As credit constraints exclude some firms from external finance and thus from market entry, they affect prices and markups by altering the degree of competition. Lower credit constraints allow less productive firms to enter with the following consequences. On the one hand, more competition tends to reduce average prices, but on the other hand, less productive firms charge above‐average prices. The overall effect is thus ambiguous. We therefore formulate and structurally estimate a quantitative multi‐country version of the model to gauge the direction and magnitude of the effects of credit constraints in a model with variable firm‐specific markups over marginal costs. In a sample of 11 European countries’ manufacturing sectors between 2000 and 2005, we find that an abolishment of credit constraints reduces markups by about 6.1% on average, while average prices are predicted to increase by 1.6%. The latter indicates that the effect of credit constraints on productivity dominates the one on competition.