Understanding the precise nature of the trade-off requires a specific model. I study a monopolist's innovation policy in an infinite-horizon dynamic model with perfect capital markets. My model features an increasing-return-to-scale gross profit function and a convex adjustment cost of innovation. I first show that the optimal innovation policy can exist in this technology type and that the firm's innovative activity is higher in markets where the value of the existing product depreciates more slowly. I then introduce price-cap regulation into this market. When an antitrust agency attempts to keep the monopolist's price close to its competitive level, the effect on the consumer welfare is twofold. The price-reduction raises consumer welfare in the short run but it can also reduce the firm's incentive to innovate, which leads to less creation of new products and services in the market in the long run. As the consumer's interest in the monopolist's existing product gradually declines, so does market demand, unless new products are created. Therefore the price-cap regulation may in the long run harm the consumer welfare. I show that in markets where the value of the existing products depreciates slowly, the benefit of the price regulation tends to exceed its harmful effects. On the other hand, in markets where the value of the existing products depreciates quickly, the harm tends to outweigh the benefit.
In the appendix, I also study a second potentially harmful effect of price-cap regulation, namely that of depriving the firm of the funds it needs to finance its innovative efforts. That is, I study a firm's innovative activity in an imperfect capital market when its innovation is constrained by its internal funds. In this case, regulation slows down or even reduces the firm's access to internal funds and, hence, its ability to finance its innovative activity. This effect only compounds the results obtained in the body of the paper, which therefore hold regardless of whether capital markets are perfect or not.