We study how loyalty behavior of customers and differing costs to produce undifferentiated products by firms can influence market outcomes. In prior works that study such markets, firm costs have generally been assumed negligible or equal, and loyalty is modeled as an additive bias in customer valuations. We extend these previous treatments by explicitly considering cost asymmetry and richer customer loyalty behavior in a game-theoretic model. Thus, in the setting where firms incur different non-negligible product costs, and customers have firm-specific loyalty levels, we comprehensively characterize the effects of loyalty and product cost difference on market outcomes such as prices, market shares, and profits. Our analysis and numerical simulations provide new insights into how firms can price, how they can survive competition even with higher product costs, and how they can control these costs and/or increase customer loyalty to change their market position.