Principles of Economics
Class 6
Input market, environmental
economics, general equilibrium
dr. sc. Tomislav Herceg
Income
• Incomes:
1. Wages (price of labour)
2. Rent (price of land)
3. Interest rate (price of capital)
4. Dividend (price of capital)
5. Transfer payments (gifts)
• Distribution of goods is based on the ability to
pay for those goods
2
Input markets
• Demand for inputs is deducted from demand for
products and is equal to MRP
• Market demand is obtained by horizontal
summation of individual demands.
• Marginal revenue product (MRP) is the additional
revenue when an additional unit of input is
employed:
MRPK = MR×MPK, MRPL = MR×MPL , MRPN = MR×MPN
• In perfect competition when MR = P we have:
MRPK = P×MPK, MRPL = P×MPL , MRPN = P×MPN
3
Demand for labour
• Demand for labour is MRPL, which shows how
revenues increase when additional worker is
employed).
• MRPL = MPL×MR, u s.k. MRPL = MPL×P
• In p.c. w = MRPL= MPL×P →MPL = w/P
(marginal product of labour equals real salary)
w
Demand for labour
MRPL = d
0
L
4
Demand for capital and land
• Demand for land is MRPN, which shows how
revenues increase when additional unit of
land is employed).
• Demand for capital is MRPK, which shows how
revenues increase when additional unit of
capital is employed).
• MRPN = MPN×MR, in p.c. MRPN = MPN×P
• MRPK = MPK×MR, in p.c. MRPK = MPK×P
5
Profit maximization on the input
markets
MR = MC
MR×MPL = MC×MPL = w
MR×MPL = w
Since in p.c. MR = P then P×MPL = w
In perfect competition the following holds:
P×MPK = r, P×MPN = rN
P×MPL = PL
MPL /PL = 1/P
• The same holds for other inputs too:
MPL /w = MPK /r = MPN /rN = 1/P
→Minimum cost rule
6
Supply of inputs
• Labour supply depends on w and demographic
structure
• Land supply depends on geography and rN.
• Capital supply depends on r and expected return
• Market supply is obtained by horizontal
summation of individual supplies.
• Equilibrium supply and demand is obtained on
the intercept of the input supply and demand
• The price of input is equal to the MRP of the last
employed unit of input
7
Individual and market supply for
labour
• Worker decides how many hours a day (24h) he wants to
work, depending on the wage (w).
• WORKFORCE = unemployed seeking job + employed
• Substitution effect: the increase in salary increases the
number of working hours
• Income effect: when the income is high enough workers start
to work less to be able to enjoy their money.
w
SL
0
L
8
Labour market equilibrium
w
SL
DL
0
D’L
L
9
Capital market equilibrium
r
r
SK
r
SK
SK
DK
0
K
Short run
DK
DK
0
K
Medium run
0
K
Long run
• Capital supply increases in time
10
Land market equilibrium
rN
SN
DN
0
N
• Land supply is fixed!!
11
RENTABILITY OF INVESTMENT
•
•
•
Profitability of an investemnt is estimated using
𝑹
Return on capital indicator 𝑹𝑶𝑪 = where R is
𝑰
the annual return, and I initial investment.
Interests are reward for savings
Nominal interest rate is a money return, and real
interest rate is a nominal rate corrected for
inflation:
𝑖+100
100+𝜋
𝑟=
− 1 ×100%
𝑟 ≈𝑖−𝜋
12
Present value of an asset
• Present value (V) is a sum of all returns doiscounted
𝑅𝑖
𝑛
for the interest rate: 𝑉 = 𝑡=1
𝑡.
1+𝑖
• Permanent rent is an investment that yield the infinite
𝐼0
number of payoffs Io: 𝑉 =
𝑖/100
• All costs and benefits of an investment are estimated in
the cost-benefit analysis
• Investment projects will be undertaken if 𝑅𝑂𝐶 ≥ 𝑖 +
𝜋 + 𝑅𝑃, where i is a nominal interest rate, 𝜋 inflation
and RP is a risk premium.
• If 𝑅𝑂𝐶 < 𝑖 + 𝜋 + 𝑅𝑃 then it is better to put the money
in the bank.
13
• 5) a company has to decide which machine to buy. There are 3 offers for 3
different machines which have the following returns:
YEAR
RETURN A
1
2
3
4
5
•
•
•
•
•
•
•
•
•
•
RETURN B
300
250
200
150
100
RETURN C
350
250
200
200
If i = 10% which offer is the best?
Machine A
V = N1/( 1+i ) + N2/( 1+i )2 + N3/( 1+i )3 + N4/( 1+i )4 + N5/( 1+i )5
V = 794.1459537 ~ 794.15
Macine B
V = 350/1.1 + 250/1.12 + 200/1.13 + 200/1.14
V = 811.6590335 ~ 811.66
Machine C
V = 400/1.1 + 300/ 1.12 + 300/ 1.13
V = 836.9646882 ~ 836.96 =>The best offer: C >B>A
400
300
300
•
6) Rent-a-car company bought several cars at price 68 000 kn
per car, and rents them for 25 000 kn per year. If the annual
depreciation is 6800 kn, insurance 5400 kn and maintenance
costs 6200 kn per annum, find ROC.
•
P = 68 000 kn, Dp = 6800 kn, Ins= 5400 kn,
Main.=6200 kn ;
•
•
Total costs= 6800 + 5400 + 6200 = 18 400 kn
Total revenue = 25 000 kn
TR – TC = 6600 kn
•
ROC = 6600 / 68 000 = 9.7 %
•
General Equilibrium Analysis
• GEA investigates relations between all the
markets and how a simultaneous equilbrium
can be obtained.
• GEA is based on Pareto efficiency
• Pareto efficiency is a situation when an
increase in utility of one person decreases
utility of others, or when an increase in
production of one good decreses production
of other goods.
Conditions for Pareto efficiency
1. 𝑀𝑅𝑆𝑥𝑦 =
𝑀𝑈𝑥
𝑀𝑈𝑦
2. 𝑀𝑅𝑇𝑥𝑦 =
𝑀𝐶𝑥
𝑀𝐶𝑦
3. 𝑀𝑅𝑇𝑆𝑖𝑗 =
𝑀𝑃𝑖
𝑀𝑃𝑗
=
𝑝𝑥
𝑝𝑦
(for all products x and y)
=
𝑝𝑥
𝑝𝑦
(for all products x and y)
=
𝑤𝑖
𝑤𝑗
(for each input i and j)
Edgeworth box (consumption)
𝑀𝑈𝑥 𝑝𝑥
=
𝑀𝑈𝑦 𝑝𝑦
(contract curve)
𝑀𝑅𝑆𝑥𝑦 =
𝐵
𝑢1
𝐵
𝑢2
𝐴
𝑢3
xj
𝐴
𝑢2
𝐵
𝑢3
𝐴
𝑢2′
𝐴
𝑢1
xi
Edgeworth box (production)
𝑀𝑃𝑖 𝑤𝑖
=
𝑀𝑃𝑗 𝑤𝑗
𝐵
𝑢
1
(contract curve)
𝑀𝑅𝑇𝑆𝑖𝑗 =
𝐵
𝑢2
𝐴
𝑢3
xj
𝐴
𝑢2
𝐵
𝑞3
𝐴
𝑢2′
𝐴
𝑢1
xi
PPF curve in general equilbrium
qy
𝑀𝑅𝑇𝑥𝑦 =
𝑀𝐶𝑥 𝑝𝑥
=
𝑀𝐶𝑦 𝑝𝑦
u
PPF
px/py
qx
Environmental economics
• Malthus (18.st.): population will increase
faster than food production (it appeared to be
wrong)
• Development is impossible without the impact
on the environment:
Pollution
per
inhabitant
GDP per
inhabitant
21
Natural resources
• Renewable n.r. can be used infinitely if preserved
(forests, rivers, lakes, sea)
• Non-renewable n.r. are limited or slowly
renewable.
• Externalities can be positive (the action of an
individual causes benefits to the others, like
vaccination) or negative (the action of an
individual causes costs to the others, like
pollution)
• Internalization of externalities is a process of
including extern costs in the individual costs by
charging an ecological tax.
22
Negative externalities and taxes
MSC = MEC + MC
p
Externalities’
control:
1. Law
2. Environment tax
MC = s
E
F
MEC
p=d
q
23
Problems
1) The government made an analysis of the SO2 pollution decrease. The data
on costs and benefits are in the table:
% decrease in the
SO2 level
Total social
benefit
0
10
20
30
40
50
60
70
80
90
100
0
180
350
510
660
800
930
1050
1160
1260
1350
Marginal social
benefit
Total social
costs
0
60
140
240
360
500
660
840
1040
1260
1500
a) Fill the table
b) What is the most efficient level of SO2 reduction?
Marginal social
costs
Net benefit
• Solution:
% decrease in the
SO2 level
Total social
benefit
0
10
20
30
40
50
60
70
80
90
100
0
180
350
510
660
800
930
1050
1160
1260
1350
Marginal social
benefit
Total social
costs
180
170
160
150
140
130
120
110
100
90
0
60
140
240
360
500
660
840
1040
1260
1500
Marginal social
costs
60
80
100
120
140
160
180
200
220
240
Net benefit
0
120
210
270
300
300
270
210
120
0
-150
• The most efficient result will be obtained when SO2 level is reduced by 50% (MSB =
MSC)
2)One ton of steel costs a steel factory 100 $. It also causes 5$ pollution
costs. Find MEC, MSC and MC.
• MC=100 $
• MEC = 5$
• MSC = 105$