1. WELFARE FOUNDATION OF CBA
The traditional approach of CBA is to evaluate the contribution a project makes to social welfare. The question of how to measure welfare therefore arises
The conventional approach is therefore to rely on the concept of consumer and producer surpluses. Consider and economy with identical income y and facing identical prices.

2. P=P(P1……Pn)
Consumers is such an economy maximize utility subject to the constraints as
Z=U(X1……..Xn) – [y- P1 X1]
For FOCS
, for all is,

3. Or ,
For all ij,

4. Suppose we initiate a project which leads to an increase in production of some good, say i…..k at the expense of goods I …..m.
Whether such changes resulting from the project would improve or diminish social welfare can be tested by examining the value of the project in terms of the increase in output value against the cost of the project in terms of the value of the output forgone.

5. In reality, the amount of output forgone may not be easy to predict
In reality, the amount of output forgone may not be easy to predict. However we can use the total value of input diverted from other uses as a guide.
It can be shown that under certain simplifying assumptions, the benefit from a project can be measured by the market value of the output produced less the market value of input diverted from other uses. Basically the equation is given as:

7. Let the value of changes in output as a result of the project be represented by
Substituting from FOC, we have:

8. Should (5) be positive then the value of U is increased after the implementation of the project.
Also let Fji represent the amount of factor j devoted to the production of good i, then the change in the output i would be equal to the sum of the inputs devoted to the production of i multiplied by the marginal product of each input, that’s:

9. Thus
Substituting (7) into (3) gives:

10. The meaning of (8) is that the net benefit from a given project equals the market value of output produced less the market value of input diverted from other uses.
The above result can only hold under certain conditions such as market being highly competitive, price being identical, incomes and preferences being identical and the fact that prices remain constant over all periods of time.

11. The above analysis can also be represented graphically as follows, suppose an increase in output leads to a shift in MC curve from MC1 to MC2 the change in welfare can be represented as follows.

12. A shift in the MC curve leads to a change is both consumer and producer benefit in terms of changes in both consumer surplus (CS) and producer surplus (PS). The change in PS due to the change in MC is given by the triangle FDG whereas the CS is given by the triangle CGD.
From this given project and from both producers and consumers surpluses, the change in welfare is given by the large triangle CFD. The sum of these surpluses could be taken as the cardinal indicators of the change in welfare.

13. Despite the convincing results from analyzing welfare change there are so many problems associated with the analysis.
The analysis only holds when the market is competitive but so long as market imperfections exist in the real would due to price controls, monopoly etc the results of the welfare analysis cannot be fully taken.
The assumption of identical utility functions and identical incomes is also unfounded in real world situations

14. The analysis implicitly assumes that in undertaking a project, relative prices don’t change but the benefit from a given project in the real world to a large extent encounter periodic changes in the relative’s price.
Individuals do not take identical prices as given as the approach assumes.

15. DIFFERENT CONCEPTS OR PARETO OPTIMUM AND WELFARE IMPROVEMENT
Pareto optimality is a situation in which it’s impossible to improve the welfare of one of the members of the society without necessarily or simultaneously reducing the welfare of others. It therefore represents the best possible arrangement.
In the real world, such an optimum situation is hardly achieved. However if certain activities are possible in allowing society to move closer to an optimum situation, such actions are called strict Pareto improvement (SPI).

16. An SPI is an action that improves the welfare of at least one of the members in a given society without any of the remaining members being worse-off.
Usually it is argued that if CBA is based on SPI rules, then only small changes in the existing distribution of Y will be possible or feasible as illustrated in the diagram below;

17. Supposing a given economy is at point S which is a sub-optimum point it becomes necessary for such an economy to move towards the frontier either from S to P or S to R to improves welfare.,
Such movement are however termed Strict Pareto Improvement because in moving towards P for eg. the utility of individual B improves whilst that of A remains unchanged. The reverse is true when we move from S towards R.
Such small movements are however Strict Pareto and are usually in connection with smaller projects.

18. But for bigger projects that moves the economy towards the line of equal distribution, it is possible for the welfare of some individuals to improve to Q whilst at the same time that of others deteriorate.
From the diagram any movement towards F or E and towards Q from S improves the welfare of individual B whilst that of A falls. Such movements are not Strict Pareto movements.

19. From the above analysis SPI are movements concerned with equity but CBA is interested in having a positive Net social benefit. Consider also four projects with two beneficiaries A and B.

20. Projects
Cost
Benefit for A
Benefit for B
Net Social Benefit X1 X2 X3 X4
Doing Nothing
100 20 30 10 95 90
120 15 40

21. Based on CBA all projects qualify to be undertaken
Based on CBA all projects qualify to be undertaken. Comparing no project with the projects, X1 is strict pareto improvement as A’s utility is constant but B’s is improved. X2 is strict pareto. X4 is not strict pareto improvement because individual A is made worse as his welfare fall from 20 to 10. SPI is concerned with welfare distribution but CBA is not.

22. From CBA perspective all projects are desirable but by considering the SPI since individual A becomes were off after the implementation of the project X4 must not be implemented on the grounds of SPI.
CBA therefore attempt to achieve Potential Pareto improvement (PPI)

23. A PPI is an action in which it is possible for a least one person in a given society to gain without anybody losing.
The possibility clause used implies that there is the tendency for some individuals to be worse off but it must the case that the gains made from the project must be enough to compensate the losers by means of transfers.

24. If CBA is based on PPI then it attempts to satisfy the Kaldor-Hicks Compensation Test.
This test specifies that if the beneficiaries of a project remain on a higher IC after sufficient compensations to return losses to the IC they would be on the absence of the projects, then the project is deemed desirable.