Market Structures Competitive Markets

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Topic 4 Part I
Market Structures Competitive Markets
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Competitive Firm

• A competitive firm is one that takes the market
  price of output as being given and outside of its
  control

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Competitive Firm

• In principle, a competitive firm is free to set
  whatever price it wants and produce whatever
  quantity it is able to produce

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Competitive Firm

• However,
• If it sets a price above the market price, no one
  will purchase its product
• If it sets a price below the market price, it
  will have as many customers as it wants but it
  will forego profits unnecessarily because it can
  also gets as many customers as it wants by
  pricing at the market price
• Then, the firm has incentives to adopt the market
  price

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Profit Maximization

• Remember, that because profit maximization
  requires cost minimization,
• max pf(x) - w x
• x ? Rn
• is equivalent to max py - c(w, y),
• y ? 0
• where c(w, y) is the cost function we obtain
  from the cost-minimization problem

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Profit Maximization

• Assume w fixed. From max py - c(y),
• y ? 0
• the optimal y satisfies the FOC
• p c'(y) 0,
• i.e., y is chosen s.t. p c'(y) MC
• the second order condition requires c''(y) ? 0
  (i.e., non-decreasing MC)

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Inverse Supply Function

• The inverse supply function denoted by p(y)
  measures the price that must prevail in order for
  a firm to find it profitable to supply a given
  amount of output
• According to the FOC and SOC, the inverse supply
  function is given by p(y) c'(y) as long as
  c''(y) ? 0 (i.e., non-decreasing MC)

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Supply Function

• The supply function y(p) gives the
  profit-maximizing output at each price.
  Therefore, the supply function must satisfy the
  FOC and SOC
• p c'(y(p))
• c''(y(p)) ? 0
• The inverse supply function p(y) and the supply
  function y(p) measure the same relationship
  between price and profit-maximizing supply of
  output

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Slope of the Supply Function

• Analyze how the supply of a competitive firm
  responds to a change in the price of output.
  Differentiate p c'(y(p)) with respect to p
• 1 c''(y(p)) y(p)
• Since normally c''(y(p)) gt 0, then y(p) should
  be gt 0, i.e., the
• slope of the competitive firm supply curve is
  positive

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Output Decision in Short-Run

• In the short-run, total cost is the sum of
  variable and fixed costs
• c(y) cv(y) F,
• where F should be paid even if y 0

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Output Decision in Short-Run

• Then, it is profitable for the firm in the
  short-run to produce a positive amount of output
  y if the profits from producing y are greater
  than or equal to the losses from producing
  nothing, given that under y 0, firm still needs
  to pay F
• py(p) - cv(y) F ? - F
• or
• p ? cv(y)/y(p) AVC
• i.e., if price is greater than or equal to the
  average variable cost

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The Industry Supply

• The industry supply function Y(p) is the sum of
  the individual firm supply functions
• Let yi(p) be the supply function of the ith firm
  in an industry with m firms. Then,
• Y(p) ?i yi(p)

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The Industry Supply

• The inverse supply function p(Y) for the industry
  is the inverse of this function and gives the
  minimum price at which the industry is willing to
  supply a given amount of output
• Remember that each firm chooses a level of output
  where price equals MC. Given that each firm
  confronts the same market price, then each firm
  that produces a positive amount of output must
  have the same MC
• The industry supply function measures the
  relationship between industry output and the MC
  of producing this output

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Market Equilibrium

• The industry supply function measures the total
  output supplied at any price
• The industry demand function measures the total
  output demanded at any price
• An equilibrium price is a price where the amount
  demanded equals the amount supplied

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Market Equilibrium

• This price is called an equilibrium price because
  at any price where demand does not equate supply,
  some economic agents would find in its interest
  to unilaterally change its behavior
• Let xi(p) be the demand function of individual i
  for
• i 1, , n and yj(p) be the supply function of
  firm j for
• j 1, , m, then equilibrium price is the
  solution to
• ?i xi(p) ?j yj(p)

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Entry/Exit to the Market in Long Run

• The short-run analysis considers an exogenously
  given number of firms
• In the long-run, the number of firms in an
  industry is variable
• If the firm expects to get profits, then it will
  enter to the market
• If the firm is persistently losing money, it will
  exit the market

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Entry/Exit to the Market in Long Run

• We will assume zero cost of entry/exit and
  perfect foresight
• Suppose we have an arbitrarily large number of
  firms with identical cost functions c(y)
• We can calculate the break-even price p where
  profits are zero at the optimal supply of output
• This p is the one where AC MC

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Long Run Supply Curve

• We can look for the largest number of firms so
  that the firms can break even
• If the equilibrium number of firms is very large,
  then the relevant supply function is very flat
• In general, it is assumed that the long-run
  supply curve of a competitive industry with free
  entry is a horizontal line at a price equal to
  the minimum AC