THE INTEGRATED FIRM (DN p. 309). If the two firms were merged, so they knew each other's costs, then they would put up the initial money, and then decide whether to go on with the project depending on whether the completion costs added up to 39.
CONTRACT 1 (DN p. 312). Each firm covers its initial costs, and if they both agree to go on, their announced completion costs are paid to each firm out of the revenue. What is left of the revenue is split in a 2:1 ratio for Hardware: Software (since Hardware has higher costs).
Problem. Each firm has some incentive to inflate its costs, and get reimbursed for more than its actual cost. Hardware won't alway claim costs of 30, because then Software would give up on the project, but Hardware will claim costs of 24 when its costs are really 18. Software has the same perverse incentives. Foreseeing this, the firms won't want to pay the initial R+D costs.
CONTRACT 2 (DN p. 313). Each firm covers its initial costs, and if they both agree to go on, each pays its own completion costs. They split revenues 2:1.
Problem. Software gets only 1/3 of the 39 revenue, which is 13. This means that if its costs are 15, it would cancel the project. That is inefficient if Hardware has costs of 18, because completing the project would be profitable overall. An integrated firm would complete it, but the joint venture wouldn't, so the joint venture has lost some potential profit.
CONTRACT 3 (DN p. 318). Use the tables on p. 318 or 319 to compensate each firm. This, it turns out,will induce each of them to tell the truth. The numbers are carefully chosen to satisfy truth- choice ("incentive compatibility") and participation constraints, but the method is too complicated to be worth going over in this class. The idea is to set up the payoffs so that each firm is (a) afraid to inflate its costs because that will kill the project; but (b) afraid to deflate its costs, because that will make the project go on but not generate enough profit for the firm.
Problem. It's hard to figure out the tables on pp. 318-319. But I wanted you to know that fancy incentive schemes exist that can sometimes improve over Contract 2.