In our hypothetical, there is a valued Product — call it Product M. There is also a law saying that every dollar you spend to acquire Product M, you must also ensure that your spending on various Product Ws is roughly proportional, though you don’t need to spend it all on a single Product W, can spread across many Ws.
Let’s assume Product W doesn’t ever add profit, even though of course in most real-life uses of this hypothetical, it might. You can think of this as being a situation where current spending on Product W is at or above the equilibrium amount, so that additional spending on Product W is not profitable, if that makes things feel more realistic for you.
Product M (in this hypothetical) is purchased in a very competitive bidding market, where dozens of would-be purchasers calculate the benefit of Product M to their overall revenue (and profit) position, and the highest bidder (in some overall sense) wins. While the highest bidder (Buyer 1) obviously needs to outbid everyone, most importantly, to win the bid, the highest bid needs to outbid the second highest bidder (Buyer 2). (This is a little like the old joke that say you don’t have to actually outrun the bear, you just need to outrun the other guy — if you beet the second highest bidder, you automatically beat the third highest, the fourth, etc.) Thus, we can ignore all the other bids and just treat this like a two-person race. And to win that race, you need to bid just a tiny bit more than the maximum amount of value the other firm places of Product M.
Thus, if we ignore the matching law for a moment, the winning bid is something like (Total Profit of Buyer 2 from acquiring Product M) +$1.
Imagine that Buyer 2 places a maximum value of $500,000 on a specific Product M, figuring that adding Product M to its production function would increase profits by slightly more than $500,000. Thus the winning bid might be $500,001, because with that bid, the profit to Buyer 2 of adding Product M to its firm would be negative ( $-1).
[This is a generic hypothetical. Obviously in some uses, it might not literally be $1 — it might climate, or a nicer set of buildings, or closeness to home, or any non-pecuniary benefit. I don’t think this simplification affects the outcome of the analysis, but feel free to email me if you disagree and I might add nuance to a future model. And when I use Profit, you can think of it as “net benefit” if you’re one of those people who thinks the word profit isn’t applicable to other situations that involve costs & benefits, such as non-profits’ purchase decisions. So the idea is if the profit is negative, that’s including *all* of the non-cash benefits too — negative profit here literally means you are worse off, in total, with the product than without it.]
Ok. But now let’s add the law that says for every dollar spent on Product M, you must also spend a dollar on some number of Product Ws. And let’s look at what that does to Buyer 2’s valuation of Product M.
Previously, Buyer 2 figured out that adding Product M would increase profits by $500,000, and so it was willing to spend up to that amount to acquire Product M, but after that, on balance, Product M would cost more than its benefits. But now, each dollar you spend on Product M brings with it a matching dollar of spending on Product W.
Since Product M adds $500,000 to Buyer 2, now the maximum Buyer 2 will spend on Product M is $250,000. This is because that $250,000 purchase of Product M brings with it a second $250,000 of spending on Product W, and so by spending any more than $250,000, Buyer 2 would incur negative profits. For example, spending $300,000 on Product M would bring with it $300,000 of spending on Product W and the total, $600,000 exceeds the benefit of bringing Product M into the fold, resulting in a loss of $100,000. Thus Buyer 2 won’t bid more than $250,000, and the winning bid for Buyer 1 is now $250,000 plus $1.
So the winning bid drops by 50%. But before Buyer 1 gets too excited, don’t forget that buyer also has to obey the law and spend an equal amount on Product W. So Buyer 1 win outbids Buyer 2 with a $250,000 (and a penny, whatever) bid, but then must set aside $250,000 for Product W. The result is that Buyer 1 spends the same amount as it would have in a market without this law linking Product M and Product W, but now instead of the payment going exclusively to the seller of Product M, half of it goes to the makers of Product W.
The law cannot raise the net value of Product M. And the law cannot raise the total best amount of spending on Product M. But what the law can do is, in essence, tax spending on Product M, and give the tax receipts to Product W. This, in turn, depresses the market rate for Product M. Since the tax ends up being 50% of total spending, the result is that the market rate for Product M is cut in half, but total spending remains the same, with the other half going to Product W.
That’s how an auction/bidding market would adjust to the imposition of a law tying spending on one product with spending on another. This is generic economics, but you can think of it as a model for how Title IX would work in a market where (some) male athletes received competitive offers without a specific maximum cap. I used Product M and Product W, but if you want to, you can imagine Product M was Andrew Wiggins and Product W was spending on women’s sports at the various schools that would have been bidding for Wiggins in an open market when he was coming out of high school. The way I describe the law in the example is not exactly how Title IX works — Title IX has not resulted in dollar-for-dollar matches between financial aid spending on men and on women (which is more like 60/40), and it certainly has not resulted in equal spending on men’s and women’s sports overall (which is far closer to 80/20 than 50/50, at least in FBS). But we can imagine it is a true dollar-for-dollar match and the example above then tells you why it doesn’t break the bank.