Dialogue Acts play an important role in conversation modeling. Research has shown the utility of dialogue acts for the response selection task, however, the underlying assumption is that the dialogue acts are readily available, which is impractical, as dialogue acts are rarely available for new conversations. This paper proposes an end-to-end multi-task model for conversation modeling, which is optimized for two tasks, dialogue act prediction and response selection, with the latter being the task of interest. It proposes a novel way of combining the predicted dialogue acts of context and response with the context (previous utterances) and response (follow-up utterance) in a crossway fashion, such that, it achieves at par performance for the response selection task compared to the model that uses actual dialogue acts. Through experiments on two well known datasets, we demonstrate that the multi-task model not only improves the accuracy of the dialogue act prediction task but also improves the MRR for the response selection task. Also, the cross-stitching of dialogue acts of context and response with the context and response is better than using either one of them individually.