A utility-theory analysis of automobile speed under uncertainty of enforcement

Highway automobile speed and uncertain enforcement of the speed limit are introduced into a standard household utility model having time and income constraints. Due to uncertainty, expected utility is maximized to obtain the optimal speed (in excess of the speed limit). The optimal amounts of all other commodities and travel are also obtained. The key feature of the model is the risk attitude of the driver and the effect on optimal speed of such attitude. A related feature is the effect of risk attitude on the amount of speed self-insurance. An important finding is that the risk avert (seeking, neutral) driver charges himself an insurance premium that is larger than (smaller than, equal to) what is actuarially sufficient. The relationship between speed, risk attitude, and efficient cost of automobile travel is developed and implications are explored. A parametric analysis is conducted to establish the effect on optimal speed (and other variables) of changes in such policy instruments as the price of gasoline, the probability of being caught exceeding the speed limit, the unit speed fine, and the speed limit. Policy implications of the theoretical results are part of the conclusions.