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
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