Second Best Pricing for the U.S postal Service

1. Second Best Pricing for the U.S postal Service By Roger Sherman & Anthony George Presented by: Sifat Sharmeen

2. U.S postal Service At a Glance • The U.S postal service is an autonomous public corporation which was previously a government funded department ( the post office Department). • The Postal Reorganization Act was passed by Congress in 1970 to change this . • It operates under economies of scale • Postal service provides some services that are imperfect substitutes for those offered by private firms.

3. Aim of this paper • To derive and assess an optimal second best pricing rule for a public sector firm like U.S postal. • The second best pricing will be applicable for a firm if it operates under these 3 conditions: • Marginal cost pricing would lead to deficit because of economies of scale • A budget constraint limits the size of the acceptable deficit • Does not enjoy a monopoly service in every one of it’s operation

4. Previous works on second best pricing.. • The framework for second-best analysis by Frank Ramsey in 1927 does not rest on the assumption of a totally isolated public sector (in terms of cross-price elasticities) • Davis and Whinston, Baumol and Bradford, Lerner have developed second-best pricing rules which make the assumption that all cross price elasticities are zero. • And the most widely quoted second-best pricing rule, the "inverse-elasticity rule," assumes zero cross-price elasticities of demand; it requires that the percentage deviation of price from marginal cost for each product be inversely proportional to its price elasticity of demand.

5. Previous Works… • R. Rees and H. Mohringdeveloped models that considered nonzero cross-price elasticity within the public sector, but they did not effectively extend this consideration to goods or services in the private sector. • M. Boiteux's model did take into account production by private sector firms, but the privately produced goods or services were identical to publicly produced ones and more general cross-elasticity conditions between public and private goods and services were not examined. • A. Bergson has developed a model that considers all possible cross-price elasticities, thereby dealing with the third condition, but he does not allow for a budget constraint so his model does not meet the second condition.

6. PURPOSE? To derive a second-best rule that can meet all three conditions and will allow direct interpretation of all cross elasticities of demand.

7. Methodology Simplifications : • avoid production details and omit intermediate goods. • Assume no interdependencies among products from the production, or cost, standpoint. • Ignore responses that private firms might make to any changes in those public prices. • Concerned primarily with the final equilibrium, where the public enterprise can adjust its price.

8. Postal Service Pricing • i= the amount of the jth service consumed by the ithindividual • Xj = = the total amount of the jthservice • X1,......., Xn= services of the public enterprise • Xn+1, ... ,X m+ 1= services produced in the private sector • = prices for public and private sector services • = the total cost of producing the jthservice • Assume Cj/ Xk= 0 for j k • = the ith individual's income • = transfer payment from (ti > 0) or to (if ti < 0) the ith individual.

9. Postal Service pricing… • The ith consumer seeks to maximize the utility function: = ( 1,……)….(1) Subject to the income constraint -=i ………….(2) = Lagrange multiplier Associated with individuals income constraint

10. Demand Function: i=i( P1……Pm,-) for j=1,……..,m+1….(5) Derivative of the budget constraint WRT pj’s and / ): i+ + and………………….(6) 1++ If we sum over I individuals we obtain, ++ =0 for j=1 …. …………(8)

11. Welfare Function • The welfare function combines the utilities of all individuals; W=W(………….) ………….(9) • Subject to the constraint that income and costs are equal =+……………........(10) • The Public sector firm earn only the amount B on all its operation so that- B=-…………………….(11)

12. Welfare Maximization • Maximizing WRT public sector prices and transfers • =+=0 for j=1….n (12) • +=0 for i=1….I (13)

13. Welfare Maximization… • Assumption : =0 for all k≠j • After simplifying equation 12 and 13 we get- -++=0 for j=1………n (14) And -++=0 for i=1………I (15)

14. Multiplying (15) by and sum the resulting expressions over all I, we can subtract that sum from (14) for each j and obtain +=0 for j=1….n (16) This is the condition for optional pricing. Isolating the jth goods difference between price and marginal cost as (-)=--/- for j=1…n (17)

15. Compensated demand Elasticity • =() Shows compensated demand elasticity of the kth good or service WRT a change in Jth price. • Optimal price-Marginal Cost ratio:

16. Implication for Postal Rate Making 1. If =0 (-)/=α= • It shows the inverse elasticity rule. • This is the simplest form of Optimal second best pricing rule by Baumol and Bradford 2. If ≠0, for some or all j/k=1…..n and j≠k • then the second term wont be zero. • Situation treated by Mohring

17. Implication for Postal Rate Making.. 3. ≠0, for some or all j=1…..n and k=n+1….m • Can take into account optimal price • The third term captures that effect • Presented by Bergson • α will approach 0 as the budget constraint is less important • α will approach 1 under monopoly pricing, because there the budget constraint will be at its greatest feasible level.

18. Solving for a Set of Public Prices • If there are several public enterprise services, as there are even within the U.S. Postal Service, equation (20) alone will not readily yield prices for all of them. • now wish to set out a solution for the entire set of public enterprise prices, taking into account the interdependencies among the public services and also with private sector services. • In matrix form equations

19. Implication for Postal Rate Making… • The relevant private sector services must be priced above (or below) marginal cost to be taken into account in (20). • The U.S. Postal Service estimates its marginal costs to be so low that the revenue raised by setting prices equal to them would cover only about one half of postal service costs. • to meet its budget constraints the Postal Service has depended to an extraordinary degree on the inverse elasticity rule. α→1 • If MC is higher for postal Services, αwill be smaller and (1-α) larger

20. Solving for a Set of Public Prices

21. Solving for a Set of Public Prices Thus if all these elasticities of demand can be known (not only among various public enterprise services but also between public and private ones) it is possible to incorporate them in a solution for all public enterprise prices that will satisfy a budget constraint with minimal welfare losses.

22. Conclusion • The second-best pricing rule does suit the three conditions that are claimed by the Postal Service to characterize the postal operation • marginal cost pricing leads to deficits • a budget constraint exists, • not all postal activities are monopolistic (which means that some services cannot be isolated from the private sector). • It is the presence of imperfect private-sector substitutes in equation (20) that differentiates them from other second-best pricing rules.

23. Conclusion • By not totally isolating the public sector we can add to the generality of second-best pricing rules in a way that allows specific demand interdependencies with private-sector services to be reflected. For U.S. mail classes we have strong evidence of the existence of these interdependencies , so it is desirable to provide for their effect in the second-best pricing rules used by the U.S. Postal Service.