We present a simple model of research, in which it is possible to compare the cost of private versus public research activity. The principal aim is to find conditions under which private firms might decide to provide funding, partially or fully, for research carried out by public research organizations. Since the underlying research problem is given, differences in cost depend mainly on the contracts between the firm or the public organization on one side and the researchers employed in the project on the other, together with the incentives which are implied by these contracts. We find that under suitable assumptions it is advantageous for the private firm to outsource its research to a public organization. The free access for the general public to research results obtained by public research organizations may however be an obstacle to outsourcing, unless some public funding is forthcoming.