In Figure 3.1, a utility possibilities curve was derived from a single Edgeworth box diagram for two consumers, Ade and Kunle. No attempt was made to argue that any one point along the utility possibilities curve was in any way superior to any other such point. However, the discussion of general equilibrium in preceding unit 1 and 2 showed that the perfectly competitive economy would come to rest at one of the contract curve points which, of course, will correspond to a point on the utility possibilities curve for our given product mix.
Unfortunately, we also know from unit 1 and 2 that any number of Edgeworth box diagrams for two consumers can be drawn under the transformation curve for the economy. In the case we have been developing, this means that there is any number of utility possibilities curves for Ade and Kunle, each one corresponding to solve Edgeworth box for a possible combination of X and Y production.
In Figure 3.2, we show the relationship between the transformation curve and a set of utility possibilities curves. The utility possibilities curve HH ' in panel (b) corresponds to the contract curve 0J0K panel (a) Points F and G on the transformation curve denote the output combinations corresponding to two of the many additional Edgeworth boxes that could be drawn under the transformation curve. If these two boxes were sketched in and their contract curves developed, the utility possibilities curves FF ' and GG ' in panel (b) could be derived from them For each of the infinity of Edgeworth boxes we could develop under the transformation curve in panel (a), a utility possibilities curve can be derived in panel (b).
On each utility possibilities curve of panel (b), there is one point that is consistent with equality between the MRTYX in production and the MRSYX in consumption for the related Edgeworth box in panel (a). For the box 0J YI 0K
X1, this condition is true at Z (SS' is parallel to TT'), which corresponds to the point Z ' on utility possibilities curve HH' . Points R [on GG ' in panel (b)] and V (on FF') are meant to correspond to the contract curve points in the two other Edgeworth boxes where MRTYX = MRSYX. In Figure 3.3, the bold, outer curve that is tangent to all points like R, Z ', and V is called the grand utility possibilities frontier.
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Figure 3.2.Relationship between Transformation Curve and Utility Possibilities Curves
If the economy is at point 0K on its transformation curve in panel (a), efficiency in both production and exchange will be reached when MRTYX = MRSYX, or when its consumers are at point Z on the Edgeworth box for goods combination (X1, Y1). Since SS' is parallel to TT', the MRT equals the MRS. In panel (b), if HH' is the utility possibilities curve for goods combination (X1, Y1), point Z' corresponds to Z in the preceding panel. The two additional utility possibilities curves, GG' and FF' correspond to points G and F on the transformation curve in panel (a). R and V are the points on these two curves consistent with MRT = MRS.
The grand utility possibilities frontier describes all possible combinations of utility for two consumers when the economy is efficient in both production and consumption (MRTYX = MRSYX).
Any point inside the grand utility possibilities frontier is suboptimal, since one person can be made better off without harming the other by simply changing the product mix (moving to a new point on the economy’s transformation
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curve).
Figure 3.3: The Grand Utility Possibilities Frontier
There is a utility possibilities curve such as GG', HH' and FF' for each possible mix of goods the economy can produce. Further, there is a point corresponding to efficiency in both production and exchange on each utility possibilities curve. The grand utility possibilities curve (bold line) is an envelope curve tangent to all such points (R, Z', V, etc). If the two consumers are at a point on the grand utility possibilities curve, it is not possible to make one of them better off without making the other one worse off, given the economy’s production possibilities.
Although the grand utility possibility frontier identifies all possible welfare optima for two consumers, it leaves us with a dilemma. We still do not know which of the points is best for our two-person world. Clearly, in Figure 3.3 movements from point Z toward point R make Kunle better off and Ade worse off, while movements toward V do the reverse. Some additional device is needed to ascertain how changes in the utility of individuals in society affect the well-being of society as a whole. The device commonly used to accomplish this feat (in theory) is the social welfare function.
4.0 CONCLUSION
Welfare economics deals with comparing alternative states of the economy (product mixes and distributions of output) to identify situations or changes that benefit society as a whole. Because welfare economics is concerned with the distribution of well-being among individuals, its application always raises problems of interpersonal comparison of utility.
In a Robinson Crusoe economy, utility (welfare) is maximized when the marginal rate of transformation in production equals the marginal rate of substitution in consumption.
Community indifference curves can be used to illustrate a theoretical welfare maximum for a multi-person economy. However, community indifference
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curves are an abstraction that tends to overlook the essential problem of defining a social welfare function.
The importance of interpersonal utility trade-offs in welfare analyses is under- scored by the utility possibilities curve, which shows that for every efficiently produced output combination, there is any number of Pareto optimal distributions of output among consumers. However, for a given product mix;
only one distribution will be Pareto optimal in terms of utility possibilities. The grand utility possibilities frontier consists of all Pareto optimal utility possibility combinations, one combination corresponding to each possible product mix.
It is not possible to identify a welfare maximum on the grand utility possibilities frontier unless a social welfare function is specified. It is not clear how such a function could be spirited, although it is certain that any such procedure would require some individual or group to make value judgments about how the economy’s benefits should be distributed among persons
5.0 SUMMARY
In this unit you were introduced to welfare economics proper as some part of the concept had well discussed in the preceding unit of this module. The meaning of the welfare economics and its nature was explained. Welfare maximization in the case of Crusoe was dealt with as well as Group Welfare and Interpersonal Comparisons of Utility.The condition that marginal rate of transformation must be equal to marginal rate of substitution for Pareto optimal position to hold.
6.0 TUTOR MARKED ASSIGNMENT
1. Suppose that the isoquants for the commodities X and Y are given by X1, X2, X3 and Y1, Y2, Y3 respectively, in the following table. Suppose also that a total of 14L and 9K are available to produce commodities X and Y.
draw the Edgeworth box diagram for exchange and show the production contract curve.
X’s Isoquant
X1 X2 X3
L K L K L K
5 7 8 5 10 7
6 2 9 3 11 5
7 1 11 2 13 4.5
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Y’s Isoquant
Y1 Y2 Y3
L K L K L K
9 2 7 4 10 4
3 4 5 6 8 7
1 6 4 8 7.5 8.5
7. 0 REFERENCES /FURTHER READINGS
Emery E.D (1984): Intermediate Microeconomics, Harcourt brace Jovanovich, Publishers, Orlando, USA
Jhingan M.L (2009): Microeconomics Theory, Vrinda Publications (P) Limited, Delhi
Pindyck R.S and Daniel L. R. (2009): Microeconomics (7ed), Pearson Education, Inc. New Jersey, USA.
Salvatore D. (2003): Microeconomics Harper Publishers Inc. New York. USA Salvatore D. (2006): Microeconomics. Schuams Series. McGraw-Hill
Companies, Inc. USA
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UNIT 4: WELFARE ECONOMICS II