The book doesn't represent any invested capital, so let's not say that it is an asset. Instead, let's say that there are shares in a book making company, tracked in the index, and also books, which will be in the CPI.
The value of being able to make one book per day is linked to the price of a book, which means that on the island, the CPI and the stock market have to rise and fall together. That causes the stock market and currency to move inversely.
Do you want an answer to your original question or do you want to try and argue that the stock market and currency move inversely?
Because if you want an answer, you aren't making changes to the example that will help you understand. You're introducing confusing factors that are not needed. The original example gave a neat little illustration of how wealth-as-measured can drop without money disappearing. Don't bring CPI in to it (and stock prices don't drive the CPI so that is a reasonable assumption).
If you want to argue that the two move inversely then go ahead and don't mind me, but you might like to add in some evidence or case studies. And you'll need to be precise about real vs nominal, and probably start modelling other effects.
My original question was how wealth-as-measured could disappear when dollars were included, not how demand for stocks could shift to demand for dollars. In a market with one good, the value of a dollar must move inversely with the value of the good (no examples needed, it's mathematically tautological) - and that is not what we see happening on the linked page. That's what my question is.
> In a market with one good, the value of a dollar must move inversely with the value of the good (no examples needed, it's mathematically tautological)
You do mean that, but it doesn't have a lot of bearing on the correctness of your argument. I suspect you've assumed that wealth is neither created or destroyed somewhere in your logic, because what you are saying would make sense if that was an assumption. But that would be a poor assumption if you've made it.
CPI is a tool for adjusting the value of a dollar, but it doesn't have any bearing on the value of the total economy vs the value of all the dollars in existence. All the dollars in existence might buy the entire economy many times over or they might buy a tiny fraction of it. And that ratio changes continuously (both from money creation and economic activity). There is no inverse relationship mediated by the CPI.
There are three charts on the linked website - bonds, dollars and stocks. None of them are exactly measures of wealth. My question is about how their properties as mutual numeraires could allow them to all fall at the same time.
tautologically the price of one dollar will always be one dollar but they can be less willing to spend those dollars on anything, and simultaneously less willing to sell assets they already own for dollars.
The value of being able to make one book per day is linked to the price of a book, which means that on the island, the CPI and the stock market have to rise and fall together. That causes the stock market and currency to move inversely.