Social Cost of Smoking for the 21st Century

Lung cancer became the leading cause of cancer deaths among males in Japan in 1993. Smoking is a major attributable risk of lung cancer. Many other diseases, such as cardiovascular and chronic obstructive respiratory disease are also related to the smoking habit. The Japanese government and the public will have to pay more social cost of smoking in the future. We estimated the social cost of smoking from 1990 to 2030 through computerized simulation introducing effective variables to assess the costs, such as medical treatment, loss of life, fire, etc. The stochastic process called Ito process and financial engineering techniques are employed for making the model. The result showed that the social cost of smoking is expected to grow and reach 2.01 and 3.32 times in the year of 2010 and 2030, respectively. Fifty percent reduction of tobacco consumption could not reduce the social cost, which still climbs up to mark 1.58 in 2020. Should Japan succeed in reducing tobacco consumption by 20% per annum starting from 1996, the social cost would peak out at 1.30 in 2001 and come down to 0.93 in 2030. We estimate that 11 trillion yen (US$ 110 billion) per annum of social cost can be saved in and around 2030 in this case. A proper development of medical economics and public health policy should be an important factor to bring fourth a sound and healthy society in the next century. J Epidemiol, 1995; 5 : 113-116.

In the U.S.A. cigarette smoking has been recognized as the most important public health issue since the 1970s. The cigarette consumption was decreased by 20% from 1980 to 1990, reflecting the fact that 20% of all the deaths are attributed to smoking1). Number of deaths from lung cancer attributed to smoking, however, increased from 85,000 to 120,000 (+41%) during the same period. The same tendency is observed in Japan. In spite of the saturation of tobacco consumption in recent years2), number of lung cancer deaths has been increasing3). In addition to the heavily painful feeling to the cancer patients and their family, their economic disadvantages are enormous. Tobacco is not an immediate poison, but its medical and social effect will appear creeping up after 20 years or mores4-6). Through these observations, the old hypothesis that tobacco's social cost is in proportion to its annual consumption was inadequate, so a new system model to forecast the social cost was elaborated.

MATERIALS AND METHODS
In order to properly assess the influence of tobacco on social cost, we have introduced a new concept of an "effective variable" , which represents tobacco's accumulated effect or inertia toward its social cost. This variable stands for an aggregate morbidity already residing in people's bodies in a nation. For example, tobacco, already consumed years ago, may still have influence over morbidity inside of the smoker's lungs. The effective variable S is a quantitative expression of the morbidity caused by smoking, and is defined as follows : time t, i.e. a degree of tobacco production plus net import into a nation. (t) is a degree of a disappearing morbidity at time t through disposal of unused tobacco and affected corpses. Burning of smoker's corpses diminishes accumulated smoking morbidity.
Regarding the content of the expenditure, the social cost is composed of two types of costs as follows : 1(S)+SC 2( , ) SC (t) : social cost total SC 1 : social cost dependent on accumulated smoking morbidity. SC 1 is defined as medical expense plus life insurance payout. SC 2 : social cost subject to annual tobacco consumption.
For this analyses, we confined the cost to be actually disbursed, but excluded such opportunity cost as lost income to be earned in the future. SC2 contains fire expense and fire insurance payout, which are obviously functions of tobacco consumption in a year itself. We have designed the system so that the social cost variables follow a stochastic process known as Ito process because of its strength that it can handle general formulae7-8).
For the calculation of number of deaths, the principle published by Hirayama and Maeda9) was employed, incorporating the recent information published by Bartecchi

RESULTS AND COMMENTS
Number of deaths attributed to smoking has been sharply increasing to 115,000 sharing 14% of all the Japanese mortality in 1990 (Table 1, Figures. 1 and 2). Number of deaths of cancer attributed to smoking reached 65,000 in 1990 ( Figure. 2).
The result of the simulation is shown in Figure. 3. The social cost of smoking is expected to grow from 1 in 1990 respectively, if any further action be not adopted. The future social cost will only be projected with probability at this stage. For example, the one sigma confidence interval in 2000 is between 1.407 and 1.542; i.e. the social cost is projected to fall in this interval with 68% of probability when the normal distribution is assumed. The volatility grows when time passes due to the nature of the Brownian movement. Expenditures for medical treatment and life insurance expand as time passes by due to the accumulated inertia of smoking, while expenditures for fires stay steady reflecting the saturation of tobacco consumption.
In order to assess the importance of the public health policy, the effect of public action on the problem is considered. A new variable P(t) was introduced, which represents people's action and public health policy toward this issue. Different from other endogenous variables, Year -W/O further action 50% cut and hold ... 20% p.a. cut

SC(t)=SC(S,
;l, p, P) P : "public action variable" to influence the cost.
Starting from 1996, we assume any kind of social consensus be obtained to reduce tobacco consumption to improve the public health status. The result of the social actions is shown in Figure. 3. If the tobacco consumption be reduced to a half, there would be a considerable improvement of the social cost from 2.63 to 1.58 in 2020. The social cost, however, would continue to rise gradually to mark 1.67 in 2030, and then peak out. If the consumption reduction be achieved by 20% per annum, the cost would peak out at 1.30 in 2001 with gradual improvement thereafter. In this case, the cost can be improved from 3.32 to 0.93 in 2030. This means that Y 11 trillion per annum of social saving could be achieved in Japan, assuming the current social cost of `-4.5 trillion in 1990. If Japan can invest the saved amount properly, ? 55 trillion of an additional gross national product (GNP) would be newly created assuming the marginal propensity to consume (mpc) of 80%ttl. Based on the theory of multiplier by Keynes, incremental GNP= investment X multiplier= l l/ (1-mpc)=55.
This accounts for 12% of the current GNP. In this way, Japan can become a healthier and wealthier nation without heavy pain nor burden.
(t) = Aexp(at) + Z clause (t) = A'exp(a't) + Z clause In the developed countries like Japan the above coefficient "a" is very close to zero . In the U.S.A. "a" has already turned to negative because of penetration of public health thought on the tobacco issue.
2. For the simulation, we have adopted the following formula.