Empathy is an emotion that plays a key role in emotional understanding and perspective-taking, and has been identified as a strong motivator for prosocial behavior. We explore people's intuitive theory of empathy, focusing more specifically on the role that the concept of empathy plays in people's causal model of prosocial behavior. We suggest that people implicitly think of empathy as indexing the weight that the actor puts on the welfare of the recipient when deciding whether to help. We test this proposal by asking participants (N=150) to read a series of vignettes in which an actor has the opportunity to help a recipient in need. We find that participants have a robust expectation that actors who feel empathy for the recipient are more likely to help. Furthermore, participants seem to expect that actors who feel empathy are more sensitive to the potential benefits of an action when deciding whether to help. We also test if people can `invert' this intuitive theory to make inferences about an actor's empathy, given their observable behavior. We find only weak evidence that they can do so, although this might be due to limitations in our experimental design. Overall, our work is a first step toward elucidating the computational principles underlying laypeople's conception of empathy.