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CHAPTER 11
Factor markets and income distribution
©McGraw-Hill Education, 2014
Capital and land
• Physical capital
– the stock of produced goods which
contributes to the production of goods
and services.
• Land
– the factor of production which nature
supplies.
• Together capital and land make up the
tangible wealth of a country.
©McGraw-Hill Education, 2014
Investment
• Capital depreciates over time
– becoming less productive and less valuable.
• Gross investment
– the production of new capital goods and the
improvement of existing capital goods.
• Net investment
– gross investment minus the depreciation of the
existing capital stock.
©McGraw-Hill Education, 2014
Stocks and flows
• A stock
– the quantity of an asset at a point in
time
– the asset price is the sum for which the
stock can be bought outright
• A flow
– the stream of services that an asset
provides during a period
– the rental rate is the cost of using
capital services
©McGraw-Hill Education, 2014
Interest and present value
• The present value of £1 at some future date is the
sum that, if lent out today, would accumulate to £1
by that future date.
– It depends upon how far into the future the sum
accumulates
– and on the rate of interest.
• The price of a capital asset should be related to the
stream of future payments that will be earned from
the services it provides discounted back to give the
present value.
©McGraw-Hill Education, 2014
Interest and present value (PV)
YEAR 0
YEAR 1
YEAR 2
At 10%
interest rate:
Value of £1
lent today in:
£1
£1.10
£1.21
PV of £1 lent
today in:
£1
£0.91
£0.83
Value of £1
lent today in:
£1
£1.05
£1.10
PV of £1 lent
today in:
£1
£0.95
£0.91
At 5% interest
rate:
©McGraw-Hill Education, 2014
Real and nominal interest rates
• The nominal interest rate
– tells us how many actual pounds will be earned in
interest by lending £1 for one year.
• The real rate of interest
– measures the return on a loan as the increase in
goods that can be purchased rather than as the
increase in the nominal value of the loan fund.
• The Fisher equation, after Irving Fisher:
Real Interest Rate = Nominal Interest Rate – Inflation
Rate
©McGraw-Hill Education, 2014
Future consumption
The equilibrium real interest rate
AA' shows the production
possibility frontier between
current and future
consumption:
A'
by devoting resources to
investment, future
consumption can be
increased.
A
Current consumption
©McGraw-Hill Education, 2014
The slope of the frontier
has magnitude –(1 + i)
where i is the rate of
return on investment.
Future consumption
The equilibrium real interest rate
Given society's preferences
between present and
future consumption, the
optimal position is at E,
where the indifference
curve UU is at a tangent to
the PPF.
U
A'
E
U
A
Current consumption
©McGraw-Hill Education, 2014
The slope of the red line
represents –(1 + r), where r
is the real interest rate that
balances the productivity
of investment and the
thriftiness of consumers.
The markets for capital and land
• The derived demand curve for capital
(and for land) services closely parallels the
earlier analysis of labour demand.
• But land is in fixed supply to the economy
as a whole.
• Rental rates tend to become equalized
across alternative uses.
©McGraw-Hill Education, 2014
Changes in capital intensity
• Over time, the UK economy is becoming
more capital-intensive
– The wage-rental ratio has increased,
leading industries to substitute capital for
labour.
– In the long run the supply of labour is less
elastic than the supply of capital.
– New capital embodies the latest
technology.
©McGraw-Hill Education, 2014
The functional distribution of
income in the UK
The distribution of income between the factors of production
changed little between 1981-89 and 2007-12.
©McGraw-Hill Education, 2014
Some maths (1)
Assuming that the interest rate remains constant, the present
value of a future stream of revenues over N years from now, is
N
given by:
Rt
PV  
t 1
(1  i) t
where Rt is the revenue in year t, i is the interest rate and ∑ is a
symbol that means the sum of each year’s discounted
Rt
earnings.
(1  i )t
The difference between the present value of the stream of
revenues from a given investment minus the actual cost of
that investment is called the Net Present Value (NPV).
©McGraw-Hill Education, 2014
Some maths (2)
For example, suppose a firm wants to buy today a machine that costs
£8000. The machine can give a revenue of £2000 a year for 4 years.
After 4 years the machine can be sold as scrap for £3000.
Assume that the interest rate is 10% in all 4 years.
The present value of this stream of future revenues is:
2000
2000
2000
5000
PV 



2
3
(1  0.1) (1  0.1)
(1  0.1)
(1  0.1) 4
Which equals £8388.7. In this case the present value of the future
revenues from the machine is higher than the cost of buying the
machine. The firm should indeed buy the machine in this case.
Note the NPV is £8388.7-£8000 = £388.7
©McGraw-Hill Education, 2014
Concluding comments (1)
• Present values convert future receipts or
payments into current values. Because
lenders can earn – and borrowers must pay
– interest over time, a pound tomorrow is
worth less than a pound today.
• Nominal interest rates measure the
monetary interest payments on a loan.
• The inflation-adjusted real interest rate
measures the extra goods a lender can
buy by lending for a year and delaying
purchases of goods.
©McGraw-Hill Education, 2014
Concluding comments (2)
• The firm’s demand for capital services is its marginal value
product of capital curve.
• In the short run, the supply of capital services is fixed. In the
long run, it can be adjusted by producing new capital goods
or allowing the existing capital stock to depreciate.
• The required rental is the rental that allows a supplier of
capital services to break even on the decision to purchase
the capital asset.
• The functional distribution of income shows how national
income is divided between the factors of production.
• The personal distribution of income shows how national
income is divided between different individuals regardless of
the factor services from which income is earned.
©McGraw-Hill Education, 2014