Lithium (carbonate) is a very old drug, cheap to manufacture, and non-patentable. It is essentially the lithium (metal) salt of carbonate (bubbling water). It is super cheap everywhere.
While you might think so, I don't think it's a fact that the psychiatrist would run out of patients without this child being diagnosed with bipolar.
But lithium is not expensive. Lithium is dirt cheap.
http://www.coventrywarksapc.nhs.uk/mf.ashx?ID=425e5245-157c-...
> Cost: For 800mg/day lithium carbonate or equivalent, at April 2015 dm+d prices, one year’s treatment costs
> Priadel® 400mg tablets £25
> Camcolit® 400mg tablets £31
> Priadel® liquid £273