In the late 1960s, Ford needed a car to compete with subcompacts from Volkswagen and Japanese car companies, so they rushed the Pinto into production. The major problem was that the machines for making the Pinto were set up before the Pinto had been fully tested and designed. Engineers were fully aware of a faulty bumper and gas tank that would easily leak fuel and explode from fairly weak rear-end impacts and often stick the doors of the car shut, but they were given strict weight and cost requirements for the car and could not add safety features, even inexpensive ones. The best method for protecting the gas tanks using a patent Ford owned and used on other cars in its line was estimated by Ford to cost $11 per car. (Later estimates ran as low as $5.06 or even $1 for a simple plastic barrier that would have prevented thousands of deaths.) In a memo, Ford explicitly compared the $11 per car cost to the costs it expected from deaths and injuries related to the defect ($200,000 per death) and put the car into production without fixing the defective fuel tank. Later on, it became clear that Ford has seriously miscalculated the number of injuries the car would cause and burn victims began to win large settlements from the company. However, it was still more profitable to manufacture the car instead of recalling it, and Ford manufactured the Pinto until it was finally ordered to recall in 1978.

a) What is the maximum value for the probability of a death caused by this defect for which Ford would have determined that it was less costly to produce the car as it was rather than pay the $11 to protect the gas tanks? Show your calculations.

b) True or false: If Fords estimate had been correct, continuing to produce the Pinto would have been socially efficient. Explain your reasoning.