Copyright © 2002 by Thomson Learning, Inc. Chapter 2 Appendix Welfare Economics Copyright © 2002 Thomson Learning, Inc. Thomson Learning™ is a trademark

Copyright © 2002 by Thomson Learning, Inc.

Chapter 2Appendix

Welfare Economics

Copyright © 2002 Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

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Efficiency Resource Use

Assumptions 2 inputs (capital and labor) 2 outputs (food and clothing)


Production Functions

F = F(LF,KF)

C = C(LC,KC)

Where F = food production C = clothing production Li = labor devoted to the production of good i

Ki = capital devoted to the production of good i


Constraints

L = LF + LK

K = KF + LF


Productive Efficiency

It is not possible to reallocate inputs to alternative uses in such a manner as to increase the output of any good without reducing the output of some alternative good.


Figure 2A.1 Productive Efficiency

F3

E* F6 F5 Z*

F3 F1

F4 Z1

C2 C3

C4

C5 C6

C1

D

0

K* F

K

L

K* C

KF

LF

LC

KC

L* F

L* C 0'


Efficiency Condition

MRTSFLK = MRTSC

LK

The Marginal Rate of Technical

substitution of Labor for Capital in each good are equal


Figure 2A.2 The Production-Possibility Curve

A

D

E 1

E 2

Fo

od

per

Yea

r

Clothing per Year 0

T

F

C T'


Pareto Efficiency

Preferences on Consumption

UA = U(FA,CA)

UB = U(FB,CB)

Where

Ui = the utility of person i

Fi = food consumed by person i

Ci = clothing consumed by person i


Constraints

F = FA + FB

C = CA + CB


Fo

od

per

Yea

r

Clothing per Year

T

T’

F

C

D

FA

CA

CB

FB

Figure 2A.3 Efficient Allocation of A Given Amount of Food and Clothing per Year For Two Consumers

UB1

UB2UB3

UB4

UB5UB6UB7

UA5

UA4

UA2UA1

UA6

FA*FB*

CB*

CA*

E*E**

UA3

UA7

0


Efficiency Criterion on Consumption and Production

MRSACF = MRSB

CF = MRTCF


Interpretation of Efficiency Criterion

Suppose we say that the “price of a unit of clothing is $1.” Then clothing is the same as “money.” We can then say that MRSA

CF is A’s willingness to substitute

clothing for money, which is their marginal benefit of clothing, MBA

C. The same is true for B. If these are

equal to the MRTCF then this represents the

capability of turning money into clothing as well. Thus it reflects the costs of production. Lastly if there are no other people who gain from either A or B consuming clothing or food then:

MSB = MBAC = MBB

C = MSCC


Social Welfare Functions

W = W(UA,UB)

Where W is social welfare UA is A’s utility

UB is B’s utility


Efficiency and Economic Institutions

Given the conditions for a market rendering a Pareto Optimal outcome referred to in Chapter 2 then if costs are:

C = PKK + PLL

then production of a particular amount of a good is efficient if the slope of the production function for each good is equal to the slope of the isocost line.


Figure 2A.4 Cost Minimization and Productive Efficiency

Ca

pit

al

Labor

F = F1 per Year

0

K

L

E


Implications of Figure 2A.4

MRTSFLK = PL/PK

MRTSCLK = PL/PK

MRTSFLK = MRTSC

LK = PL/PK


Pure Market Economy and Pareto Efficiency

Step 1So far we know that PF = MCF and PC = MCC

from perfect competition dividing one by the other we get

PC MCC

PF MCF

=



Step 2 MCF is the amount of other resources

that must be given up to produce more Food. We will denote this fact by saying:

MCF = C.

It is the forgone clothing to produce more Food.

The same applies the other way around

MCC = F.



Step 3

Dividing these by each other we get:

MCC FMCF C

=



Step 4

= MRTCF

F

C

Since

AndMRTCF =

PC

PF

Then

= MRTCF =PC

PF

F

C

MCC

MCF

=


Figure 2A.5 Consumer Choice

E

UA3

UA2 UA1

Fo

od

per

Yea

r

Clothing per Year 0

FA

A

B CA



Step 5As just seen the slopes of the individual’s indifference curves are equal to the ratio of the prices. So

MRSCF =PC

PF

A

MRSCF =PC

PF

B



Final

MRSCF = MRSCF = MRTCF =PC

PF

A B


Market Imperfections

Monopoly P > MC Others are affected so MB = MSB or

MC = MSC

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Copyright © 2002 by Thomson Learning, Inc. Chapter 2 Appendix Welfare Economics Copyright © 2002 Thomson Learning, Inc. Thomson Learning™ is a trademark