Microeconomics 2

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Microeconomics 2

• John Hey

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Lecture 26 The Labour Market

• The supply of labour (consumer leisure
  time/money trade-off).
• The demand for labour (theory of the firm).
• Equilibrium.
• Minimum wage legislation.
• Two questions for you
• Does an increase in the wage rate imply an
  increase in the supply of labour? Is it therefore
  a good idea to reduce income tax (Mrs T and next
  lecture)
• Is minimum wage legislation a Good Thing? (old?
  Labour)
• Last year there was no question on this chapter
  in the examination. This year there will be.

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The supply of labour

• We use the analysis of Chapter 6 (Supply and
  Demand with income in the form of endowments)
• The space (l,m)
• l leisure time in hours (Initially L24 hours)
• m money (to spend on) consumption (Initial
  holding M could be zero)
• w is the wage rate per hour
• Budget constraint is m M w(L-l)
• The supply of labour L-l
• ...depends upon the preferences.
• Obviously both money/consumption and leisure time
  are desirable (both are goods).
• Let us go to Maple

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The demand for labour

• We use the analysis of Chapters 11, 12 and 13
  (Theory of the Firm/Production).
• We use a space with Ld (the demand for) labour on
  the horizontal axis and the Cost and total
  Revenue of the firm on the vertical axis.
• We keep things simple by assuming that we are in
  the short run (capital fixed) with fixed costs
  equal to 5, and the wage fixed at 1 per unit.
• Total costs are fixed costs plus labour costs
  (linear in labour). The slope is the wage rate.
• Total revenue is the price of output multiplied
  by the output produced and so is concave.
• The slope of this curve is the price of output
  multiplied by the marginal product of labour.

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Total revenue and costs

• Note crucially that the cost curve (the red line)
  is linear because the only variable input is
  labour (capital is fixed).
• Its slope is the wage rate w.
• The revenue curve is concave as capital is fixed
  and the rate at which revenue increases is the
  value of the marginal product of labour (which is
  decreasing as output goes up since capital is
  fixed).
• The slope of the revenue curve is the value of
  the marginal product of labour.
• Which (for a competitive firm) is equal to the
  price of output multiplied by the marginal
  product of labour.
• Let us go back to Maple...

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The optimality condition for the demand for labour

• The slope of the total cost curve must be equal
  to the slope of the total revenue curve.
• The slope of the total cost curve is equal to the
  wage rate.
• The slope of the total revenue curve is equal to
  the price of output multiplied by the marginal
  product of labour.
• Hence the optimality condition the real wage
  rate (the wage rate divided by the price of
  output) must be equal to the marginal product of
  labour.

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A minimum wage?

• What happens in this market if the government
  introduces a minimum wage?
• Obviously at a level higher than the equilibrium
  wage in the competitive market.

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Chapter 26

• Goodbye!