Dear Economist,

为什么我要洗车呢？明天它就又脏了！

Why should I wash my car? It will be dirty again tomorrow!

克里斯o史密斯(Chris Smith)

Regards,


汉普郡

Chris Smith,Hampshire


亲爱的克里斯：

Dear Chris,

那么，你为什么非得刷牙呢？它们明天也会再变脏。这种争论可能会打动某些多愁善感的哲学家，但经济学家会给出清楚的建议。你无法使自己的车保持得完全像你想象的那么干净，所以必须在洗车的成本与让车太脏的成本之间找到平衡。

Why, indeed, should you brush your teeth? They, too, will be dirty tomorrow. Such arguments may impress a certain melancholy¹ breed of philosopher, but economics offers clear advice. You cannot keep your car exactly as clean as you would want, so must balance the costs of washing it against the costs of having it too dirty.


想想一个类似的问题：在你的钱包里放多少钱合适？放的太多，会有被盗或遭遇通货膨胀的风险。放的太少，要钱包就没有用。由于取现有点儿麻烦，理性消费者会取出超过理想数额的钱，逐渐把它们花掉，直到钱少于理想数额，然后再往钱包里放钱。 Consider an analogous² problem: how much money to keep in your wallet? Too much and you will suffer from theft or inflation. Too little and the wallet serves no purpose. Since it is troublesome to obtain cash, the rational customer will take out more than is ideal, gradually spend the money until there is less than ideal, and then replenish³ the wallet.


一段时间内持有现金数额的曲线，会像锯齿一样，有规律地上升和下降。如今既然我们有了自动取款机，提现就变得更容易了，所以我们这么做的频率上升了，使现金余额更趋近于最优数额，这样"锯齿"就被很完美地抹去了。

A graph of cash held over time would look like a sawtooth, regularly leaping up and sloping down. Now that we have ATMs it is easier to get cash, we do so more often, hold cash balances closer to the optimum, and the saw is finely grained.


这种锯齿模型可以用到更广泛的领域。例如，它解释了你为什么应该--像许多人所做的那样--把头发剪得过短，这样在头发长出来时，平均长度就与应该的长度差不多。 The sawtooth model applies more widely. It explains, for example, why you should - as many people do - cut your hair too short, so that as it grows it is on average the correct length.


至于你的车，你必须找出一种办法，把它洗得比你理想中的状况干净，考虑到你的问题，这应该不难。考虑一下包括打蜡和地毯香波的一整套洗车服务吧。在清洗后一、两周内，车会干净得要死，甚至让你有点儿不好意思，然后你将不耐烦地等着它开始变脏。

As for your car, you must find a way to wash it so that it is cleaner than you would ideally like, which considering your question should not be difficult. Consider a full service wash with wax and carpet shampooing. The car will be so extravagantly⁴, embarrassingly clean that for a week or two after the wash you will be waiting impatiently for the dirt to begin accumulating.