Matt Berman at Quartz is very excited about a putative $380 million stimulus for the U.K. economy that we can expect from spending related to the new royal baby.
Note that even if this figure is correct, the United Kingdom has a GDP of $2.445 trillion a year so we're talking about a drop in the bucket. But it's actually worse than that, as fully $238 million of the spending is expected to come on "commemorative trinkets." My guess is that a very large share of those trinkets will be manufactured in Asia so this spending will mostly be adding to British imports rather than British GDP. But what's more, a baby takes a fairly predictable 9 months (or three quarters in National Income and Product Accounts terms) to gestate, so a lot of baby-related production will have already happened in anticipation of final sales. So the entire stimulative impact, if any, will have been both small and rolled out over a period of months.
A more interesting issue, I think, is the extent of lost productivity as people follow the baby news this week rather than doing their jobs. No estimates on that so far, but I assume someone will try to quantify it retroactively.