When looking at the InventoryItem object, there is no field defined for cost. However, there is a field named unitCost. This unitCost field corresponds to the ‘Cost per item’ field in the dashboard:
Note: what is called ‘Unit price’ in the dashboard, is data that is part of the ProductVariant object.
Curiously, when you want to update the ‘Cost per item’ with the inventoryItemUpdate mutation, using the InventoryItemInput input object, there is no unitCost field available. However, there is a field named cost, which corresponds the the ‘Cost per item’ field in the dashboard.
So, the value of InventoryItem.unitCost.amount field value is set by using the InventoryItemInput.cost field… 
Why?
Not long ago, we had a topic named: GraphQL Api is a Hot Mess.
@Liam-Shopify In that topic, you asked for examples, on where the GraphQL API is falling short. So please consider the issue in this topic as such.