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This paper proposes a methodology for examining the effects of algorithmic recommendations on competition in product markets. It addresses concerns raised in both academic and policy circles about the potential anti-competitive impact of recommender systems (RSs). The analysis shows that RSs can increase market concentration, raise prices, and enable platforms to manipulate recommendations to their advantage. However, RSs can also have pro-competitive effects by enhancing the match between products and consumers and reducing the need for costly search. For reasonable parameter values, recommender systems are overall likely to lead to higher consumer surplus. However, increasing data available to the algorithms may result in reduced consumer surplus. We also explore the potential for manipulation of recommendations and its impact on competition, finding it more likely represents an exclusionary abuse than an exploitative one.