This summer, the Trump administration touted a deal where Japan would invest $550 billion in U.S. projects while America runs a trade surplus with Japan. Here’s why both can’t be true at the same time—and why our brains make us want to believe they can be.
Your brain hears “more exports” and “more foreign investment” as two separate good things. Like getting a raise AND winning the lottery on the same day – why not both? This is called mental accounting – we put different benefits into separate mental buckets instead of seeing them as parts of one connected system. Politicians exploit this by promising wins in multiple buckets without mentioning they’re connected by mathematical rules.
Picture two jars on your counter: “Money I Lend Out” and “Money I Borrow.” If you’re filling the first jar with spare cash, that same dollar can’t simultaneously appear in the “borrow” jar. You can’t be both the person with money to spare AND the person who needs to borrow. This feels obvious with personal money, but our brains struggle to apply the same logic to countries.
Countries face identical math through the balance of payments: Current account (mostly trade in goods & services) plus Financial account (net investment flows in bonds, factories, real estate). The identity: Current Account + Financial Account ≈ 0. If one goes positive, the other must go negative. No exceptions.
The Mathematical Impossibility
The accounting identity operates simultaneously – both sides must balance in the same accounting period between the same two countries. If U.S. runs a trade surplus with Japan, surplus dollars must be matched by U.S. lending to Japan in that same period. If Japan invests $550B in U.S., that must be matched by Japan lending to U.S. in that same period.
You can’t be both net lender and net borrower to the same country in the same time period. Every dollar of trade surplus must be matched by a dollar of lending. Every dollar of foreign investment must be matched by a dollar of borrowing. Same dollars, same timeframe, mathematical impossibility.
Think of it this way: If Japan hands you $550 billion to invest in American factories while you simultaneously hand Japan a $550 billion trade surplus, they offset in the ledger – you’re back where you started. (Ignoring small statistical errors and timing effects that don’t change the core constraint.)
Why do smart people fall for this? Overconfidence bias makes us think clever policy can overcome mathematical constraints. Politicians frame this as “America wins on all fronts” rather than the accurate framing: “Choose whether America lends to Japan or borrows from Japan – you can’t do both.” Loss aversion means we focus on promised gains while ignoring necessary tradeoffs.
The U.S. trade deficit widened 22.1% to $103.6B in July 2025—far above expectations. Consumer demand and government borrowing needs mathematically required foreign savings inflow, overwhelming tariff policies. Markets price mathematical reality. Our psychology craves impossible promises.
This demonstrates your “Impossible Rescue” thesis: when human psychology meets mathematical constraints, mathematics always wins – but not before politicians exploit the psychological gap.
Your Edge
Recognize mental accounting in political promises. When politicians promise benefits in separate categories, ask whether they’re mathematically connected. Question overconfidence framing – “We’ll be so good at X that math won’t apply” signals impossible promises. Look for hidden tradeoffs when promises sound like pure upside. Follow data, not psychology – trade and investment flows reveal mathematical reality while political promises exploit cognitive biases.
Understanding these psychological patterns helps you spot mathematical impossibilities before they become obvious to everyone else.
Source: U.S. Bureau of Economic Analysis, July 2025 trade data
What political promises have you noticed that exploit mental accounting? Email me at george@mtwx.ca.