1

Chapter 2Appendix

Welfare Economics

2

Efficiency Resource Use Assumptions 2 inputs (capital and labor) 2 outputs (food and clothing)

3

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

4

Constraints

L = LF + LK

K = KF + LF

5

Productive Efficiency

It is not possible to reallocate inputs to alternative uses so that we can increase the output of any good without reducing the output of some alternative good.

6

Figure 2A.1 Productive Efficiency

F3

F6 F5

F2 F1

F4 C2 C3

C4

C5 C6

C1

E* Z*

D

F C

F

K* K*

L*

L* C

0

K

L

0'

LF

LC

KC

KF

Z1

7

Efficiency Condition MRTSF

LK = MRTSCLK

  The Marginal Rate of Technical

substitution of Labor for Capital for each good are equal

8

Figure 2A.2 The Production-Possibility Curve

A

E 1

E 2

0

T

T'

D F

C

Fo

od

per

Yea

r

Clothing per Year

9

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

10

Constraints

F = FA + FB

C = CA + CB

11

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

UB1

UB2UB3

UB4

UB5UB6UB7

FA*FB*

CB*

CA*

E*E**

CA

FA

CB

FB

F

C

D

UA5

UA4

UA2UA1

UA6

UA3

UA7

Fo

od

per

Yea

r

Clothing per Year

T

T’0

12

Efficiency Criterion on Consumption and Production

MRSACF = MRSB

CF = MRTCF

13

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

14

Social Welfare Functions W = W(UA ,UB)

Where W is social welfare UA is A’s utility

UB is B’s utility

15

Efficiency and Economic Institutions Given the conditions for a market rendering a Pareto Optimal outcome referred to in Chapter 2,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.

16

Figure 2A.4 Cost Minimization and Productive Efficiency

Ca

pit

al

Labor 0

F = F1 per Year

K

L

E

17

Implications of Figure 2A.4 MRTSF

LK = PL/PK

MRTSCLK = PL/PK

MRTSFLK = MRTSC

LK = PL/PK

18

Pure Market Economy and Pareto Efficiency

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

perfect competition, so dividing one by the other we get

PC MCC

PF MCF

=

19

Pure Market Economy and Pareto Efficiency

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.

20

Pure Market Economy and Pareto Efficiency

Step 3Dividing these by each other we get:

MCC FMCF C

=

21

Pure Market Economy and Pareto Efficiency

Step 4

= MRTCF

F

C

Since

AndMRTCF =

PC

PF

Then

= MRTCF =PC

PF

F

C

MCC

MCF

=

22

Figure 2A.5 Consumer Choice

A

B

E FA

CA

Fo

od

per

Yea

r

Clothing per Year 0

UA3

UA2 UA1

23

Pure Market Economy and Pareto Efficiency

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

24

Pure Market Economy and Pareto Efficiency Final

MRSCF = MRSCF = MRTCF =PC

PF

A B

25

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

MC = MSC