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Chapter 2 Appendix. Welfare Economics. Efficiency Resource Use. Assumptions 2 inputs (capital and labor) 2 outputs (food and clothing). Production Functions. F = F ( L F ,K F ) C = C ( L C ,K C ) Where F = food production C = clothing production - PowerPoint PPT Presentation
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1
Chapter 2Appendix
Welfare Economics
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Efficiency Resource Use Assumptions 2 inputs (capital and labor) 2 outputs (food and clothing)
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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
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Constraints
L = LF + LK
K = KF + LF
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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.
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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
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Efficiency Condition MRTSF
LK = MRTSCLK
The Marginal Rate of Technical
substitution of Labor for Capital for each good are equal
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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
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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
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Constraints
F = FA + FB
C = CA + CB
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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
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Efficiency Criterion on Consumption and Production
MRSACF = MRSB
CF = MRTCF
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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
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Social Welfare Functions W = W(UA ,UB)
Where W is social welfare UA is A’s utility
UB is B’s utility
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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.
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Figure 2A.4 Cost Minimization and Productive Efficiency
Ca
pit
al
Labor 0
F = F1 per Year
K
L
E
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Implications of Figure 2A.4 MRTSF
LK = PL/PK
MRTSCLK = PL/PK
MRTSFLK = MRTSC
LK = PL/PK
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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
=
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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.
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Pure Market Economy and Pareto Efficiency
Step 3Dividing these by each other we get:
MCC FMCF C
=
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Pure Market Economy and Pareto Efficiency
Step 4
= MRTCF
F
C
Since
AndMRTCF =
PC
PF
Then
= MRTCF =PC
PF
F
C
MCC
MCF
=
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Figure 2A.5 Consumer Choice
A
B
E FA
CA
Fo
od
per
Yea
r
Clothing per Year 0
UA3
UA2 UA1
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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
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Pure Market Economy and Pareto Efficiency Final
MRSCF = MRSCF = MRTCF =PC
PF
A B
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Market Imperfections Monopoly P > MC Others are affected so MB = MSB or
MC = MSC