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Optimal Pricing of Publicly Supplied Private Goods: A Case Study of NIST Standard Reference Materials.

pdf icon Optimal Pricing of Publicly Supplied Private Goods: A Case Study of NIST Standard Reference Materials. (10381 K)
Fuller, S. K.

NISTIR 6302; 154 p. June 1999.

Available from:

National Technical Information Service (NTIS), Technology Administration, U.S. Department of Commerce, Springfield, VA 22161.
Telephone: 1-800-553-6847 or 703-605-6000;
Fax: 703-605-6900.
Order number: PB99-147720


standard reference materials; costs; average-cost pricing; Boiteux model; budget constraint; cost recovery; decreasing-cost production; demand analysis; economic analysis; inverse-elasticity rule; pricing; multi-product enterprises; Ramsey prices; user fees; welfare maximization


This study provides a framework for determining optimal prices and production plans for a welfare-maximizing public enterprise that produces multiple goods, faces a budget constraint, and is obligated to meet all demand. Public enterprises often operate under conditions of decreasing marginal cost where first-best, profit-maximizing rules lead to deficits. In order to cover costs, prices therefore need to exceed marginal cost. A public-sector pricing model in the Boiteux tradition computes price and output combinations that minimize the loss from charging prices that do not equal marginal cost. The report describes the Boiteux model and its extensions. The Ramsey version of the model is applied to the pricing problem of the Standard Reference Materials Program (SRMP) at the National Institute of Standards and Technology (NET). The NIST SRMP supplies samples of materials whose physical or chemical properties are precisely characterized; they are used as intermediate goods by firms and laboratories to calibrate manufacturing equipment or scientific apparatus for quality control. The SRMP is faced with the problem of how to calculate prices that will cover the cost of the program and will result in quantities that just meet demand at those prices. The model was applied to a group of 11 SRMs. After estimating their demand and cost functions and combining them with the theoretical principles of the model, optimal prices and production plans were calculated for the group of 11 SRMs for the years 1978 to 1992. The results fulfilled the optimality requirements of the Ramsey-Boiteux model: Deviations of price from marginal cost were inversely proportionate to the goods' price elasticities of demand, and the corresponding optimal'quantities of SRMs maintained the same proportions as the quantities that would have been demanded at prices equal to marginal cost. In every year of the study period there would have been a welfare gain if Ramsey prices had been charged rather than average-cost prices, and unit sales and revenues would have been higher than they were under the actual pricing policy of the SRMP in the years from 1978 to 1992. The analysis shows that in the case of NET SRMs the Ramsey-Boiteux model can provide concrete and relatively simple pricing rules that yield welfare-optimizing prices and quantities.