Applied Microeconomics

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Applied Microeconomics

• Competitive Markets

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Outline

• Rationale
• Assumptions
• Short-run supply and equilibrium
• Long-run supply and equilibrium
• Rents

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Readings

• Kreps Chapter 11
• Perloff Chapter 8
• Zandt Chapters 7 and 8
• Case Growth and profitability

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What is Interesting about Competitive Markets?

• Reasonable description of many markets
• Interesting benchmark
• Important for analysis of efficiency

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Assumptions

• Firms and consumers are price takers they
  assume that the consumption and production
  decisions they make have no impact on prices (at
  least in equilibrium)
• In reality, all firms have some impact, but given
  that this is small with many firms, a reasonable
  assumption
• Experimental support (Smith, 1982)
• Evolutionary rationale even with few firms
  (Vega-Redondo, 1997, Ania and Ferrer, 2003)
• Homogeneous good

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Assumptions

• Free entry and exit of firms
• Firms are profit maximizers
• Economic profit is not accounting profit
• Managers and owners interest may not coincide
  (Parmalat, Enron)
• As-if, evolutionary forces
• Consumers are utility maximizers
• A unique market price for each good
• Buyers and sellers know the prices
• Transaction costs are low

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Examples of Competitive Markets

• Agricultural markets corn, wheat, soy beans
• Natural Resource Commodities copper, gold,
  silver, natural gas
• Financial markets for many instruments

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Partial vs. General Equilibrium Analysis

• In this course we generally study the market for
  a single good, assuming the prices and quantities
  of all other goods remain fixed
• This simplifies analysis and it is justified
  when
• There are limited wealth effects
  ?D1(p1,p2,W)/?W0
• There are limited price effects on other goods,
  or the prices of a a group of goods move together
  ?D1(p1,p2,W)/?p20

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Partial vs. General Equilibrium Analysis

• Likely when total expenditure on the good is a
  small fraction of total wealth
• Both of the properties are satisfied if consumers
  have quasi-linear utility functions U(x,m)mv(x)

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The Demand Curve A Competitive Firm Faces

• If the firm sets a price p lower than the market
  price p, it faces the entire market demand
• If it sets a price higher than the market price,
  demand is zero
• If pp the firm can sell any quantity up to the
  market demand

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Profit Maximizing Level of Production

• This means that a price-taking firm takes the
  market price p as given
• It has revenue function R(x)px
• So the marginal revenue function is just MR(x)p

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Profit Maximizing Level of Production

• The firm solves maxx0 px-TC(x)
• Finding the solution is a two-step procedure
• First, find all outputs x such that pMC(x)
• Second, check whether the most profitable of such
  outputs gives higher profit than shutting down
  production

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Profit Maximizing Level of Production

• Remarks
• If MC(x) is decreasing at x, this cannot be a
  solution
• With a decreasing marginal cost function, there
  may not exist any solution

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Firm Supply

• The firms supply function Si(p) is given by the
  inverse of the upward-sloping part of its its
  marginal cost curve above the price at which it
  is better to shut down
• Mathematically, MC(Si(p))p for ppsd and Si(p)0
  otherwise
• What is the shut-down level of price?

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Supply without Fixed Cost
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Firm Supply with Constant Marginal Cost
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Firm Supply with Unavoidable Fixed Costs

• Remember that fixed cost may be either avoidable
  (TC(0)0) or unavoidable (TC(0)gt0)
• If all of the firms fixed costs are unavoidable,
  they are irrelevant for the firms production
  decision and should be disregarded
• The firm should produce at price p provided
  px-VC(x)0 for some non-negative x, or
  equivalently pminx0VC(x)/xminx0AVC(x)

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Firm Supply with Avoidable Fixed Costs

• If all of the firms fixed costs are avoidable,
  they are relevant for the firms production
  decision
• The firm should produce at price p provided
  px-TC(x)0 for some output x, or equivalently
  pminx0TC(x)/xminx0AC(x)

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Supply with Fixed Cost
Unavoidable fixed cost
Avoidable fixed cost
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Example

• If the firm has total cost function TC(x)x2, the
  supply function is_____
• If the firm has total cost function TC(x)x21
  and unavoidable fixed costs, the supply function
  is_____
• If the firm has total cost function x21 and
  avoidable fixed costs, the supply function is____

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Short-Run Supply

• The firms short-run supply function SSi(p) is
  given by its short-run marginal cost curve above
  minimum average cost (net of average unavoidable
  costs)
• The short-run industry supply function is the
  horizontal sum of the supply curves of the firms
  in the market SS1(p)SSN(p)

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Short-Run Industry Supply

• Firm supply is given by the inverse of the firms
  short-run marginal cost function for prices above
  the shut-down level
• Short-run industry supply is the horizontal sum
  of firm supply

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Short-Run Equilibrium

• A short-run equilibrium is a price p and a
  quantity x such that
• Firms maximize profit given price
• Consumers maximize utility given price
• Short-run industry supply equals market demand

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Short-Run Equilibrium
Quantity
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Long-Run Supply

• In the long run, the firm has a flatter marginal
  cost curve and all fixed costs are avoidable
• The firms long-run supply curve SLi(p) is given
  by the long-run marginal cost curve above minimum
  average cost
• The long-run industry supply function is the
  horizontal sum of the supply functions of all
  firms in the market
• However, in the long run the number of firms in
  the market varies with price due to exit and entry

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Long-Run Supply

• A firm enters the market if it can make an
  economic profit and exits otherwise
• Suppose
• All firms have equal technology,
• There is unlimited supply of firms who can enter
  the market,
• Input prices are constant,
• Then the long-run industry supply function is
  flat at the level minx0AC(x) and all firms are
  producing at their efficient scale

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Long-Run Supply

• Firms must be producing at this level since firms
  would enter if economic profits where positive
  and exit otherwise
• What about if n firms make profits and n1 makes
  a loss?
• In theory repeated entry and exit, in practice
  firms would learn and the n1 firm would stay out

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Reasons for Increasing Long-Run Supply Curve

• Limited number of firms
• Heterogeneous cost functions
• Varying input prices

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Definition of Long-Run Competitive Equilibrium

• A long-run equilibrium is a price p and a
  quantity x such that
• Firms maximize profit given price
• Consumers maximize utility given price
• Long-run industry supply equals market demand
• All firms are earning zero economic profit

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Long-Run Equilibrium
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Rents

• Suppose a price-taking farmer owns a particularly
  fertile piece of land
• Then he would be making positive profits in the
  long run!
• This is called economic rent and is consistent
  with the long-run equilibrium using the following
  argument

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Rents

• Suppose instead that the farmer rented the land
• The competitive bidding among farmers would
  increase the price of the land until profits were
  zero
• Other examples patents, superior athletes,
  superior technology in relatively fixed supply
• Rents affects average but not marginal cost

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Conclusions

• In competitive market there is a unique market
  price and consumers and producers are price
  takers
• Firm supply is given by the inverse of the
  marginal cost function above minimum average cost
  (minimum average variable cost with unavoidable
  fixed costs)
• Short-run industry supply is given by the
  horizontal sum of firm supply functions
• In the long-run firms enter the market until
  profits are zero