Chapter 32 Production. Exchange Economies (revisited) No production, only endowments, so no description of how resources are converted to consumables

Chapter 32Production

Exchange Economies (revisited) No production, only endowments, so

no description of how resources are converted to consumables.

General equilibrium: all markets clear simultaneously.

1st and 2nd Fundamental Theorems of Welfare Economics.

2

Now Add Production ... Add input markets, output markets,

describe firms’ technologies, the distributions of firms’ outputs and profits …

3

Now Add Production ... Add input markets, output markets,

describe firms’ technologies, the distributions of firms’ outputs and profits … That’s not easy!

4

Robinson Crusoe’s Economy One agent, 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 Crusoe’s Technology Technology: Labor produces output

(coconuts) according to a concave production function.

6

Robinson Crusoe’s Technology

Labor (hours)

Coconuts

Production function

240

Feasible productionplans

7

Robinson Crusoe’s Preferences RC’s preferences:

coconut is a good leisure is a good

8

Robinson Crusoe’s Preferences

Leisure (hours)

Coconuts

More preferred

240

9

Robinson Crusoe’s Preferences

Leisure (hours)

CoconutsMore preferred

24 0

10

Robinson Crusoe’s Choice

Labor (hours)

Coconuts


Production function

240

11


Labor (hours)

Coconuts


Production function

240Leisure (hours)24 0

12


Labor (hours)

Coconuts


Production function


13


Labor (hours)

Coconuts

Production function


C*

L*

14


Labor (hours)

Coconuts

Production function


C*

L*Labor

15


Labor (hours)

Coconuts

Production function


C*

L*Labor Leisure

16


Labor (hours)

Coconuts

Production function


C*

L*Labor Leisure

Output

17


Labor (hours)

Coconuts

Production function


C*

L*Labor Leisure

MRS = MPL

Output

18

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.

RC’s wage rate is w. Coconut output level is C.

19

Robinson Crusoe as a Firm RC’s firm’s profit is = C - wL. = C - wL C = + wL, the

equation of an isoprofit line. Slope = + w . Intercept = .

20

Isoprofit Lines

Labor (hours)

Coconuts

24

C wL Higher profit; 1 2 3

Slopes = + w 3 21

0

21

Profit-Maximization

Labor (hours)

Coconuts


Production function

240

22

Profit-Maximization

Labor (hours)

Coconuts

Production function

240

23

Profit-Maximization

Labor (hours)

Coconuts

Production function

240

24

Profit-Maximization

Labor (hours)

Coconuts

Production function

24

C*

L*0

25

Profit-Maximization

Labor (hours)

Coconuts

Production function

24

C*

L*

Isoprofit slope = production function slope i.e. w = MPL

0

26

Profit-Maximization

Labor (hours)

Coconuts

Production function

24

C*

L*

Isoprofit slope = production function slope i.e. w = MPL = 1 MPL = MRPL.

0

27

Profit-Maximization

Labor (hours)

Coconuts

Production function

24

C*

L*


*

* * * C wLRC gets

0

28

Profit-Maximization

Labor (hours)

Coconuts

Production function

24

C*

L*


* * * C wL

* Given w, RC’s firm’s quantitydemanded of labor is L*Labor

demand

RC gets

0

29

Profit-Maximization

Labor (hours)

Coconuts

Production function

24

C*

L*


* Given w, RC’s firm’s quantitydemanded of labor is L* andoutput quantity supplied is C*.

Labordemand

Outputsupply

* * * C wLRC gets

0

30

Utility-Maximization Now consider RC as a consumer

endowed with $* who can work for $w per hour.

What is RC’s most preferred consumption bundle?

Budget constraint is C wL * .

31

Utility-Maximization

Labor (hours)

Coconuts

*

240

C wL * .Budget constraint; slope = w

32


Labor (hours)

CoconutsMore preferred

240

33


Labor (hours)

Coconuts

*

240

C wL * .Budget constraint; slope = w

34


Labor (hours)

Coconuts

*

Budget constraint; slope = w

240

C wL * .

35


Labor (hours)

Coconuts

*

240

C wL * .C*

L*

Budget constraint; slope = w

36


Labor (hours)

Coconuts

*

240

C wL * .C*

L*

MRS = wBudget constraint; slope = w

37


Labor (hours)

Coconuts

*

240

C wL * .C*

L*

Laborsupply

Budget constraint; slope = wMRS = w

Given w, RC’s quantitysupplied of labor is L*

38


Labor (hours)

Coconuts

*

240

C wL * .C*

L*

Given w, RC’s quantitysupplied of labor is L* andoutput quantity demanded is C*.

Laborsupply

Outputdemand

Budget constraint; slope = wMRS = w

39

Utility-Maximization & Profit-Maximization

Profit-maximization: w = MPL

quantity of output supplied = C*quantity of labor demanded = L*

40




Utility-maximization: w = MRSquantity of output demanded = C*quantity of labor supplied = L*

41




Utility-maximization: w = MRSquantity of output demanded = C*quantity of labor supplied = L*

Coconut and labormarkets both clear.

42


Labor (hours)

Coconuts

24

C*

L*

*

0

MRS = w = MPL

Given w, RC’s quantitysupplied of labor = quantitydemanded of labor = L* andoutput quantity demanded =output quantity supplied = C*.

43

Pareto Efficiency Must have MRS = MPL.

44

Pareto Efficiency

Labor (hours)

Coconuts

240

MRS MPL

45

Pareto Efficiency

Labor (hours)

Coconuts

240

MRS MPL

Preferred consumptionbundles.

46

Pareto Efficiency

Labor (hours)

Coconuts

240

MRS = MPL

47

Pareto Efficiency

Labor (hours)

Coconuts

240

MRS = MPL. The common slope relative wage rate w that implements the Pareto efficient plan by decentralized pricing.

48

First Fundamental Theorem of Welfare Economics

A competitive market equilibrium is Pareto efficient ifconsumers’ preferences are convexthere are no externalities in

consumption or production.

49

Second Fundamental Theorem of Welfare Economics Any Pareto efficient economic state

can be achieved as a competitive market equilibrium ifconsumers’ preferences are convexfirms’ technologies are convexthere are no externalities in

consumption or production.

50

Non-Convex Technologies Do the Welfare Theorems hold if

firms have non-convex technologies?

51


firms have non-convex technologies? The 1st Theorem does not rely upon

firms’ technologies being convex.

52

Non-Convex Technologies

Labor (hours)

Coconuts

240

MRS = MPL The common slope relative wage rate w that implements the Pareto efficient plan by decentralized pricing.

53


firms have non-convex technologies? The 2nd Theorem does require that

firms’ technologies be convex.

54

Non-Convex Technologies

Labor (hours)

Coconuts

240

MRS = MPL. The Pareto optimal allocation cannot be implemented by a competitive equilibrium.

55

Production Possibilities Resource and technological limitations

restrict what an economy can produce. The set of all feasible output bundles is

the economy’s production possibility set.

The set’s outer boundary is the production possibility frontier.

56

Production Possibilities

Fish

CoconutsProduction possibility frontier (ppf)

57


Fish

CoconutsProduction possibility frontier (ppf)

Production possibility set

58


Fish

Coconuts

Feasible butinefficient

59


Fish

Coconuts


Feasible and efficient

60


Fish

Coconuts


Feasible and efficient

Infeasible

61


Fish

CoconutsPpf’s slope is the marginal rateof product transformation.

62


Fish

CoconutsPpf’s slope is the marginal rateof transformation.

Increasingly negative MRT increasing opportunitycost to specialization.

63

Production Possibilities If there are no production

externalities then a ppf will be concave w.r.t. the origin.

Why?

64

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.

65

Comparative Advantage Two agents, RC and Man Friday (MF). RC can produce at most 20 coconuts

or 30 fish. MF can produce at most 50 coconuts

or 25 fish.

66

Comparative Advantage

F

C

F

C

RC

MF

20

5030

25 67


F

C

F

C

RC

MF

20

5030

25

MRT = -2/3 coconuts/fish so opp. cost of onemore fish is 2/3 foregone coconuts.

68


F

C

F

C

RC

MF

20

5030

25


MRT = -2 coconuts/fish so opp. cost of onemore fish is 2 foregone coconuts.

69


F

C

F

C

RC

MF

20

5030

25


MRT = -2 coconuts/fish so opp. cost of onemore fish is 2 foregone coconuts.

RC has the comparativeopp. cost advantage inproducing fish.

70


F

C

F

C

RC

MF

20

5030

25

MRT = -2/3 coconuts/fish so opp. cost of onemore coconut is 3/2 foregone fish.

71


F

C

F

C

RC

MF

20

5030

25


MRT = -2 coconuts/fish so opp. cost of onemore coconut is 1/2 foregone fish.

72


F

C

F

C

RC

MF

20

5030

25


MRT = -2 coconuts/fish so opp. cost of onemore coconut is 1/2 foregone fish.

MF has the comparativeopp. cost advantage inproducing coconuts.

73


F

CEconomy

F

C

F

C

RC

MF

20

5030

25

70

55

50

30

Use RC to producefish before using MF.

Use MF toproducecoconuts before using RC.

74


F

CEconomy

F

C

F

C

RC

MF

20

5030

25

70

55

50

30

Using low opp. costproducers first resultsin a ppf that is concave w.r.t the origin.

75


F

CEconomy

More producers withdifferent opp. costs“smooth out” the ppf.

76

Coordinating Production & Consumption The ppf contains many technically

efficient output bundles. Which are Pareto efficient for

consumers?

77

Coordinating Production & Consumption

Fish

Coconuts

C

F

Output bundle isand is the aggregateendowment for distribution to consumers RC and MF.

( , ) F C

78


Fish

Coconuts

ORC

OMFC

F

Output bundle isand is the aggregateendowment for distribution to consumers RC and MF.

( , ) F C

79


Fish

Coconuts

ORC

OMFC

F

Allocate efficiently;say to RC and to MF.

( , ) F C

CRC CMF

FMF

FRC

( , ) F CRC RC( , ) F CMF MF

80


Fish

Coconuts

ORC

OMFC

F

CRC CMF

FMF

FRC

81


Fish

Coconuts

ORC

OMFC

F

CRC CMF

FMF

FRC

82


Fish

Coconuts

ORC

OMFC

F

CRC CMF

FMF

FRC

MRS MRT

83


Fish

Coconuts

ORC

OMFC

F

CRC CMF

FMF

FRC

O’MFC

F

( , ). F CInstead produce

84


Fish

Coconuts

ORC

OMFC

F

CRC CMF

FMF

FRC

C

F

( , ). F C

O’MF

CMF

Instead produceGive MF same allocation as before.FMF

85


Fish

Coconuts

ORC

OMFC

F

CRC CMF

FMF

FRC

C

F

( , ). F C

O’MF

CMF

Instead produceGive MF same allocation as before. MF’s utility is unchanged.

FMF

86


Fish

Coconuts

ORC

OMF

C

F

( , ). F C

O’MFFMF

Instead produceGive MF same allocation as before. MF’s utility is unchanged

CMF

87


Fish

Coconuts

ORC

OMF

FRC

C

F

( , ). F C

O’MF

CRC

FMF

CMF

Instead produceGive MF same allocation as before. MF’s utility is unchanged

88


Fish

Coconuts

ORC

OMF

FRC

C

F

( , ). F C

O’MF

CRC

FMF

CMF

Instead produceGive MF same allocation as before. MF’s utility is unchanged, RC’s utility is higher

89


Fish

Coconuts

ORC

OMF

FRC

C

F

( , ). F C

O’MF

CRC

FMF

CMF

Instead produceGive MF same allocation as before. MF’s utility is unchanged, RC’s utility is higher; Pareto improvement.

90

Coordinating Production & Consumption MRS MRT inefficient coordination

of production and consumption. Hence, MRS = MRT is necessary for a

Pareto optimal economic state.

91


Fish

Coconuts

ORC

OMF

FRC

C

F

CRC

FMF

CMF

92

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. RC’s wage rate = wRC. MF’s wage rate = wMF.

93

Decentralized Coordination of Production & Consumption LRC, LMF are amounts of labor

purchased from RC and MF. Firm’s profit-maximization problem is

choose C, F, LRC and LMF tomax . p C p F w L w LC F RC RC MF MF

94

Decentralized Coordination of Production & Consumptionmax . p C p F w L w LC F RC RC MF MF

Isoprofit line equation isconstant p C p F w L w LC F RC RC MF MF

95



which rearranges to

C w L w Lp

pp

FRC RC MF MFC

FC

.

96



which rearranges to

.

slopeintercept

Fpp

pLwLwC

C

F

C

MFMFRCRC

97

Decentralized Coordination of Production & Consumption

Fish

Coconuts Higher profit

Slopes = pp

FC

98


Fish

Coconuts

The firm’s productionpossibility set.

99


Fish

Coconuts

Slopes = pp

FC

100


Fish

Coconuts

Profit-max. plan

Slopes = pp

FC

101


Fish

Coconuts

Profit-max. plan

Slope = pp

FC

102


Fish

Coconuts

Profit-max. plan

Slope = pp

FC

Competitive marketsand profit-maximization

.C

F

ppMRT

103

Decentralized Coordination of Production & Consumption So competitive markets, profit-

maximization, and utility maximization all together cause

the condition necessary for a Pareto optimal economic state.

,MRSppMRTC

F

104


Fish

Coconuts

ORC

OMF

FRC

C

F

CRC

FMF

CMF

Competitive marketsand utility-maximization

MRS pp

FC

.

105


Fish

Coconuts

ORC

OMF

FRC

C

F

CRC

FMF

CMF

Competitive markets, utility-maximization and profit- maximization

.MRTppMRSC

F

106

Documents

Chapter 32 Production. Exchange Economies (revisited) No production, only endowments, so no description of how resources are converted to consumables