花旗總管Mohammed Apabhai的一篇神文，他在上周四奇跡般地押中了特朗普的關稅稅率安排，華爾街甚至有人覺得Mohammed是不是拿到了什么內幕消息..

全文共三部分，精校會在這幾天陸續發出，

本文是第一部分，大家撥冗閱讀。

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.

在特朗普總統預計于4月2日宣布關稅措施之前，本文探討了可能的結果，并提出了一個分析特朗普決策過程的框架。

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?

假設兩個人在玩一個游戲——A得到了一百美元，但必須與B分享。A提出給B多少錢的建議，B可以選擇接受或拒絕。

如果B接受，雙方將按約定金額獲得各自的錢；如果B拒絕，則雙方都得不到任何錢。那A應該提出多少金額的分配才合理？

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.

這個問題在數學上是個很有趣的案例——經濟學中最精彩的部分永遠是數學。乍一看，似乎“公平”的提議應該是五五分成。但一旦意識到B手頭一無所有，那么即使只得到1美元，他的處境也比最初更好。

按照納什均衡的理論，A最優的選擇是提出一個盡可能低的金額。

然而，如果B意識到A將帶走絕大部分的錢，這種不公感可能會促使他拒絕提議，因為他知道這樣會對A造成更大的損失。

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.

這一“最后通牒問題”是一個引人入勝的研究領域，廣泛應用于保險理賠、工資談判，尤其是與我們關系最密切的貿易戰。

保險公司通常只提供約11%的理賠金額，這種策略依賴于索賠人急需財務救濟、希望盡快了結問題的心理，以及保險公司自身強大的財務能力，從而壓低報價。在某些效用函數條件下可以證明，A提出并被B接受的最優金額是30美元。任何低于30美元的報價往往會被拒絕，因為它會引發強烈的不滿情緒。

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.

我們在全球范圍內對上百甚至上千名觀眾重復了這個實驗（在達成交易時必須真的送出不少錢），結果顯示各國和各行業之間的差異十分明顯。

馬來西亞的參與者尤其愿意達成公平交易，醫療行業的從業者也傾向于提出50%的對半分成。律師通常提出大約30%的分配，而金融從業者則傾向于低于30%（很多時候甚至不到10%），并且他們遭遇交易被拒絕的比例最高。

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.

在中美貿易爭端的背景下來看這一問題尤其有趣。

當我們觀察雙邊貿易份額時會發現，自2008年全球金融危機以來，美國的平均份額僅為21.1%，這在一定程度上引發了“不公平”的情緒。

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年美中達成的貿易協議原意在于糾正這一失衡局面。但該協議顯然未能奏效——特朗普總統離任時，美國在雙邊貿易中的份額僅從2018年的18.2%升至2020年的22.4%；而到拜登總統任期結束時，這一比例也僅升至24.5%。長期的低占比令美國產生了持續的不滿情緒。

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.

奧巴馬、特朗普與拜登政府在遏制貿易逆差和提升美方貿易份額方面的表現可謂好壞參半。從統計數據來看，這幾屆政府的政策效果差異甚微。

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.

特朗普總統對這一問題的回應是加征關稅。外界普遍認為他設定的關稅稅率純屬隨意——似乎只是隨口報出一串數字。然而，有跡象表明，情況可能并非如此，這些舉措背后或許存在一套系統性的考量。

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，美國自中國進口商品總額達4296億美元，而出口僅1397億美元，雙邊貿易總額為5693億美元，貿易逆差高達2899億美元。

此時關稅的意義不僅在于“征收了多少錢”，更值得關注的是它在誰身上生效。在這種背景下，關稅本質上被視為一種“美國稅”，2019年中國出口商被迫通過壓縮利潤來消化其中一部分，另一部分則由消費者承擔。至于新一輪關稅的最終負擔將由誰承擔，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.

如果將關稅納入“整體”貿易平衡的分析之中，就能看清真實的結構性問題。若要徹底消除對華貿易逆差，美國需要對所有中國出口商品征收67.5%的關稅——且假設中國不實施任何報復性關稅。

特朗普總統曾威脅以每月10%的速度遞增關稅，最高可達70%，其中多出的部分可能用于抵消中國的反制。

67.5%這個數字，就是理論上消除逆差所需的關稅水平。

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”.

特朗普總統于2月1日依據第14195號行政命令宣布對所有中國商品加征10%關稅，該政策覆蓋全部中國產品。

此次加征將美國在雙邊貿易中的占比從24.5%拉升至29.8%，略低于納什均衡所定義的“最低可接受區間”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.

中國方面迄今的報復措施是對大約200億美元商品加征平均12.5%的關稅，使美國在雙邊貿易中的份額達到29.7%。雖然加征的關稅規模本身并不顯著，但低于30%的占比意味著激發了美方的報復動機。

目前美國的份額仍處于29.7%，仍未達到滿意水平，不滿情緒依然存在。

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，美國隨后的加稅升級——將所有中國產品的關稅提高至20%——并不令人意外。目前，美國在雙邊貿易中的占比升至34.4%，處于“最低可接受”區間。但考慮到歷史失衡的背景、持續時間，以及特朗普當下的預期效用函數，這一水平仍難被視為“滿意”。

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.

美國很有可能對中國商品加征接近70%的關稅，以徹底消除貿易逆差——這將成為重新啟動貿易談判的一個“合理起點”。最終達成協議的位置，將取決于中美兩國領導人各自的效用函數。

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，美國似乎比中國更迫切地希望達成協議，即便條件并不理想。從這個角度來看，拜登在雙邊貿易中的做法在某些方面反而更接近“次優解”，盡管并不完全理性最優。

It is also instructive to look at the relationships with some of the other US trading partners with which it suffers large trade deficits.

觀察美國與其他存在較大貿易逆差的國家的關系，同樣具有啟發意義。

Of the top ten deficit countries, trade with Mexico and Canada is more balanced than with the others.

在十大逆差國中，美國與墨西哥和加拿大之間的貿易相較其他國家更加平衡。

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.

這意味著特朗普實際上正在將部分國家（如墨西哥、加拿大）作為“演練對象”，為未來瞄準越南、中國等更“大體量目標”做準備。在美方視角下，許多國家被劃入“可接受但并不公平”的范疇。

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.

值得進一步分析的是：要實現貿易關系再平衡，美國需要對各國商品加征的“理論關稅比例”。可以證明，所需比例等于美國的貿易逆差除以該國對美出口。

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%.

若要完全重構美墨關系，則需對墨西哥征收34%的關稅（前提是不遭報復）；對加拿大則為15.3%。假設無報復行為，對墨征收25%關稅會使美方在雙邊貿易中的份額升至47.6%；對加同樣比例，則美方份額為52.3%。若以北美自由貿易區（NAFTA）為整體，美國以25%關稅可將其在區域雙邊貿易中的份額恢復至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.

除中國67.5%的目標關稅外，模型預測美國可能對臺灣加征63.6%、對印度52.2%、對韓國50.2%、對日本46.2%的關稅——若遭報復，美國或進一步上調稅率以恢復貿易平衡。

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.

若按此關稅幅度全面實施，且不考慮國際貿易收縮影響，則理論上可帶來約1.3萬億美元的稅收。這一數字接近2025年美國預計財政赤字2.5萬億美元的一半——前提是這些關稅能夠真正成功落地。

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…

研究達到“最低30%可接受區間”所需的關稅水平也很有價值——這或可作為貿易談判的起點……

…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.

……不過必須指出，目前美國的目標似乎不是妥協性談判，而是徹底消除貿易逆差。

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…

特朗普政府最終可能會達成某種貿易協議，尤其考慮到特朗普個人在政治周期中對“成交”有較強訴求，即使協議條件并不理想……

…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.

雖然當下尚未走到這一步，但若市場變化顯著影響其“效用曲線”，多數國家可能有機會通過談判削弱關稅壓力。交易遲早會達成——雖然還不是現在，但在合適的市場條件下，終將實現。

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.

貿易戰的直接影響是減少雙邊貿易。特朗普總統第一任期內的貿易戰導致雙邊貿易總量下降15.8%。預計新一輪貿易戰將更為激烈，可能使雙邊貿易減少25%，而中國及其他美國主要貿易伙伴將首當其沖。在上一次貿易戰中，中國對美出口下降了16.8%，而美國對華出口僅下降11.4%。

This can be analysed through the perspective of Rubinstein Bargaining, a simple game of alternating offers bargaining with a costly delay.

這一現象可以通過“魯賓斯坦議價”（Rubinstein Bargaining）的視角來分析，它是一種帶有延遲成本的交替出價博弈模型。

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.

與“最后通牒博弈”類似，100美元將在兩方之間分配，但若提議被拒，則將產生一定的“懲罰性成本”，即100美元的總價值會隨時間貶值，直到最終歸零。

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.

隨著貿易戰的演進，后續文章將深入分析這一模型。這里只需指出，魯賓斯坦在1982年的論文中已證明，確實存在最優解。

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?

那么關稅究竟有效嗎？為了理解這個問題，需要換個方式來看：你愿意花5美元買一塊價值10美元的巧克力，還是免費拿一塊價值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.

顯然，10美元的巧克力具有更高的經濟價值，但從理論與實證實驗都可以證明，約81.6%的人會選擇那塊免費但價值較低的巧克力。這與“免費理論”（Theory of Free）密切相關，影響范圍從醫療服務到廣告激勵，覆蓋廣泛。

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.

一旦必須為某物付費，我們的效用函數就會發生變化——若某物免費，人們通常會對“擁有與否”無感，但只要它未來可能有用，大多數人便會傾向于“先拿著再說”。

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.

這也許能解釋，為何美國乃至整個西方的許多家庭都堆滿了便宜、并不實用、但可能“某天會用得上”的中國產品。

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.

中國將這類商品定價在“零邊際效用值”區間，即消費者對是否擁有毫不在意——他們樂意花極低價格去買，只因“萬一有用”。

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.

若要令消費者擺脫這種“囤積式消費”，或停止購買這些“低效”產品，就必須將他們所支付的成本提升至“零邊際效用值”之上——這正是關稅可能發揮作用的經濟邏輯。

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.

要驗證這一點，可以觀察食品浪費現象：在俄烏沖突爆發前，食品價格低、供應充足，相對可支配收入來說極具可得性，因此浪費程度也偏高。

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年食品價格飆升后，食品浪費大幅減少——消費者不再無差別購入不需要的食品，消費變得更為理性與謹慎。

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.

從結構性角度看，長期減少貿易逆差的唯一路徑，是改變美國消費者的支出模式——關稅作為“價格杠桿”，可在其中發揮作用。

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.

當然，也存在一個根本性問題：是否有必要完全消除貿易逆差？許多出口國積累了大量美元儲備，這些美元被重新投入美債市場，從而壓制了美債收益率。

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.

若徹底消除貿易逆差，將減少這些美元儲備，進而推高債券收益率和美元匯率。我們將在后續文章中具體分析這一路徑對美債收益率的潛在影響。

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，我們將探討關稅對匯率市場和通脹的影響，嘗試回答兩個問題：貿易戰是否真能贏？是否存在一個所有參與方都可以接受的“最優解”？

明天會發第二部分的精譯，如果有幫助還請大家多多支持。

感謝閱讀！

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