Production, Cost, and Profit: A More Advanced Treatment

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Production, Cost, and Profit A More Advanced
Treatment
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Production Function

• The physical relationship during a specific
  period of time between resource inputs and
  product output, given available technology

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• As an example of a specific form of the
  production function, economists often use the
  Cobb-Douglas form

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• For example, if we let ? be 0.8 and ? be 0.2 and
  let K equal 5, then

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Isoquants

• An isoquant is a curve showing all the
  combinations of inputs that produce a given level
  of output
• just a useful way to show output-input
  relationship
• negative slope showing substitutability of inputs
• convex to origin reflecting decreasing
  substitutability as use of one input increase
• slope is marginal rate of technical substitution
  (MRTS)

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• Using our Cobb-Douglas illustration, the
  following shows several combinations of L and K
  that produce 10 units of Q

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Isoquants for three levels of output
Capital
Q20
Q15
Q10
0
Labor
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Costs

• Cost is a function of the inputs used and the
  prices of the inputs
• For instance, assuming two inputs,

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Isocost Curves

• Curve showing all combinations of inputs that
  cost the same
• Given input prices, isocost curves have negative
  slopes and are linear
• to see this, rearrange equation to get

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Capital
K (C/r) - (w/r)L
Vertical intercept
Slope
The higher the cost, the further from the origin
the isocost curve (C2gtC1)
C2
C1
0
Labor
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Profit Maximization

• Remember that we start from the assumption that
  firms maximize profit
• This implies that firms minimize costs of
  producing a given output
• Also implies that firms maximize output for a
  given cost incurred
• Therefore, firms operate at tangency of isoquant
  and isocost curves

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The firm always operates on its expansion path.
If it is not, then it could either increase
output without increasing cost or decrease cost
without reducing output by changing the
combination of inputs used.
Capital
C1,000
C686
Expansion path
10
Q L0.8K0.2 C 50L 20K
6.8
Q 14.6
Q 10
11
16
0
Labor
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Long Run Average and Marginal Costs

• Note that, since capital is variable in this
  analysis, we must be dealing with the long run
• By plotting the various combinations of output
  and cost we can draw the Long Run Average Cost
  Curve
• Using the output-cost data, we can calculate and
  plot Long Run Marginal Cost

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Note When LRMCltLRAC, LRAC falls When LRMAgtLRAC,
LRAC rises LRMCLRAC at min of LRAC

LRMC
Decreasing costs or economies of scale
LRAC
Increasing costs or diseconomies of scale
Constant costs or constant returns to scale
0
Q