Perfectly Competitive Supply: The Cost Side of The Market

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Perfectly Competitive Supply The Cost Side of
The Market
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This chapter aims at explaining

• Based on opportunity cost, how would an
  individual allocate his time in different jobs?
• What constitutes the upward sloping Supply Curve?
• How would firms make a production decision under
  a perfectly competitive market?
• How does producer surplus explain the social
  optimal production level?

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Example 6.1. How should Leroy divide his time
between
picking apples
and working in McDonalds?
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Example 6.1. How should Leroy divide his time
between

• McDonalds paying Leroy 20/hour
• He must decide how to divide his time between
  working in the McDonalds, and harvesting apples
  from the trees growing on his land, a task only
  he can perform.

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Example 6.1. How should Leroy divide his time
between

• 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 working in the
  McDonalds.
• 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, both jobs bring equal benefit to
  Leroy.
• The amount of apples he can harvest depends on
  the number of hours he devotes to this activity

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Example 6.1. How should Leroy divide his time
between

• For example, if apples sell for 2.50 per bushel

• Leroy will devote only the first hour to picking
  apples. That is, a total of 8 apples.
• As opportunity cost of picking apples is 20/hour.

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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

• Leroy will devote 2 hours in picking apples.
  That is, a total of 12 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

• Leroy would devote 3 hours in 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

• Leroy would devote 4 hours in 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

• Leroy would devote 5 hours in 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 of apple production can be
  computed

The perfectly competitive firms supply curve is
its marginal cost curve. (to be explained later)
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The Market Supply Curve

• 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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Adding individual supply curves

• If the market consists of 100 suppliers just like
  Leroy, what would be the market supply curve for
  apples?

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Why upward sloping Supply Curves?

• The Fruit Picker's Rule (An analogy 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.
• i.e. people exploits his/her most attractive
  opportunities first. (ref e.g. 6.1)

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Why upward sloping Supply Curves?

• 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.

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Profit-Maximizing Firms

• 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 profit.

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Perfectly Competitive Markets

• Definition. A perfectly competitive market is
  one in which no individual supplier has
  significant influence on the market price of the
  product.
• i.e. each supplier takes the market price as
  given.
• implication to sell an additional unit, the
  extra revenue always equal to the given market
  price.
• i.e. Marginal Revenue Market Price
• We call these suppliers price takers

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Profit-Maximizing Firms and price takers

• Definition. A price taker is a firm that has no
  influence over the price at which it sells its
  product.
• note it is hard to find an example in reality, a
  close one would be

Stock exchange firms
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On the contrary Price setters
Intel microprocessors
Microsoft operating systems
We will discuss Price setters in later chapters.
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Profit-Maximizing Firms in Perfectly Competitive
Markets

• The Characteristics of Perfect Competition
• All firms sell the same standardized/ homogeneous
  product.
• The market has many buyers and sellers, each of
  which buys or sells only a small fraction of the
  total quantity exchanged.
• Productive resources are mobile
• Buyers and sellers are well informed.

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The Demand Curve Facing a Perfectly Competitive
Firm/ Price Taker
Market supply and demand
Price (/unit)
1. The market determines the equilibrium price
Market Quantity (units/month)
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The Demand Curve Facing a Perfectly Competitive
Firm
Individual firm demand
Price (/unit)
Individual Firms Quantity (units/month)
2. Each price taking firm will take this market
price as given sell as many units as it wishes
constant Marginal Revenue line/ constant demand
for its product
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Cost-Benefit Analysis

• Thus, with marginal revenue line defined, we have
  obtained the benefit data in this analysis.
• Next, lets take a look at the production cost
  data.
• Remember, our aim is to define both Cost and
  Benefit data in analyzing the optimal production
  plan for a price-taking firm.

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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 expense will not vary with the
  production level.
• It cannot be altered in the short run.

Example Transmission tower for TV broadcast.
Short Run a production period where both fixed
factors and variable factors of production will
be included.
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Variable factor of production

• Definition. A variable factor of production is an
  input whose expenses will increase with the
  production level.
• It can be altered in the short run.

Example Music library for the TV station.
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Example 6.2. tennis racket production

• Suppose in producing tennis rackets, Company A
  uses two factors of production
• Labour (variable factor) ANDCapital (fixed
  factor)

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The short-run production
Observation marginal output begins to diminish
with the third employee. ? economists refer
this situation to be the Law of Diminishing
Returns
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Law of Diminishing Returns

• It says that when some factors of production are
  fixed, increased production of the good
  eventually requires ever-larger increases in the
  variable factor

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Some Important Cost Concepts

• Suppose the lease payment for Company As factory
  is 80 per day.
• Note the factory is a Fixed Factor of
  production.
• This lease is both a fixed cost (since it does
  not depend on the number of rackets produced per
  day) and, for the passed duration of the lease, a
  sunk cost.
• Fixed Cost (FC) lease payment

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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 rackets the company
  produces.
• Variable Cost (VC) wage X units of labour

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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

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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
• Why is fixed cost absent in calculating marginal
  costs?

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Example 6.2. tennis racket production

• If Company A pays a fixed cost of 80 per day,
  and to each employee a wage of 24/day,
  calculate the companys variable cost, total cost
  and marginal cost for each level of employment.

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Example 6.2. tennis racket production
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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.
• Recall Benefit data is represented by the
  constant marginal revenue line for a price-taking
  firm.
• We should compare this data to the marginal cost
  of production.

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Choosing a profit-maximizing output plan

• Suppose the wholesale price of each racket (net
  of materials costs) is 2.50.
• How many rackets should Company A produce?

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Choosing a profit-maximizing output plan

• If we compare this marginal revenue (2.50 per
  racket) with the marginal cost entries shown in
  table, we see that the firm should keep producing
  until it reaches 175 rackets per day.

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Choosing a profit-maximizing output plan

• Lets calculate the respective profit level and
  see if the former case really results in the
  profit-maximizing output.

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Choosing a profit-maximizing output plan
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Choosing Output to Maximize Profit

• When the law of diminishing returns applies
  (i.e., 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 producing output as long as marginal
  cost is less than price (marginal revenue).

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Choosing Output to Maximize Profit

• The profit maximizing output level for the
  perfectly competitive firm
• P MC

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e.g. 6.3 How fixed cost affect production level?

• if the company's fixed cost is more than 293.50
  per day (say, 300), Company A would have made a
  loss at every possible level of output.

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e.g. 6.3 How fixed cost affect production level?

• As long as it still has to pay its fixed cost,
  however, its best bet would have been to continue
  producing 175 rackets per day (by PMC), because
  a smaller loss (6.5) is better than a larger one
  (300).
• If a firm in that situation expects conditions to
  remain the same, it would want to get out of its
  business as soon as its fixed factors expires.

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Short-Run Shut-Down Condition

• It might seem that a price-taking firm 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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Short-Run 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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Short-Run Shut-Down Condition

• If 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 (total) VC
  for every level of Q.

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Short-Run Shut-Down Condition Average
interpretation

• 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
In e.g. 6.2, we have
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Example 6.2 A Graphical Approach to
Profit-Maximization
Properties of the cost curves
/racket

• 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.

/racket
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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).

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Price Marginal Cost The Maximum-Profit
Condition

• But when output and employment can be varied
  continuously, the profit-max condition is that
  price be equal to marginal cost.
• i.e. PMC for continuous functions.

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Example 6.4

• For the tennis racket maker whose cost curves are
  shown in the next slide, find the
  profit-maximizing output level if rackets 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 6.4

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

unit
unit
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Example 6.4

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

unit
MB
MC
unit
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Example 6.4

• So by selling the 101st racket 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.

unit
MB
MC
unit
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Example 6.4

• Conversely, suppose that the firm were currently
  selling more than 130 racket per daysay, 150at
  a price of 80 cents each.
• Marginal cost at an output of 150 is 1.32 per
  racket. If the firm then reduces its output by
  one racket 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.

unit
MC
MB
unit
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Example 6.4

• Thus, if the firm were selling fewer than 130
  rackets per day, it could earn more profit by
  expanding productions and that if it were
  selling more than 130, it could earn more by
  reducing production.
• 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 6.4

• Total revenue PxQ
• (0.80/racket)x(130 racket/day)
• 104 per day.
• Total cost ATCxQ
• 0.48/racket x 130 racket/day
• 62.40/day
• So the firms profit is 41.60/day.

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Example 6.4

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

unit
unit
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Producer Surplus socially optimal output

• So far our discussion limits on individual
  price-taking firms production decision.
• Now, lets evaluate how would a perfectly
  competitive market (that includes ALL
  price-taking firms) bring forth the optimal
  output level for the society.

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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 6.5 Calculating Producer Surplus

• How much is the producer surplus in this market?

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Example 6.5 Calculating Producer Surplus

• producer surplus equals 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 sellers in
  this market is the area of the shaded triangle
  between the supply curve and the market price

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

• Producer surplus is the maximum amount sellers
  are willing to pay for the right to continue
  participating in the market.

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Producer surplus

• Note Producer Surplus does NOT equal to
  Profit!!!
• Producer Surplus difference between price and
  marginal cost of every unit
• Profit difference between total revenue and
  total cost!

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End of Chapter