In the 1920’s, General Motors purchased its auto bodies from an independent firm, Fisher Body. GM decided to build a new plant and, in order to improve the reliability of supply and also to decrease shipping costs, GM asked Fisher Body to build a new auto body plant adjacent to GM’s new assembly plant. Fisher refused. We’ll explore why using a simple dynamic game. Suppose the new investment cost $2 (in millions) and would create potential gains from trade of $4 between GM and Fisher (not including the investment cost). Once the investment has been made, it is a sunk cost, so the $4 in GFT after the investment has been made is up for grabs. GM, player 2, can be a Tough Bargainer (TB) or a Fair Bargainer (FB), as illustrated in Figure 2.

(a) Find the subgame perfect Nash equilibria by backward induction. Use your solution to explain the “holdup problem” that Fisher Body faced.

(b) The possibility of an underdevelopment trap: One solution to the holdup problem is vertical integration (e.g., eventually GM purchased Fisher Body). But sometimes this is impossible. Suppose now that player 1 is a rich country considering making direct foreign investment in an underdeveloped country (player 2). Use the holdup problem to explain why the poor country may remain underdeveloped.