花旗总管Mohammed Apabhai的一篇神文，他在上周四奇迹般地押中了特朗普的关税税率安排，华尔街甚至有人觉得Mohammed是不是拿到了什么内幕消息..
全文共三部分，精校会在这几天陆续发出，
本文是第一部分，大家拨冗阅读。
Ahead of the expected announcement of tariffs by President Trump on 2 Apr we look at what could be expected and present a framework that examines the decision making process of President Trump.
在特朗普总统预计于4月2日宣布关税措施之前，本文探讨了可能的结果，并提出了一个分析特朗普决策过程的框架。
Imagine that two people are playing a game - person A has been given $100 but has to share that with person B. Person A makes the offer of how much to share with person B which can either be taken or rejected - if person B takes the offer both people get the amount of money they have agreed to. If person B rejects the offer then neither party gets anything. How much should person A offer?
假设两个人在玩一个游戏——A得到了一百美元，但必须与B分享。A提出给B多少钱的建议，B可以选择接受或拒绝。
如果B接受，双方将按约定金额获得各自的钱；如果B拒绝，则双方都得不到任何钱。那A应该提出多少金额的分配才合理？
The answer to this problem is an interesting problem in mathematics - the best part of economics is always mathematics. At first glance, it appears that the “fair” offer that should be made should be to split the money 50:50. Until it is realized that person B has got no money so even the offer of $1 leaves him better than where he starts off. The optimal Nash equilibrium is for person A to offer the smallest amount of money possible. However, if person B knows that person A is going to walk away with the bulk of the money, the sense of injustice may trigger person B to reject the offer because he knows he is causing more damage to person A.
这个问题在数学上是个很有趣的案例——经济学中最精彩的部分永远是数学。乍一看，似乎“公平”的提议应该是五五分成。但一旦意识到B手头一无所有，那么即使只得到1美元，他的处境也比最初更好。
按照纳什均衡的理论，A最优的选择是提出一个尽可能低的金额。
然而，如果B意识到A将带走绝大部分的钱，这种不公感可能会促使他拒绝提议，因为他知道这样会对A造成更大的损失。
This “ultimatum problem” is a fascinating area of study and has applications in many areas including insurance claims, wage negotiations and most importantly for us, trade wars. Insurance companies generally offer around 11% of the amount claimed relying on the claimant’s desperation for financial relief and for the problem to go away as well as their financial strength to low ball offers. Under certain utility conditions it can be shown that the optimal level for person A to offer and which person B will consider acceptable is $30. Anything below $30 tends to get rejected as it causes a sense of grievance.
这一“最后通牒问题”是一个引人入胜的研究领域，广泛应用于保险理赔、工资谈判，尤其是与我们关系最密切的贸易战。
保险公司通常只提供约11%的理赔金额，这种策略依赖于索赔人急需财务救济、希望尽快了结问题的心理，以及保险公司自身强大的财务能力，从而压低报价。在某些效用函数条件下可以证明，A提出并被B接受的最优金额是30美元。任何低于30美元的报价往往会被拒绝，因为它会引发强烈的不满情绪。
We have repeated this experiment with audiences of hundreds if not thousands of people around the world (having to give away a lot of money in the process when a deal is reached) and the differences in countries and professions is stark. Audiences in Malaysia in particular are willing to strike a fair bargain while healthcare workers also offer 50%. Lawyers generally tend to offer around 30% while those in finance tend to offer less than 30% (often less than 10%) and subsequently seem to have the highest proportion of deal rejections.
我们在全球范围内对上百甚至上千名观众重复了这个实验（在达成交易时必须真的送出不少钱），结果显示各国和各行业之间的差异十分明显。
马来西亚的参与者尤其愿意达成公平交易，医疗行业的从业者也倾向于提出50%的对半分成。律师通常提出大约30%的分配，而金融从业者则倾向于低于30%（很多时候甚至不到10%），并且他们遭遇交易被拒绝的比例最高。
It is interesting to see this within the context of the Sino-US trade dispute. When we look at the share of bilateral trade, we find that the US share has been averaging just 21.1% since the GFC triggering the sense of unfairness.
在中美贸易争端的背景下来看这一问题尤其有趣。
当我们观察双边贸易份额时会发现，自2008年全球金融危机以来，美国的平均份额仅为21.1%，这在一定程度上引发了“不公平”的情绪。
The trade agreement that was reached between the US and China in 2019 was aimed at redressing that imbalance. That agreement has clearly failed as the US share of bilateral trade has increased only from 18.2% in 2018 to 22.4% in 2020 when President Trump left office and had risen to only 24.5% when President Biden left office. The low share of bilateral trade has left the US with a sense of grievance.
2019年美中达成的贸易协议原意在于纠正这一失衡局面。但该协议显然未能奏效——特朗普总统离任时，美国在双边贸易中的份额仅从2018年的18.2%升至2020年的22.4%；而到拜登总统任期结束时，这一比例也仅升至24.5%。长期的低占比令美国产生了持续的不满情绪。
The track record of the Obama, Trump and Biden administrations, in terms of curbing the trade deficit and increasing the US share of bilateral trade is mixed. Statistically there appears to be little difference between any of the administrations.
奥巴马、特朗普与拜登政府在遏制贸易逆差和提升美方贸易份额方面的表现可谓好坏参半。从统计数据来看，这几届政府的政策效果差异甚微。
President Trump’s answer to the problem is the introduction of tariffs. It is often thought that the numbers that President Trump talks about are random - that he just pulls out some fairly random numbers for the tariff rates that he is setting. The evidence suggests that this may not be the case, that there may be a plan behind the action.
特朗普总统对这一问题的回应是加征关税。外界普遍认为他设定的关税税率纯属随意——似乎只是随口报出一串数字。然而，有迹象表明，情况可能并非如此，这些举措背后或许存在一套系统性的考量。
Last year the US imported $429.6bn of goods from China and exported only $139.7bn resulting in total bilateral trade of $569.3bn and a trade deficit of $289.9bn. It is instructive to look not only at how much the application of tariffs would raise - in this context tariffs are seen as a US tax which would fall partly on the Chinese exporter who in 2019 was forced to absorb them by cutting their margins and partly by the consumer. It is unclear at this moment where the burden of the new round of tariffs will fall.
去年，美国自中国进口商品总额达4296亿美元，而出口仅1397亿美元，双边贸易总额为5693亿美元，贸易逆差高达2899亿美元。
此时关税的意义不仅在于“征收了多少钱”，更值得关注的是它在谁身上生效。在这种背景下，关税本质上被视为一种“美国税”，2019年中国出口商被迫通过压缩利润来消化其中一部分，另一部分则由消费者承担。至于新一轮关税的最终负担将由谁承担，目前仍不明朗。
Now if we look at the “whole” trade balance including the tariffs we start to see what is happening. To completely eliminate the trade deficit with China, the US would need to impose a 67.5% tariff on all Chinese exports – with no retaliatory tariffs from China. President Trump has threatened to impose escalating tariffs of 10% per month up to a maximum of 70% (link), with the remainder likely to compensate for Chinese retaliation. This is the number needed to eliminate the US trade deficit with China.
如果将关税纳入“整体”贸易平衡的分析之中，就能看清真实的结构性问题。若要彻底消除对华贸易逆差，美国需要对所有中国出口商品征收67.5%的关税——且假设中国不实施任何报复性关税。
特朗普总统曾威胁以每月10%的速度递增关税，最高可达70%，其中多出的部分可能用于抵消中国的反制。
67.5%这个数字，就是理论上消除逆差所需的关税水平。
The 10% tariff on all Chinese goods that President Trump announced on 1 Feb under Executive Order 14195 applies to all Chinese imports. The 10% tariff had the effect of rebalancing the US portion of bilateral share from 24.5% to 29.8%, just under the 30% minimum that the Nash equilibrium would have deemed as the “minimum acceptable”.
特朗普总统于2月1日依据第14195号行政命令宣布对所有中国商品加征10%关税，该政策覆盖全部中国产品。
此次加征将美国在双边贸易中的占比从24.5%拉升至29.8%，略低于纳什均衡所定义的“最低可接受区间”30%。
Chinese retaliation so far has targeted an average of 12.5% tariffs on around $20bn of goods, taking the US share of bilateral trade to 29.7%. The small amount of tariff that it raised was hardly worth it, but falling below 30% meant that it invited US retaliation. The US share of bilateral trade is currently 29.7%, which is still not enough – the sense of grievance continues.
中国方面迄今的报复措施是对大约200亿美元商品加征平均12.5%的关税，使美国在双边贸易中的份额达到29.7%。虽然加征的关税规模本身并不显著，但低于30%的占比意味着激发了美方的报复动机。
目前美国的份额仍处于29.7%，仍未达到满意水平，不满情绪依然存在。
It was for this reason that the next round of tariffs, which raised the levy to 20% on all Chinese imports, was not a surprise. The US now has 34.4% of bilateral trade which is in the minimum acceptable zone but given the past history and duration of the imbalance, as well as President Trump’s current expected utility function, this is unlikely to be satisfactory.
正因如此，美国随后的加税升级——将所有中国产品的关税提高至20%——并不令人意外。目前，美国在双边贸易中的占比升至34.4%，处于“最低可接受”区间。但考虑到历史失衡的背景、持续时间，以及特朗普当下的预期效用函数，这一水平仍难被视为“满意”。
It is quite likely that the US will impose tariffs of close to 70% on Chinese goods to eliminate the trade deficit – that would then provide a good starting point to start trade negotiations. The actual point of agreement will depend on the individual utility functions of the respective leaderships in China and the USA.
美国很有可能对中国商品加征接近70%的关税，以彻底消除贸易逆差——这将成为重新启动贸易谈判的一个“合理起点”。最终达成协议的位置，将取决于中美两国领导人各自的效用函数。
So far it would seem that the USA is keener to reach an agreement than China, even if it is a “bad” agreement. From that perspective the Biden approach to bilateral trade was, in some ways, more (although not quite) optimal.
截至目前，美国似乎比中国更迫切地希望达成协议，即便条件并不理想。从这个角度来看，拜登在双边贸易中的做法在某些方面反而更接近“次优解”，尽管并不完全理性最优。
It is also instructive to look at the relationships with some of the other US trading partners with which it suffers large trade deficits.
观察美国与其他存在较大贸易逆差的国家的关系，同样具有启发意义。
Of the top ten deficit countries, trade with Mexico and Canada is more balanced than with the others.
在十大逆差国中，美国与墨西哥和加拿大之间的贸易相较其他国家更加平衡。
What this suggests is that President Trump is using this as a “dry run” against relatively soft targets before moving onto the bigger targets like Vietnam, China. Most of the other countries are in the “acceptable but not fair” categorization.
这意味着特朗普实际上正在将部分国家（如墨西哥、加拿大）作为“演练对象”，为未来瞄准越南、中国等更“大体量目标”做准备。在美方视角下，许多国家被划入“可接受但并不公平”的范畴。
It is also instructive to look at the percentage tariffs needed on each country to rebalance the trade relationship. It can be shown that to rebalance trade requires a tariff percentage equal to the US trade deficit / imports.
值得进一步分析的是：要实现贸易关系再平衡，美国需要对各国商品加征的“理论关税比例”。可以证明，所需比例等于美国的贸易逆差除以该国对美出口。
To completely rebalance the relationship requires tariffs of 34% on Mexico with no retaliatory tariffs and 15.3% on Canada. The 25% tariff on Mexico gives the USA 47.6% of bilateral trade assuming no retaliation and with Canada gives 52.3% of bilateral trade – taken as a NAFTA block the 25% tariffs restores the US share of bilateral trade to 49.8%.
若要完全重构美墨关系，则需对墨西哥征收34%的关税（前提是不遭报复）；对加拿大则为15.3%。假设无报复行为，对墨征收25%关税会使美方在双边贸易中的份额升至47.6%；对加同样比例，则美方份额为52.3%。若以北美自由贸易区（NAFTA）为整体，美国以25%关税可将其在区域双边贸易中的份额恢复至49.8%。
Outside of China’s 67.5% tariffs, we expect tariffs of 63.6% on Taiwan, 52.2% on India, 50.2% on South Korea and 46.2% on Japan – retaliation will cause an increase in the US tariffs as it attempts to restore balance.
除中国67.5%的目标关税外，模型预测美国可能对台湾加征63.6%、对印度52.2%、对韩国50.2%、对日本46.2%的关税——若遭报复，美国或进一步上调税率以恢复贸易平衡。
Tariffs of this magnitude, if applied in full, would raise $1.3tn assuming no drop in international trade. This is to be compared to the projected US fiscal debt in 2025 of $2.5tn. Tariffs of this magnitude would fund over half the fiscal debt – if they could be successfully applied.
若按此关税幅度全面实施，且不考虑国际贸易收缩影响，则理论上可带来约1.3万亿美元的税收。这一数字接近2025年美国预计财政赤字2.5万亿美元的一半——前提是这些关税能够真正成功落地。
It is also instructive to see the level of tariffs needed to get to the minimum 30% acceptable region which could be the basis for trade negotiations…
研究达到“最低30%可接受区间”所需的关税水平也很有价值——这或可作为贸易谈判的起点……
…although we have to caution that at this stage it does not appear that the US is going for anything other than a complete elimination of the trade deficit.
……不过必须指出，目前美国的目标似乎不是妥协性谈判，而是彻底消除贸易逆差。
It is possible that the Trump administration will do a deal on trade, especially given the seeming need for President Trump to achieve a deal, no matter how bad it is…
特朗普政府最终可能会达成某种贸易协议，尤其考虑到特朗普个人在政治周期中对“成交”有较强诉求，即使协议条件并不理想……
…we are not there yet but especially if market movements impact his utility curve most countries may get away by negotiating away the tariffs. A deal is there to be done – not yet but under the right market conditions.
虽然当下尚未走到这一步，但若市场变化显著影响其“效用曲线”，多数国家可能有机会通过谈判削弱关税压力。交易迟早会达成——虽然还不是现在，但在合适的市场条件下，终将实现。
The impact of a trade war is to reduce bilateral trade. The trade war during President Trump’s first term reduced bilateral trade by 15.8%. We would expect this trade war to be more ferocious, reducing bilateral trade by 25%, with the brunt of the impact falling on China and other US trading partners. In the first term, the trade war resulted in a 16.8% drop in Chinese exports to the US but only an 11.4% drop in US exports to China.
贸易战的直接影响是减少双边贸易。特朗普总统第一任期内的贸易战导致双边贸易总量下降15.8%。预计新一轮贸易战将更为激烈，可能使双边贸易减少25%，而中国及其他美国主要贸易伙伴将首当其冲。在上一次贸易战中，中国对美出口下降了16.8%，而美国对华出口仅下降11.4%。
This can be analysed through the perspective of Rubinstein Bargaining, a simple game of alternating offers bargaining with a costly delay.
这一现象可以通过“鲁宾斯坦议价”（Rubinstein Bargaining）的视角来分析，它是一种带有延迟成本的交替出价博弈模型。
The $100 is to be divided between the two players as in our Ultimatum Game, but if the offer is rejected then there is a financial penalty that is paid and the $100 reduces to some lower value until eventually it drops to zero.
与“最后通牒博弈”类似，100美元将在两方之间分配，但若提议被拒，则将产生一定的“惩罚性成本”，即100美元的总价值会随时间贬值，直到最终归零。
We will examine this in more detail as the trade war evolves. Suffice it to say that the 1982 paper by Rubinstein suggests that an optimal solution does exist.
随着贸易战的演进，后续文章将深入分析这一模型。这里只需指出，鲁宾斯坦在1982年的论文中已证明，确实存在最优解。
So will tariffs work? To understand this we need to play another game. Would you prefer a $10 chocolate for $5 or a $3 chocolate for nothing?
那么关税究竟有效吗？为了理解这个问题，需要换个方式来看：你愿意花5美元买一块价值10美元的巧克力，还是免费拿一块价值3美元的？
Clearly the $10 chocolate offers the higher economic value but theoretically as well as experimentally it can be shown that approximately 81.6% of people will take the $3 chocolate – it is to do with the “Theory of Free” which has implications for everything from healthcare services to advertising incentives.
显然，10美元的巧克力具有更高的经济价值，但从理论与实证实验都可以证明，约81.6%的人会选择那块免费但价值较低的巧克力。这与“免费理论”（Theory of Free）密切相关，影响范围从医疗服务到广告激励，覆盖广泛。
Our utility function changes as soon as we need to pay for something – if something is free then we are invariant between having it or not having it and if it may potentially prove useful at some point in the future, we seem to prefer to have it.
一旦必须为某物付费，我们的效用函数就会发生变化——若某物免费，人们通常会对“拥有与否”无感，但只要它未来可能有用，大多数人便会倾向于“先拿着再说”。
This probably explains why most households in the US and in the West more generally are full of cheap, fairly useless, Chinese products that may potentially be useful one day.
这也许能解释，为何美国乃至整个西方的许多家庭都堆满了便宜、并不实用、但可能“某天会用得上”的中国产品。
China has priced these goods at a “zero marginal utility value” where consumers are invariant to owning or not – consumers are happy to pay a minimal amount for something just in case it comes in useful some day.
中国将这类商品定价在“零边际效用值”区间，即消费者对是否拥有毫不在意——他们乐意花极低价格去买，只因“万一有用”。
To get them away from this and to stop them from purchasing these “useless” products, what needs to be done is to raise the cost that the consumer pays above the “zero marginal utility value”. This is potentially what tariffs might do.
若要令消费者摆脱这种“囤积式消费”，或停止购买这些“低效”产品，就必须将他们所支付的成本提升至“零边际效用值”之上——这正是关税可能发挥作用的经济逻辑。
To see an example of this at work, we can look at food wastage. When food is cheap and plentiful relative to disposable income, as it was before the Ukraine conflict, food wastage was relatively high.
要验证这一点，可以观察食品浪费现象：在俄乌冲突爆发前，食品价格低、供应充足，相对可支配收入来说极具可得性，因此浪费程度也偏高。
The sharp rise in food prices in 2022 resulted in a drop in food wastage as consumers were no longer invariant to buying food that they did not need and were more discerning in their purchases.
2022年食品价格飙升后，食品浪费大幅减少——消费者不再无差别购入不需要的食品，消费变得更为理性与谨慎。
Structurally the only long term way to reduce the trade deficit seems to be to change the spending patterns of US consumers – and tariffs can play a role in doing that by raising prices.
从结构性角度看，长期减少贸易逆差的唯一路径，是改变美国消费者的支出模式——关税作为“价格杠杆”，可在其中发挥作用。
There is of course the question about whether eliminating the trade deficit completely is desirable. Many of the exporting countries have run up large reserves of USD which have been re-circulated into the purchase of Treasuries which has kept a cap on yields.
当然，也存在一个根本性问题：是否有必要完全消除贸易逆差？许多出口国积累了大量美元储备，这些美元被重新投入美债市场，从而压制了美债收益率。
Eliminating the trade deficit would reduce these reserves, causing bond yields and the USD to go even higher. We will work out the impact that eliminating the trade deficit would have on bond yields in a future piece.
若彻底消除贸易逆差，将减少这些美元储备，进而推高债券收益率和美元汇率。我们将在后续文章中具体分析这一路径对美债收益率的潜在影响。
In our next piece we will look at the impact of tariffs on currency markets and inflation and suggest how a trade war can be winnable but also whether an optimal solution that can be acceptable to all parties exists or not.
在下一篇文章中，我们将探讨关税对汇率市场和通胀的影响，尝试回答两个问题：贸易战是否真能赢？是否存在一个所有参与方都可以接受的“最优解”？
明天会发第二部分的精译，如果有帮助还请大家多多支持。
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