Production

1
Production
2
Exchange Economies (revisited)

• No production, only endowments, so no description
  of how resources are converted to consumables.
• General equilibrium all markets clear
  simultaneously.

3
Now Add Production ...

• Add input markets, output markets, describe
  firms technologies, the distributions of firms
  outputs and profits Thats not easy!

4
Robinson Crusoes Economy

• One agent, Robinson Crusoe (RC)
• Endowed with a fixed quantity of one resource --
  24 hours.
• Use time for labor (production) or leisure
  (consumption).
• Labor time L. Leisure time 24 - L.
• What will RC choose?

5
Robinson Crusoes Technology

• Technology Labor produces output (coconuts)
  according to a concave production function.

6
Robinson Crusoes Technology
Coconuts
Production function
Feasible productionplans
24
0
Labor (hours)
7
Robinson Crusoes Preferences

• RCs preferences
• coconut is a good
• leisure is a good

8
Robinson Crusoes Preferences
Coconuts
More preferred
24
0
Leisure (hours)
9
Robinson Crusoes Choice
Coconuts
More preferred
Production function
Feasible productionplans
24
0
Labor (hours)
Leisure (hours)
24
0
10
Robinson Crusoes Choice
Coconuts
Production function
C
24
L
0
Labor (hours)
Leisure (hours)
24
0
11
Robinson Crusoe as a Firm

• Now suppose RC is both a utility-maximizing
  consumer and a profit-maximizing firm.
• Use coconuts as the numeraire good i.e. price of
  a coconut 1.
• RCs wage rate is w.
• Coconut output level is C.

12
Robinson Crusoe as a Firm

• RCs firms profit is ? C - wL.
• ? C - wL ? .., the equation of an
  isoprofit line.
• Slope w .
• Intercept ? .

13
Isoprofit Lines
Coconuts
Higher profit
Slopes w
24
0
Labor (hours)
14
Profit-Maximization
Coconuts
Production function
C
24
L
0
Labor (hours)
15
Utility-Maximization

• Now consider RC as a consumer endowed with ?
  who can work for w per hour.
• What is RCs most preferred consumption bundle?
• Budget constraint is

16
Utility-Maximization
Coconuts
Budget constraint
slope w Intercept
24
0
Labor (hours)
17
Utility-Maximization
Coconuts
More preferred
24
0
Labor (hours)
18
Utility-Maximization
Coconuts
Budget constraint slope w
C
24
L
0
Labor (hours)
19
Utility-Maximization Profit-Maximization

• Profit-maximization
• w MPL
• quantity of output supplied C
• quantity of labor demanded L
• Utility-maximization
• w MRS
• quantity of output demanded C
• quantity of labor supplied L

Coconut and labor markets both clear.
20
Utility-Maximization Profit-Maximization
Coconuts
MRS w MPL
Given w, RCs quantity supplied of labor
quantity demanded of labor L and output
quantity demanded output quantity supplied C.
C
24
L
0
Labor (hours)
21
Pareto Efficiency
Coconuts


24
0
Labor (hours)

• MRS ? MPL, not Pareto efficient

22
Pareto Efficiency

• To achieve Pareto Efficiency
• must have MRS MPL.

23
Pareto Efficiency
Coconuts
MRS MPL. The common slope ? relative
wage rate w that implements
the Pareto
efficient plan by
decentralized pricing.
24
0
Labor (hours)

• MRS MPL, ..

24
First Fundamental Theorem of Welfare Economics

• A competitive market equilibrium is Pareto
  efficient if
• consumers preferences are ..
• there are .. in consumption or
  production.

25
Second Fundamental Theorem of Welfare Economics

• Any Pareto efficient economic state can be
  achieved as a competitive market equilibrium if
• consumers preferences are .
• firms technologies are .
• there are . in consumption or
  production.

26
Non-Convex Technologies

• Do the Welfare Theorems hold if firms have
  non-convex technologies?
• The 1st Theorem does not rely upon firms
  technologies being convex.

27
Non-Convex Technologies
Coconuts
MRS MPL The common slope ? relative
wage rate w that
implements the Pareto
efficient plan by
decentralized pricing.
24
0
Labor (hours)
28
Non-Convex Technologies

• Do the Welfare Theorems hold if firms have
  non-convex technologies?
• The 2nd Theorem does require that firms
  technologies be convex.

29
Non-Convex Technologies
Coconuts
MRS MPL. The Pareto optimal allocation
be implemented by
a competitive
equilibrium.
24
0
Labor (hours)
30
Production Possibilities

• Resource and technological limitations restrict
  what an economy can produce.
• The set of all feasible output bundles is the
  economys ...
• The sets outer boundary is the ...

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Production Possibilities
Coconuts
Production possibility frontier (PPF)
Production possibility set
Fish
32
Production Possibilities
Coconuts

Infeasible
Feasible but inefficient
Fish
33
Production Possibilities
Coconuts
PPFs slope is the
Increasingly negative MRPT ? increasing
opportunity cost to specialization.
Fish
34
Production Possibilities

• If there are no production externalities then a
  PPF will be concave w.r.t. the origin.
• Why?
• Because efficient production requires
  exploitation of comparative advantages.

35
Comparative Advantage
C
RC
MRPT -2/3 coconuts/fish so opp. cost of
one more fish is foregone coconuts.
20
RC has the comparative opp. cost advantage
in producing fish.
30
F
C
MF
50
MRPT -2 coconuts/fish so opp. cost of one more
fish is foregone coconuts.
25
F
36
Comparative Advantage
C
RC
MRPT -2/3 coconuts/fish so opp. cost of
one more coconut is foregone fish.
20
30
F
C
MF
50
MRPT -2 coconuts/fish so opp. cost of one more
coconut is foregone fish.
MF has the comparative opp. cost advantage
in producing coconuts.
25
F
37
Comparative Advantage
C
RC
Economy
C
20
Use .. to produce fish before using
70
30
F
C
MF
50
Use .. to produce coconuts before using ..
50
55
30
F
25
F
38
Comparative Advantage
Economy
C
Using low opp. cost producers first results in a
ppf that is concave w.r.t the origin.
More producers with different opp. costs smooth
out the ppf.
F
39
Coordinating Production Consumption

• The PPF contains many technically efficient
  output bundles.
• Which are Pareto efficient for consumers?

40
Coordinating Production Consumption
Coconuts
Output bundle is and is the
aggregate endowment for distribution to
consumers RC and MF.
Fish
41
Coordinating Production Consumption
Coconuts
OMF
Contract Curve
ORC
Fish
42
Coordinating Production Consumption
Coconuts
However, .
OMF
RCs indifferent curve
MFs indifferent curve
ORC
Fish
43
Coordinating Production Consumption
Coconuts
If instead produce and give MF same
allocation as before. ? MFs utility is
..
OMF
ORC
Fish
44
Coordinating Production Consumption
Coconuts
MFs utility is unchanged, But RCs utility is
... Pareto improvement
OMF
OMF
ORC
Fish
45
Coordinating Production Consumption

• MRS ? MRPT ? inefficient coordination of
  production and consumption.
• Hence, MRS MRPT is necessary for a Pareto
  optimal economic state.

46
Coordinating Production Consumption
Coconuts
OMF
ORC
Fish
47
Decentralized Coordination of Production
Consumption

• The above Pareto optimal production and
  consumption can be achieved by decentralized
  behaviours of firms and consumers
• Competitive markets, profit-maximization, and
  utility maximization all together can result in a
  Pareto optimal economic state

48
Decentralized Coordination of Production
Consumption

• RC and MF jointly run a firm producing coconuts
  and fish.
• RC and MF are also consumers who can sell labor.
• Price of coconut pC.
• Price of fish pF.
• RCs wage rate wRC.
• MFs wage rate wMF.

49
Decentralized Coordination of Production
Consumption

• LRC, LMF are amounts of labor purchased from RC
  and MF.
• Firms profit-maximization problem is choose
• C, F, LRC and LMF to

50
Decentralized Coordination of Production
Consumption
Equation for Isoprofit line is
which rearranges to
51
Decentralized Coordination of Production
Consumption
Coconuts
Higher profit
The firms production possibility set.
Fish
52
Decentralized Coordination of Production
Consumption
Coconuts
Profit-max. plan
Competitive markets and profit-maximization ?
Fish
53
Decentralized Coordination of Production
Consumption

• So competitive markets, profit-maximization, and
  utility maximization all together causethe
  condition necessary for a Pareto optimal economic
  state.

54
Decentralized Coordination of Production
Consumption
Coconuts
Competitive markets and utility-maximization
?
OMF

ORC
Fish
55
Decentralized Coordination of Production
Consumption
Coconuts
Competitive markets, utility- maximization and
profit- maximization ?
OMF

ORC
Fish