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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

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2 distribution of national income
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

factor prices
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

demand for the factors of production
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

demand for the factors of production1
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

demand for the factors of production2
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

demand for the factors of production3
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

demand for the factors of production4
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

demand for the factors of production5
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

demand for the factors of production6
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

demand for the factors of production7
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

demand for the factors of production8
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

demand for the factors of production9
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

demand for the factors of production10
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

demand for the factors of production11
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

demand for the factors of production12
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

demand for the factors of production13
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

demand for the factors of production14
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

demand for the factors of production15
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

demand for the factors of production16
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

the division of national income
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

the division of national income1
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

the division of national income2
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

the division of national income3
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

the division of national income4
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

the division of national income5
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

summary
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

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