Labor Demand in the Long Run

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Labor Demand in the Long Run
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The long run

• in the long run, all inputs are variable,
• model used in discussion has 2 inputs L (labor)
  and K (capital).
• Q f(L,K)
• isoquant - a graph that contains all of the
  combinations of inputs that result in a given
  level of output.

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Isoquant
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Isoquant
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Isoquants
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Marginal rate of technical substitution
The marginal rate of technical substitution of L
for K (MRTS) is defined as the additional amount
of capital needed to replace a unit of labor,
holding output constant. Mathematically, the MRTS
can also be expressed as
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Law of diminishing MRTS

• Law of diminishing MRTS the MRTS declines as
  the level of labor use rises along an isoquant
  (i.e., isoquant curves are convex)

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Alternative derivation of the MRTS
Along an isoquant
With a little manipulation
More precisely
Or
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Isocost curves
TC wL cK where TC total cost w wage c
price of capital L quantity of labor K
quantity of capital
In slope-intercept form, this equation becomes K
(-w/c)L (TC/c)
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Isocost curve
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Isocost curves
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Cost minimization
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Cost-minimization rule

• cost minimization occurs when an isocost curve is
  tangent to the isoquant
• -MRTS -w/c
• MRTS w/c

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Substitution and scale effects

• the substitution effect associated with a change
  in the wage rate is the change in the mix of
  inputs that results from the change in relative
  prices, holding output constant.
• the scale effect is the change in the mix of
  inputs that occurs because of the change in the
  level of output resulting from a change in factor
  prices, holding relative factor prices constant.

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Substitution effect
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Scale effect