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2. Distribution of National Income

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					 2. Distribution of National Income
• Factors of production and production
  function determine output and therefore
  national income
• Circular flow: national income flows from
  firms to households through the markets
  for the factors of production
• The neoclassical theory of distribution:
  theory of how national income is divided
  among the factors of production
 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   1
                         Factor Prices
• Factor prices
   – determine the distribution of national income
   – The amounts paid to the factors of production
     = wages, rent
   – Price of each factor depends on the supply
     and demand for that factor
   – Vertical factor supply curve
   – Downward sloping factor demand curve
   – Intersection = determines equilibrium factor
     price
 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   2
           Demand for the factors of
                production
• Examine a typical firm to look at decisions
  taken by firms on how much of these
  factors to demand
• Assume: firm is competitive
   – Little influence on market prices
   – Firm produces and sells at market prices
• Firm’s production function:
   Y = F(K, L)

 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   3
           Demand for the factors of
                production
• Y = firm’s output
• K = machines used (amount of capital)
• L = number of hours worked by employees
  (amount of labour)
• P = price the firm sells its output for
• W = wages firm hires workers at
• R = rent of capital paid by the firm
Assume: that households own the economy’s
  stock of capital. Firms produce output and
  households own capital
 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   4
           Demand for the factors of
                production
• Goal of firm: to maximise profits
• Profit = revenue – costs
• Revenue = P x Y
   – P = price of goods
   – Y = amount of good produced
• Costs: labour costs and capital costs
   – Labour costs = W x L (wage times amount of labour)
   – Capital costs = R x K (rental times amount of capital)


 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76     5
            Demand for the factors of
                 Production
Profit = revenue – labour costs – capital costs
Profit = PY – WL                – RK

Y = F(K,L)

Therefore:
Profit = PF(K,L) – WL – RK

  Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   6
           Demand for the factors of
                production
• Profit depends on the product price, P, the
  factor prices, W and R, and the factor
  quantities, L and K
• Competitive firm: takes the product price
  and the factor prices as given and
  chooses amounts of labour and capital
  that will maximise profits.
• P, W and R are given
• Firm chooses L and K
 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   7
           Demand for the factors of
                production
• Firm will hire labour and capital that will
  maximise profits
• But what are those profit-maximising
  quantities?




 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   8
           Demand for the factors of
                production
• Quantity of labour
• More labour employed, more output firm
  produces
• Marginal Product of Labour (MPL) = the
  extra output the firm gets from one extra
  unit of labour, holding amount of capital
  fixed


 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   9
           Demand for the factors of
                production
MPL = F(K, L+1) – F(K,L)

Equation: MPL is the difference between the
 amount of output produced with L+1 units
 of labour and the amount produced with
 only L units of labour



 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   10
           Demand for the factors of
                production
• Diminishing marginal product:
   – Most production functions have this property
   – Holding the amount of capital fixed, MPL
     decreases as the amount of labour increases
   – “too many cooks spoil the broth”
• Graph of a production function when we
  hold capital fixed and allow labour to vary


 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   11
           Demand for the factors of
                production
• Deciding to hire an additional unit of labour
  depends on how it will affect profits
• Firm compares:
   – the extra revenue from the increased
     production as a result of that extra labour
   – to the cost of that extra labour, i.e. the wages
     given to that extra labour
• Extra revenue depends on the MPL and
  the price of the output
 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   12
           Demand for the factors of
                production
• Extra revenue = P x MPL
• Cost of the extra labour = W
ΔProfit = ΔRevenue – ΔCost
         = (P x MPL) – W
• How much labour does the firm hire?
• Answer: if the extra revenue (P x MPL) is
  greater than the cost of (W), then the
  profits increase and the firm will hire the
  extra unit of labour
 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   13
           Demand for the factors of
                production
• The firm will continue to hire labour until
  the next unit of labour would no longer be
  profitable
• That is until:
     P x MPL = W
        Revenue of extra labour = cost of that labour
• That can be written as:
     MPL = W/P
 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   14
           Demand for the factors of
                production
• MPL = W/P
• W/P = real wage
• Graph: the Marginal Product of Labour
  Schedule




 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   15
           Demand for the factors of
                production
• The firm decides how much capital to rent
  in the same way it decides how much
  labour to hire
• Marginal product of capital (MPK) =
  amount of extra output the firm gets from
  one extra unit of capital, holding the
  amount of labour fixed
MPK = F(K + 1, L) – F(K, L)
 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   16
           Demand for the factors of
                production
• Diminishing marginal product of capital
• Firm compares:
   – the extra revenue from the increased
     production as a result of that extra capital
   – to the cost of that extra capital, i.e. the rent
• Extra revenue = P x MPK
• Cost of the capital = R

 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   17
           Demand for the factors of
                production
ΔProfit = ΔRevenue – ΔCost
        = (P x MPK) – R
• To maximise profits the firm continues to
  rent more capital until the MPK falls to
  equal the real rental price
 MPK = R/P



 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   18
           Demand for the factors of
                production
• Summary: How a firm decides how much
  of each factor to employ
   – The firm will hire additional labour up to the
     point when MPL = W/P
   – The firm will rent additional capital up to the
     point when MPK = R/P




 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   19
The Division of National Income
• We can now see how the markets for the
  factors of production distribute the
  economy’s total income
• Assuming all firms are competitive and
  profit-maximising then:
   – Each factor of production is paid its marginal
     contribution to the production process



 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   20
The Division of National Income
• The real wage paid to each worker = MPL
• The real rental price paid to each capital-owners
  = MPK
• For the whole economy then:
   – Total real wages paid to labour is MPL x L
   – Total rental paid to all capital-owners is
   MPK x K
• Income that remains after firms pay the factors
  of production = economic profit of the owners of
  firms

 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   21
The Division of National Income
Economic profit = Y – (MPL x L) – (MPK x
   K)
• Rearrange to see how total income is
   divided:
Y = (MPL x L) + (MPK x K) + economic profit
• How large is economic profit?
• Answer: if production function has
   constant returns to scale then economic
   profit is zero
  Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76 22
The Division of National Income
• Reason: if
   – each factor is paid its marginal product i.e.
     labour is paid the additional output it produces
     and capital-owners are paid the additional
     output it produces AND
   – if there is constant returns to scale, i.e. output
     increases by the same amount that the factors
     have increased by
   – THEN
   – Economic profit left over is zero
 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   23
The Division of National Income
• Constant returns to scale, profit
  maximisation and competition implies
  economic profit is zero
• Why is there ‘profit’ in the economy?
• Assumed
   – three agents in economy: workers, owners of
     capital and owners of firms
   – Total output or income is divided among
     wages, return to capital and economic profit

 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   24
The Division of National Income
• But most firms own rather than rent the
  capital they use, so firm owners and
  capital owners are the same people
• Accounting profit = economic profit +
  (MPK x K)
• So the ‘profit’ is the return to capital



 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   25
                               Summary
1. What determines the level of production?
Answer: the factors of production and the
  production function determine total output
  in the economy
2. How the income is distributed:
Answer: wages paid to labour, rent paid to
  capital-owners and economic profit
3. What determines the demand for goods
  and services?
 Source: Mankiw (2000) Macroeconomics, Chapter 3 p. 42-76   26

				
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