Microeconomia Corso E

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MicroeconomiaCorso E

• John Hey

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Compito a casa/Homework

• CES technology with parameters c10.4, c20.5,
  ?0.9 and s1.0.
• The production function
• y ((0.4q1-0.9)(0.5q2-0.9))-1/0.9
• I have inserted the isoquant for output 40 (and
  also that for output60).
• I have inserted the lowest isocost at the prices
  w1 1 and w2 1 for the inputs.
• The optimal combination q1 33.38 q2 37.54
• and the cost 33.5837.54 70.92.

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What you should do

• Find the optimal combination (either graphically
  or otherwise) and the (minimum) cost to produce
  the output for the following
• w1 2 w2 1 y40
• w1 3 w2 1 y40
• w1 1 w2 1 y60
• w1 2 w2 1 y60
• w1 3 w2 1 y60
• Put the results in a table.

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Results
y w1 w2 q1 q2 costo
40 1 1 32.4 37.5 70.9
40 2 1 27.9 45.2 101.1
40 3 1 25.5 51.2 127.7
60 1 1 50.1 56.3 106.4
60 2 1 41.9 67.9 151.7
60 3 1 38.3 76.7 191.6
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Chapter 12

• The total cost C(y) is the minimum cost to
  produce a given level of output y.
• It is always upward-sloping (in the long period
  passes through the origin) and its shape depends
  upon the returns to scale
• decreasing ? convex
• constant ? linear
• increasing ? concave

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Chapter 12

• The total cost C(y) is the minimum cost to
  produce a given level of output y.
• The average cost C(y)/y is the slope of the
  line from the origin to the total cost curve.
• The marginal cost the rate at which total cost
  increases with output is equal to the slope of
  the total cost curve.

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Constant returns to scaleTotal cost
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Constant returns to scaleMarginal cost
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Decreasing returns to scaleTotal cost
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Two examples
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Average cost at an output of 40
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Average cost at the output of 80
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The average cost curve
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Marginal cost at the output 40
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Marginal cost at the output 80
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The marginal cost curve
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From the total cost curve to the marginal cost
curve and back.

• The marginal cost curve is the slope of the total
  cost curve...
• ... hence the total cost curve is the area under
  the marginal cost curve.
• The marginal cost curve is the derivative of the
  total cost curve...
• ... hence the total cost curve is the integral of
  the marginal cost curve.

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Constant returns to scale
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Constant returns to scale
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Decreasing returns to scale
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Decreasing returns to scale
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Chapter 13

• Today we find the optimal output for a perfectly
  competitive firm...
• ...that takes the price of its output as given.
• We will assume to begin with that the firm has
  decreasing returns to scale.
• We will see later that there are problems if the
  firm has increasing returns to scale.

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Chapter 13

• We use the following notation
• y for the level of output.
• p for the price of the output.
• C(y) for the total (minimum) cost to produce a
  level of output y.
• We find the condition for the optimal output of
  the firm and hence its supply curve.
• We prove a familiar result about the
  profits/surplus of the firm.

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Chapter 13

• The condition for the optimal output
• p marginal cost...
• ... where marginal cost is rising.
• It follows that the supply curve of the firm is
  simply its marginal cost curve.
• The profit/surplus of the firm is the area
  between the price and its supply curve.

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Chapter 13

• Goodbye!

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