Evidence points toward the Council of Wage and Price Stability (COWPS) price guidelines as the constraint causing U.S. petroleum refinery shortages during 1979-1980. This report develops the theory of a profit-maximizing firm's behavior when complying with a COWPS-like restraint. Results include: (1) When the production technology displays a certain type of fixed proportions (as appears relevant for refineries), shortages can — but need not — emerge. (2) Product output decreases in response to the COWPS control, causing market prices to rise. (3) Product supply diminishes as market demand increases. (4) Use of some factors, e.g., crude oil, increases as factor prices increase, which, because of fixed proportions, implies expanded product output. (5) Product mix likely shifts towards lower-grade products. (6) Dispersion of product prices across firms increases. (7) Relative product prices for a multiproduct firm become indeterminant. Casual empirical evidence supports the relevance of this theory.