We consider a market in which both suppliers and consumers compete for a product via scalar-parameterized supply offers and demand bids. Scalar-parameterized offers/bids are attractive due to their modeling simplicity and desirable mathematical properties, with the most prominent being bounded efficiency loss and price markup under strategic interactions. Our model incorporates production capacity constraints and minimum inelastic demand requirements. Under perfect competition, the market mechanism yields allocations that maximize social welfare. We show that there exists a unique Nash equilibrium when the market participants are price-anticipating and compute efficiently the resulting market allocation. Moreover, we explicitly characterize the bounds on the welfare loss and prices observed at the Nash equilibrium.