Uncovering regulators’ social welfare weights

1. Uncovering regulators’ social welfare weights By Thomas W. Ross* Presented by: UgonnaNwaokwu

2. Introduction • The purpose of this article is basically to describe a simple technique for uncovering interesting information about the preferences of regulators from the pricing decisions. • It uses the familiar Ramsey pricing model.

3. We begin by supposing that regulators choose prices to maximize some weighted sum of consumers' and producer's surpluses.

4. Weighted Ramsey-optimal pricing • The familiar problem of second-best pricing for a regulated firm, as it is usually presented, involves maximizing total consumers' surplus subject to some profit constraint for the firm.

5. Consider a simple model in which the enterprise sells two goods (i = 1, 2) to two classes of consumers (k = A, B). Consumers within a class are assumed to be identical, but tastes can differ between classes. Letting p = (PI, P2) represent the vector of regulated prices, we denote the total consumers' surplus obtained by consumers of group k as (p) and the total surplus obtained by all consumers as Z(p) = (p) + (p). • For now we assume that demands are independent. Thus, we can write (p) = () + () , where () is group k's surplus from good i. We shall also use the expression () = () + (), the total surplus from good i. The firm's profit function is written as: • π(p) = px - C(x), where x = (XI, X2) is the vector of total outputs, a function of the prices, and C(x) is the total cost of producing vector x.

6. max Z(p) subject to π ≥ π * and they solve the first ( - ) = (λ- 1)/ λ, i= 1, 2, ……….(1) where and are, respectively, the marginal cost and (absolute value) own-price elasticity of demand of good i. Equation (1) is often called the "inverse elasticity rule" and the expression (λ - 1)/ λ the "Ramsey number" which will be common to all goods. For convenience let us refer to the markup term ( - ) /as .

7. We can usefully think of weights entering the Ramsey calculus in two ways: the weights may be attached to the goods or to the consumers. With "goods weights," the maximand becomes Z*(p) = () + () where the are the weights. The equation (1) becomes: ( - ) = (λ - )/ λ, i= 1, 2, ……….(2)

8. Under the "consumer-weights" approach, the maximand is now Z**(p)= (p) + (p). and (1) becomes ( - ) =λ–(+ )/ λ, i= 1,2,...(3) Where the are the consumer weights and the are the shares of consumption of good i (i.e., = /). .Equations (3) are seen to be of the same form as (2) except that now the goods weights are endogenous, determined by consumer weights and shares of consumption.

9. Extracting the implied social weights • Now that we understand the role weights play in determining weighted Ramsey-optimal prices, we can pose the principal question of this article. Given an observed set of prices charged by a certain regulated firm, can we extract the implied weights? • To extract goods weights, equations (2) can be written as: = To find the relative goods weights, we need only the markup and demand elasticity values for each good.

10. = • = ………(6)

11. Conclusion • This article used a simple method to extract interesting information about regulators’ preferences that is implicit in the pricing structures of the firms they regulate. • Although this is, to my knowledge, the first such attempt to uncover the preferences of regulators, there has been related revealed-preference work. • Research in this area should continue on at least three fronts. First, the procedures derived here should be applied to some real data and to a number of interesting questions. • Second, there is more work to be done on the theory itself. Regulatory pricing schemes are often so complicated that our formulas do not apply. For example, we cannot use (4) or (6) if a firm uses a block-price schedule. How must our rules be changed to allow us to analyze more of the price schedules that are used in regulatory situations? Finally, what is the source of social weight? Are they part of a polictical support function of the type described by Peltzman (1976), or do they simply represent some regulator's concept of social justice?