US President Donald Trump and Chinese President Xi Jinping during the G20 summit in Osaka, Japan. AP

In all the chaos of markets convulsing and tariffs rising, it's been easy to forget the main objectives of the US's trade war with China.

And in doing so, it's easy to forget that those objectives are at odds with one another.

On the one hand, you have US Trade Representative Robert Lighthizer and his stated aim of turning China into a market-based economy. On the other hand, you have Donald Trump, a populist obsessed with forcing China to buy more goods - a market-distorting demand.

This inconsistency has seriously hurt negotiations and contributed to putting China in a position where it cannot simply lose to Trump. Under these conditions, a stalemate is the best we hope for.

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The markets have been a whipsaw, the US economy has slowed down, and one report suggests that US companies shed 10,488 jobs because of the trade war between the US and China - a trade war that has worsened over the past few weeks.

So the two sides have laid down their arms and agreed to a cease-fire in hopes of creating the conditions that will make it possible for discussions to resume in October.

Unfortunately, those talks, should they ever occur, will achieve little aside from temporarily calming financial markets. Donald Trump's trade war is a trade war that cannot be won.

The reality is that from the start, the objectives of Donald Trump's trade war have been at odds with one another, making it impossible for his administration to construct a deal that one might consider a win for US markets.

What's more is that throughout this process, Trump's conflicting demands and brutish tactics have put Chinese President Xi Jinping in a position where he and his administration cannot concede.

So we had better hope this cease-fire lasts beyond Trump's next tweetstorm, because it's about as good as things are going to get.

Why Trump can't win

Before we get into any of this, let's remember that China has three demands that the US must meet in order to end the trade war:

That the US respect China's national sovereignty. That the US remove all tariffs it has imposed since the beginning of the trade war. That the US cease demanding that China buy an unrealistic amount of goods from the US.

Remember No. 3, because it's the one that's really messing things up here. And of course, it's the one Trump is obsessed with.

It is easy to forget that initially this trade war was about making China's markets fairer for US businesses - ending favoritism for domestic companies, forced technology transfers, and intellectual-property theft. In March 2018, US Trade Representative Robert Lighthizer wrote a report to Congress outlining all these issues and all the ways China was in violation of World Trade Organization rules. It all made sense.

But at the same time there was Trump and his obsession with trade deficits - with getting China to buy more US stuff. This did not, and still does not, make any sense. In sophisticated economies, bilateral trade deficits don't mean anything.

Lighthizer wants changes that would make China a more free-market economy like the US. Trump wants changes that further distort the Chinese economy by explicitly forcing it to buy goods from one place rather than another. The former is capitalism. The latter is Trump's variety of populist nationalism. And they do not play well together.

"There are various ways in the short run to reduce the bilateral trade deficit, but this would be done in ways that are essentially market-distorting," Lee Branstetter, a Carnegie Mellon University economist, told Business Insider.

These two conflicting goals have repeatedly caused issues during the on-again, off-again negotiations. Think back to December: Trump ratcheted up the tariffs, China managed to negotiate a temporary peace by promising to buy US soybeans, negotiations resumed, and then they collapsed as China refused to yield to the US's conflicting demands.

Before, Trump making a trade deal with China "was always about setting the rules and structures and accepting the market outcomes," Branstetter said.

Now it's about sales.

And on the other hand, if Lighthizer's objectives (changing the rules to open up China for US companies) are met, it's likely that Trump's core nationalist objectives (forcing companies to move to the US) will suffer.

"If China were to fix those problems, the result would be that the Chinese market would become more hospitable for American and other Western companies to set up production within China," Chad Bown, an economist with the Peterson Institute, told Business Insider via email.

"There seems to be a fundamental inconsistency between achieving that outcome and the Trump administration's other economic nationalist priorities, which focuses on bringing manufacturing production back to the United States, even if that comes at the expense of everything else, including American farmers."

Why Xi can't lose

Making matters more complicated, on the other side of this deal we have Xi, a man who cannot lose. There are political reasons for that, and there are practical reasons. On the latter point, we need to return to Trump's obsession with China buying more US goods.

Even if China could buy enough US goods to close its trade deficit, according to Citigroup analysts, the US doesn't have enough to sell to China without disrupting trade with its partners or changing US production.

From Citigroup:

"The US likely can increase supplies of soy products to China in the short run, as well as select meats. However, meeting the proposed $1.2 trillion of additional shipments of goods to China over six years, including energy, machinery and tech products, will require major adjustments in the US and China's current trading partners, as well as a reconfiguration of US domestic production of these items."

And Citigroup's researchers also found that when it comes to foods, motor vehicles, semiconductors, and aerospace, the US is at or near full-production capacity-utilization rates. We can't make any more. When it comes to energy and poultry, the US doesn't have enough to sell to meet China's demand.

Of course, there are also political reasons Xi cannot just cave to Trump's demands.

Since talks collapsed in May, Xi has adopted the language of struggle. He used the word about 60 times in a speech last week. Using China's state-controlled media, he has cast the US as an aging power hell-bent on stopping the country's rise. It is a position he and the Chinese Communist Party are very comfortable being in. It allows the party to blame its economic problems on the US, and it raises nationalist sentiment to a fever pitch that makes it impossible for Xi to lose face and back down.

So what's this deal supposed to look like? What does a win even look like to Trump? For some China watchers, it simply does not exist.

"There's no deal to make," Anne Stevenson-Yang, the founder of the China-focused investment firm J Capital Markets, told Business Insider. "Everyone is going through a pantomime for the markets. It's super stupid that the markets believe it."

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