The efficient use of natural resources is considered a necessary condition for their sustainable use. Extending the lifetime of products and using resources circularly are two popular strategies to increase the efficiency of resource use. Both strategies are usually assumed to contribute to the eco-efficiency of resource use independently. We argue that a move to a circular economy creates opportunity costs for consumers holding on to their products, due to the resource embedded in the product. Assuming rational consumers, we develop a model that determines optimal replacement times for products subject to minimizing average costs over time. We find that in a perfectly circular economy, consumers are incentivized to discard their products more quickly than in a perfectly linear economy. A direct consequence of our finding is that extending product use is in direct conflict with closing resource loops in the circular economy. We identify the salvage value of discarded products and technical progress as two factors that determine the impact that closing resource loops has on the duration of product use. The article highlights the risk that closing resource loops and moving to a more circular economy incentivizes more unsustainable behavior.