In this paper we explore the link between monetary policy and market power. We start by establishing several facts on market power in UK markets using micro data. First, while no clear trend emerges for market concentration, market power measured by markups estimated at the firm level have clearly increased in recent years, with the rise being reasonably broad-based across sectors. Second, we show that the increase is heavily concentrated in the upper tail of the distribution -companies whose mark-ups are in, say, the top quartile. Third, internationally-oriented firms are the driving force behind the rise in markups. Fourth, following Díez et al (2018), we find some reduced-form evidence of a non-monotonic relation between markups and investment at the firm level, with high levels of markups being associated with lower investment. Having established these facts, we show that the Phillips curve becomes steeper in the textbook New Keynesian model when firms tend to have more market power, reducing the sacrifice ratio for monetary policy. As inflation becomes less costly in an economy with high market power, however, the optimal targeting rule for monetary policy also changes. A rise in both the trend and volatility of mark-ups may lead to a significant rise in inflation variability. But a secular rise in mark-ups by itself improves monetary policy's ability to stabilise inflation without inducing large movements in output.

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