Ka-fu Wong University of Hong Kong

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Ka-fu WongUniversity of Hong Kong
Perfectly Competitive Supply The Cost Side of
The Market
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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)
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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.

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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
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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
1 8 8
2 12 4
3 15 3
4 17 2
5 18 1
for the additional hour
20 8x2.5
10 4x2.5
7.5 3x2.5
5 2x2.5
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.

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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
1 8 8
2 12 4
3 15 3
4 17 2
5 18 1
for the additional hour
40 8x5
20 4x5
15 3x5
10 2x5
5 1x5

• It would pay Leroy to devote a second hour to
  picking, which would mean a total of 12 bushels
  of apples.

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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
1 8 8
2 12 4
3 15 3
4 17 2
5 18 1
for the additional hour
53.36 8x6.67
26.68 4x6.67
20.00 3x6.67
13.34 2x6.67
6.67 1x6.67

• Leroy would devote a third hour to picking
  apples, for a total of 15 bushels.

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Example 6.1. How should Leroy divide his time
between

• If the price rose to 10 per bushel

Hours Total bushels Additional bushels
1 8 8
2 12 4
3 15 3
4 17 2
5 18 1
for the additional hour
80 8x10
40 4x10
30 3x10
20 2x10
10 1x10

• Leroy would devote a fourth hour to picking
  apples, for a total of 17 bushels.

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Example 6.1. How should Leroy divide his time
between

• If the price rose to 20 per bushel

Hours Total bushels Additional bushels
1 8 8
2 12 4
3 15 3
4 17 2
5 18 1
for the additional hour
160 8x20
80 4x20
60 3x20
40 2x20
20 1x20

• Leroy would devote a fifth hour to picking
  apples, for a total of 18 bushels.

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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.
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Example 6.1. How should Leroy divide his time
between

• Marginal cost can be computed

Hours Total bushels Additional bushels
1 8 8
2 12 4
3 15 3
4 17 2
5 18 1
Marginal cost (of an additional bushel)
2.520/8
520/4
6.6720/3
1020/2
2020/1
The perfectly competitive firms 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.

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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?

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Reasons for upward sloping supply

• The Fruit Picker's Rule (Always pick the
  low-hanging fruit first).
• When fruit prices are low, it might pay to
  harvest the low-hanging 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.
• 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.

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Supply and opportunity cost
At what price would Andy Lau consider it worth
his while to pick apples?
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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 costsexplicit and
  implicitincurred 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.

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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
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Price setters
Intel microprocessors
Microsoft operating systems
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Price setter vs. price taker
Apple iPod Price setter
Generic USB MP3 player price taker
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Factor of production

• Definition. A factor of production is an input
  used in the production of a good or service.

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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.
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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.
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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).
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The short-run production function
Total number of employees per day Total number 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.
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Some Important Cost Concepts

• Suppose the lease payment for the Louisville
  Sluggers 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

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Some Important Cost Concepts

• The companys payment to its employees is called
  variable cost, because unlike fixed cost, it
  varies with the number of bats the company
  produces.
• VC wL

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Some Important Cost Concepts

• The firms total cost is the sum of its fixed and
  variable costs
• Total cost Fixed Cost Variable Cost
• TC FC VC
• TC rK wL

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Some Important Cost Concepts

• The firms marginal cost is the change in total
  cost divided by the corresponding change in
  output.
• MC DTC/DQ
• MC DVC/DQ

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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 companys 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 ( 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
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Choosing Output to Maximize Profit

• If a companys 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?

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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
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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
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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.

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A Note on the Firms 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.

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A Note on the Firms Shut-Down Condition

• Suppose, for example, that the market price of
  the firms 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.

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A Note on the Firms 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.

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Average Variable Cost and Average Total Cost

• Suppose that the firm is unable to cover its
  variable cost at any level of outputthat is,
  suppose that PxQ lt VC for all levels of Q.
• Then P lt 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 firms 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).

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Short-run shut-down condition (alternate version)

• P lt minimum value of AVC

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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.

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A Graphical Approach to Profit-Maximization

• For Louisville Slugger, we have

Employees per day Bats per day Variable Cost (/day) Avg Variable Cost (/day) Total Cost (/day) Avg Total Cost (/bat) Marginal Cost (/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
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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.

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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
  profit-maximizing 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.

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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?

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Example 6.6.

• The cost-benefit principle tells us that this
  firm should continue to expand as long as price
  is at least as great as marginal cost.
• If the firm follows this rule it will produce 130
  bats per day, the quantity at which price and
  marginal cost are equal.

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Example 6.6.

• Suppose that the firm had sold some amount less
  than 130say, only 100 bats per day.
• Its benefit from expanding output by one bat
  would then be the bat's market price, 80 cents.
• The cost of expanding output by one bat is equal
  (by definition) to the firms marginal cost,
  which at 100 bats per day is only 40 cents.

MB
MC
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Example 6.6.

• So by selling the 101st bat for 80 cents and
  producing it for an extra cost of only 40 cents,
  the firm will increase its profit by 80 40 40
  cents per day.
• 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 profit
  by expanding production.

MB
MC
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Example 6.6.

• Conversely, suppose that the firm were currently
  selling more than 130 bats per daysay, 150at a
  price of 80 cents each.
• Marginal cost at an output 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. As
  a result, its profit would grow by 52 cents per
  day.

MC
MB
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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.

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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 firms profit is 41.60/day.

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Example 6.6.

• Profit is equal to (P ATC)xQ, which is equal to
  the area of the shaded rectangle.

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Example The Holiday Store at Tung Lung Island
Why does the store open only on holidays?
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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.

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Example 6.7. Calculating Producer Surplus

• How much do sellers benefit from their
  participation in the market for cashews?

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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

PS (1/2)(8,000 lbs/day)x(8/lb) 32,000/day
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Producer surplus

• Producer surplus is the highest price sellers
  would pay, in the aggregate, for the right to
  continue participating in the cashew market.

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Supply is all about marginal cost.
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Does demand ever affect supply?
P
S
D
Q
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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?

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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.

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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.

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Shaquille ONeal NBA star extraordinaire.
Earnings from basketball-related activities
during last championship season 25,000,000.
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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.

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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.

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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.

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End