TABLE 3.

Calibrating Optimal Internality Taxes on Cigarettes in the United States in the Presence of Hyperbolic Discounting

	Short-Term Discount Factor
	1a	0.9	0.8	0.6
Discounted health damages,b $	35.64	35.64	35.64	35.64
Fraction of discounted health damages ignored by hyperbolic discounters	0	0.1	0.2	0.4
Implied optimal internality tax, $	0.00	3.56	7.13	14.26
Implied optimal tax (offsetting externality + internality), $	0.40	3.96	7.53	14.66

Note. Tobacco taxes should offset externalities that tobacco users’ behavior imposes on society plus the internalities associated with difficulty in self-control. Taxes do not interfere with the component of use that reflects a personal preference, but do counter the considerable component of harm that arises from users overconsuming because they underestimate the magnitude of future costs of present actions.

Source. Adapted from Gruber and Köszegi, 2008.⁶

^aExponential discounting.

^bHealth costs reflect age-specific usage and the lower value placed on periods further into the future and were calculated in 6 steps: (1) assess the value of life, assuming that the main health damage from smoking is loss of life ($6.8 million); (2) assess the average loss of life for a smoker relative to the life expectancy of 79 years for nonsmokers (typically 6 years); (3) value the 6 extra years lost at the end of a smoker's life; (4) compute, for each year of life between 15 and 73, the discounted value of 6 years of life lost with a discount factor of 3% (i.e., the mortality cost at each age); (5) adjust mortality cost incurred by a smoker at each age by the fraction of cigarettes smoked at that age; (6) divide the costs of lifetime cigarette consumption by the average number of cigarettes smoked for a cost per pack of $35.64.