How Fast to Drive? Suppose Duke is driving to a nearby town to attend a dance party, and must decide how fast to drive. The marginal benefit of speed is the extra dance time he will get by driving faster, and the marginal cost is the additional risk of a collision.

The marginal-benefit curve is negatively sloped, and the marginal-cost curve is positively sloped.

a. Draw a pair of curves that suggest Duke will drive 40 mph.

b. Suppose the normal country band is replaced by Adam Smith and the Invisible Hands, Duke’s favorite punk band. Duke’s utility from slam dancing is twice his utility from the two-step. Use your curves to show how Duke’s chosen speed will change.

c. Suppose Duke’s favorite dance partner, Daisy, is grounded for makeup violations. Use your curves to show how Duke’s chosen speed will change.

d. Suppose the legal speed limit is set at 35 mph, and there is a 50 percent chance that Duke will be caught if he speeds. Use your curves to show how Duke’s chosen speed will change.