Microeconomics Corso E

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MicroeconomicsCorso E

• John Hey

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Summary of Chapter 8

• The contract curve shows the allocations that are
  efficient in the sense of Pareto.
• There always exist the possibility of mutually
  advantageous exchange if preferences are
  different and/or endowments are different (unless
  the endowment point is on the contract curve).
• Perfect competitive equilibrium (with both
  individuals taking the price as given) always
  leads to a Pareto efficient allocation.
• If one of the individuals chooses the price the
  allocation is not Pareto efficient.

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The competitive equilibrium depends on the
preferences and the endowments.

• If one individual changes his or her preferences
  in such a way that he or she now prefers more a
  particular good than before...
• ... the relative price of that good rises.
• If an individual is endowed with more of a good
  than before...
• ... the relative price of that good falls.

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Part 1 and Part 2

• Part 1 an economy without production...
• ... just exchange
• Part 2 an economy with production...
• ... production and exchange.

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Part 1

• Reservation prices.
• Indifference curves.
• Demand and supply curves.
• Surplus.
• Exchange.
• The Edgeworth Box.
• The contract curve.
• Competitive equilibrium.
• Paretian efficiency and inefficiency.

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Part 2

• Chapter 10 Technology.
• Chapter 11 Minimisation of costs and factor
  demands.
• Chapter 12 Cost curves.
• Chapter 13 Firms supply and profit/surplus.
• Chapter 14 The production possibility frontier.
• Chapter 15 Production and exchange.

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Chapter 10

• Firms produce...
• ...they use inputs to produce outputs.
• In general many inputs and many outputs.
• We work with a simple firm that produces one
  output with two inputs...
• ...capital and labour.
• The technology describes the possibilities open
  to the firm.

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Chapter 5 Chapter 10

• Individuals
• Buy goods and produce utility
• depends on the preferences
• which we can represent with indifference
  curves..
• in the space (q1,q2)

• Firms
• Buy inputs and produce output
• depends on the technology
• which we can represent with isoquants ..
• in the space (q1,q2)

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The only difference?

• We can represent preferences with a utility
  function ...
• ... but this function is not unique...
• ... because/hence we cannot measure the utility
  of an individual.
• We can represent the technology of a firm with a
  production function ...
• ... and this function is unique
• because we can measure the output.

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An isoquant

• In the space of the inputs (q1,q2) it is the
  locus of the points where output is constant.
• (An indifference curve the locus of the points
  where the individual is indifferent. Or the locus
  of points for which the utility is constant.)

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Two dimensions

• The shape of the isoquants depends on the
  substitution between the two inputs.
• The way in which the output changes form one
  isoquant to another depends on the returns to
  scale.

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Perfect substitutes 11

• an isoquant q1 q2 constant
• y A(q1 q2) constant returns to scale
• y A(q1 q2)0.5 decreasing returns to scale
• y A(q1 q2)2 increasing returns to scale
• y A(q1 q2)b returns to scale decreasing (blt1)
  increasing (bgt1)

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y q1 q2 perfect substitutes 11 and
constant returns to scale
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y (q1 q2)2 perfect substitutes 11 and
increasing returns to scale
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y (q1 q2)0.5 perfect substitutes 11 and
decreasing returns to scale
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Perfect Substitutes 1a

• an isoquant q1 q2/a constant
• y A(q1 q2/a) constant returns to scale
• y A(q1 q2/a)b returns to scale decreasing
  (blt1) increasing (bgt1)

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Perfect Complements 1 with 1

• an isoquant min(q1,q2) constant
• y A min(q1,q2) constant returns to scale
• y Amin(q1,q2)b returns to scale decreasing
  (blt1) increasing (bgt1)

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y min(q1, q2) Perfect Complements 1 with 1 and
constant returns to scale
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y min(q1, q2)2 Perfect Complements 1 with 1
and increasing returns to scale
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Y min(q1, q2)0.5 Perfect Complements 1 with
1 and decreasing returns to scale
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Perfect Complements 1 with a

• an isoquant min(q1,q2/a) constant
• y A min(q1,q2/a) constant returns to scale
• y Amin(q1,q2/a)b returns to scale decreasing
  (blt1) increasing (bgt1)

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y q10.5 q20.5 Cobb-Douglas with parameters 0.5
and 0.5 hence constant returns to scale
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y q1 q2 Cobb-Douglas with parameters 1 and 1
hence increasing returns to scale
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y q10.25 q20.25 Cobb-Douglas with parameters
0.25 and 0.25 hence decreasing returns to scale
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Cobb-Douglas with parameters a and b

• an isoquant q1a q2b constant
• y A q1a q2b
• ablt1 decreasing returns to scale
• ab1 constant returns to scale
• abgt1 increasing returns to scale

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Chapter 5 Chapter 10

• Individuals
• The preferences are given by indifference curves
• in the space (q1,q2)
• .. can be represented by a utility function u
  f(q1,q2)
• which is not unique.

• Firms
• The technology is given by isoquants
• in the space (q1,q2)
• ..can be represented by a production function
• y f(q1,q2)
• which is unique .

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Chapter 10

• Goodbye!

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