay its fixed cost, however, its
best bet would have been to continue producing 175
bats per day, because a smaller loss is better than a
larger one.
 If a firm in that situation expected conditions to remain
the same, it would want to get out of the bat business
as soon as its equipment lease expired.
37
A Note on the Firm’s Shut-Down Condition
 It might seem that a firm that can sell as much output
as it wishes at a constant market price would always do
best in the short run by producing and selling the
output level for which price equals marginal cost.
 But there are exceptions to this rule.
38
A Note on the Firm’s Shut-Down Condition
 Suppose, for example, that the market price of the
firm’s product falls so low that its revenue from sales is
smaller than its variable cost at all possible levels of
output.
 The firm should then cease production for the time
being.
 By shutting down, it will suffer a loss equal to its
fixed costs.
 But by remaining open, it would suffer an even larger
loss.
39
A Note on the Firm’s Shut-Down Condition
 P = market price of the product
 Q = number of units produced and sold
 PxQ = total revenue from sales
Shutdown rule:
 Cease production if PxQ is less than VC for every
level of Q.
40
Average Variable Cost and Average Total Cost
 Suppose that the firm is unable to cover its variable cost
at any level of output—that is, suppose that PxQ < VC
for all levels of Q.
 Then P < VC/Q for all levels of Q, since we obtain the
second inequality by simply dividing both sides of the
first one by Q.
 The firm’s short-run shut-down condition may thus be
restated a second way:
 Discontinue operations in the short run if the product
price is less than the minimum value of its average
variable cost (AVC).
41
Short-run shut-down condition (alternate
version):
P < minimum value of AVC
42
Profitability
Average total cost:
ATC = TC/Q.
Profit = total revenue – total cost
= PxQ – ATCxQ
= (P – ATC) Q
A firm can be profitable only if the price of its product
price (P) exceeds its ATC.
43
A Graphical Approach to Profit-Maximization
 For Louisville Slugger, we have
Avg
Variable
Cost
($/day)
Total
Cost
($/day)
Employe
es per
day
Bats per
day
Variable
Cost
($/day)
Avg Total Marginal
Cost
Cost
($/bat)
($/bat)
0
0
0
0
80
1
40
24
0.6
104
2.6
0.6
2
100
48
0.48
128
1.28
0.4
3
130
72
0.554
152
1.169
0.8
4
150
96
0.64
176
1.173
1.2
5
165
120
0.727
200
1.21
1.6
6
175
144
0.823
224
1.28
2.4
7
181
168
0.927
248
1.37
4.0
44
A Graphical Approach to Profit-Maximization
Properties of the cost curves:
 The upward sloping portion
of the marginal cost curve
(MC) corresponds to the
region of diminishing returns.
 The marginal cost curve
must intersect both the
average variable cost curve
(AVC) and the average total
cost curve (ATC) at their
respective minimum points.
45
Price = Marginal Cost: The Maximum-Profit
Condition
 In earlier examples, we implicitly assumed that the firm
could employ workers only in whole number amounts.
 Under these conditions, we saw that the profitmaximizing output level was one for which marginal
cost was somewhat less than price (because adding yet
another employee would have pushed marginal cost
higher than price).
 But when output and employment can be varied
continuously, the maximum-profit condition is that price
be equal to marginal cost.
46
Example 6.6.
 For the bat-maker whose cost curves are shown in the
next slide, find the profit-maximizing output level if bats
sell for $0.80 each.
 How much profit will this firm earn?
 What is the lowest price at which this firm would
continue to operate in the short run?
47
Example 6.6.
 The cost-benefit
principle tells us that
MC
this firm should
ATC
continue to expand as
AVC
long as price is at least
as great as marginal
cost.
Price
 If the firm follows this
rule it will produce 130
bats per day, the
quantity at which price
and marginal cost are
equal.
$/bat
1.40
1.32
1.20
1.00
0.80
0.60
0.48
0.40
0.28
80 100
130
150
Bats/day
48
Example 6.6.
$/bat
1.40
1.32
1.20
1.00
MB 0.80
0.60
0.48
MC 0.40
0.28
 Suppose that the firm
had sold some amount
MC
less than 130—say, only
ATC
100 bats per day.
AVC
 Its benefit from
expanding output by
one bat would then be
Price
the bat's market price,
80 cents.
 The cost of expanding
output by one bat is
equal (by definition) to
the firm’s marginal cost,
Bats/day
80 100 130
which at 100 bats per
150
day is only 40 cents.
49
Example 6.6.
$/bat
1.40
1.32
1.20
1.00
MB 0.80
0.60
0.48
MC 0.40
0.28
 So by selling the 101st
bat for 80 cents and
MC
producing it for an extra
ATC
cost of only 40 cents,
AVC
the firm will increase its
profit by 80 – 40 = 40
cents per day.
Price
 In a similar way, we can
show that for any
quantity less than the
level at which price
equals marginal cost,
the seller can boost
Bats/day
80 100 130
profit by expanding
150
production.
50
Example 6.6.
$/bat
1.40
MC 1.32
1.20
1.00
MB 0.80
0.60
0.48
0.40
0.28
 Conversely, suppose that
the firm were currently
MC
selling more than 130
ATC
bats per day—say, 150—
AVC
at a price of 80 cents
each.
 Marginal cost at an output
Price
of 150 is 1.32 per bat. If
the firm then contracted
its output by one bat per
day, it would cut its costs
by 1.32 cents while losing
only 80 cents in revenue.
Bats/day
80 100 130
As a result, its profit
150
would grow by 52 cents
per day.
51
Example 6.6.
 The same arguments can be made regarding any
quantities that differ from 130.
 Thus, if the firm were selling fewer than 130 bats per
day, it could earn more profit by expanding; and that if
it were selling more than 130, it could earn more by
contracting.
 So at a market price of 80 cents per bat, the seller
maximizes its profit by selling 130 units per week, the
quantity for which price and marginal cost are exactly
the same.
52
Example 6.6.
Total revenue = PxQ
= ($0.80/bat)x(130 bats/day)
= $104 per day.
Total cost = ATCxQ
= $0.48/bat x 130 bats/day
= $62.40/day
So the firm’s profit is $41.60/day.
53
Example 6.6.
 Profit is equal to (P – ATC)xQ, which is equal to the
area of the shaded rectangle.
MC
$/bat
ATC
AVC
0.80
Price
Profit = $41.60/day
0.48
130
Bats/day
54
Example: The Holiday Store at Tung Lung Island
Why does the store open only on holidays?
55
SUPPLY AND PRODUCER SURPLUS
 The economic surplus received by a buyer is called consumer
surplus.
 The analogous construct for a seller is producer surplus, the
difference between the price a seller actually receives for the
product and the lowest price for which she would have been willing
to sell it (her reservation price, which in general will be her
marginal cost).
 Producer surplus sometimes refers to the surplus received by a
single seller in a transaction, sometimes to the total surplus
received by all sellers in a market or collection of markets.
56
Example 6.7. Calculating Producer Surplus
 How much do sellers benefit from their participation in
the market for cashews?
Price
($/lb)
12
10
8
6
4
2
0 2 4 6 8
S
D
Quantity
12 16 20 24
(1000s of
lbs/day)
57
Example 6.7. Calculating Producer Surplus
 For all cashews sold up to 8,000 pounds per day, sellers receive a
surplus equal to the difference between the market price of $8 per
pound and their reservation price as given by the supply curve.
 Total producer surplus received by buyers in the cashew market is
the area of the shaded triangle between the supply curve and the
market price
Price
($/lb)
12
10
8
6
4
2
0 2 4 6 8
S
PS= (1/2)(8,000 lbs/day)x($8/lb) = $32,000/day
D
12 16 20 24
Quantity
(1000s of
lbs/day)
58
Producer surplus
 Producer surplus is the highest price sellers would pay,
in the aggregate, for the right to continue participating
in the cashew market.
59
Supply is all about marginal cost.
60
Does demand ever affect supply?
P
S
D
Q
61
Example 6.8.
 Is the cost of a ticket to the
NBA finals so high because the
salaries of NBA players (such
as YAO Ming) is so high?
62
Example 6.8.
 Partly. But then why are the wages of NBA players so
high?
 Because so many people are willing to pay so much to
be able to watch them.
63
Example 6.8.
 But a starving person would be willing to pay even
more for food than for watching an NBA game.
 Food is cheap and NBA games are expensive because
many people can produce food, but only few have the
skills to play in the NBA.
64
Shaquille O’Neal: NBA star extraordinaire.
Earnings from
basketball-related
activities during
last championship
season:
$25,000,000.
65
Does demand ever affect supply?
 Supply depends on costs and costs always depend on
demand.
 In many (perhaps most) cases the prices of the inputs
required to produce a product will not be much
affected by the demand for that product.
66
Does demand ever affect supply?
 The demand for bicycles will have no significant effect on the price
of steel, an input for making bicycles, because the steel used in
making bicycles is only a tiny fraction of the total amount of steel
sold.
67
Does demand ever affect supply?
 So for most markets, we can assume that a shift in the
demand curve will not lead to a shift in the supply curve.
 Assume this independence, unless otherwise stated.
68
End
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