In math, we often take things to the extreme. Not in the "party hard" or "risk death" meaning of the word, but in the "as large as possible" meaning. The extreme case isn't real, but it often simplifies the concept and makes the effects stand out.
Let's take the minimum lot size to the extreme. Assume the minimum lot size was so large that a city only had 1 single-family lot. If you want to use your imagination, split the city in half and 1 family gets half. All other families are crammed into Soviet-style identical apartments that are spread over the other half. In this extreme world, who gets a house?
The richest family get the house, obviously! The land is zoned single-family, so only one family can live on that singular lot. The owner would have to outbid every other family to get it. And the richest family can do that.
If the city was Austin, that owner would probably be Elon Musk, our richest resident. He would have to outbid Michael Dell, our second richest resident. Dell has $50 billion, so let's say he was willing to bid $5 billion for the lot. Musk can outbid him with $5 billion and 1 cent. After the auction, Musk lives on a 85,000 acre lot and Dell is forced into the monoculture apartments where he shares his average .085 acres with the other 1 million residents.
Elon Musk gets a lot of land for cheap. It's clear he gets a lot of land — half the city — but why do I say "cheap"? Because he only had to outbid Michael Dell by himself. If the land wasn't zoned single-family, Dell could form a consortium with Austin's 5 other billionaires to bid for it. The consortium could bid more than $5 billion for the lot and, if they won, agree to share the lot 6 ways. Musk is worth more than all other other billionaires combined, so he can outbid them for the huge single lot, but he'd be forced to pay more than when Dell has to bid by himself.
The same pattern holds for less extreme minimum lot size. If Austin had just 2 single-family lots, Musk and Dell would own those lots by outbidding Austin's third-richest resident, Robert Smith. That poor shlump only has $8 billion dollars, so he might bid $800 million for a lot. Again, Musk and Dell get a lot of land (42,500 acres each) and pay a low price, $800 million and 1 cent. If the lots were not single-family, Robert Smith and the other 4 billionaires would form a consortium that could bid more than $800 million and share a lot if they won.
In reality, Austin has a minimum lot size of .13 acres and about 200,000 single-family lots. Those lots are bought by families with a household income over $160,000 per year. Those families get more land for a lower price, thanks to the minimum lot size and single-family zoning. Those laws prevent consortiums of poorer families (ones earning only $150,000 a year!) from buying that land and sharing it.
Now, a critic of this argument will say that families can just live outside of Austin and commute in. That's true, but consortiums of those exurban residents would still prefer to buy land in Austin and share it. These laws give rich families more of Austin's land for cheap. And they cause other families seeking houses to drive more, wasting their time and money. And, for those living in Austin, they experience more traffic, road wear, and air pollution.
The combination of single-family zoning and minimum lot sizes is harmful. My preference is to eliminate the minimum lot size. Austin's City Council has proposed moving to three-units per lot and cutting the minimum lot size by more than half. These are great steps. They will increase middle-class affordability in Austin and I hope they become law.