Can increasing market power cause a decrease in the aggregate savings? We answer this question by using a heterogeneous agents model that features both idiosyncratic labor and capital income risk. Under complete markets, the saving rate does not depend on the degree of market power, but when markets are incomplete, higher markups substantially reduce the aggregate saving rate. This is due to endogenous changes in the distribution of income and wealth. A calibration of the model using the observed changes in market power in the United States since the 1970s closely matches the decline in the US saving rate. Furthermore, when market power increases, the model generates distributional changes that are consistent with the data.