We construct a growth model with status preference to explore the effects of patents on innovation and social welfare. We find a nonmonotonic effect of patent protection on innovation. Additionally, the growth-rate-maximizing degree of patent protection decreases when the strength of status preference is larger. The effect of patent protection on social welfare is ambiguous, depending on the strength of status preference. Moreover, wealth inequality widens as patent protection is reinforced. Finally, by using cross-section regression analysis, we document that a nonmonotonic relationship between patent protection and economic growth is statistically significant and that the growth-rate-maximizing degree of patent protection decreases with the strength of status preference.