AX purchase price variance (STD costing). Do we need to setup trade agreement?

STD costing model. Setup cost price (costing version) for an item (PCX01). for e.g. cost price is defined as $10.

In the item purchase fast tab, price is not defined.

Received an item at $12.

how does PPV is calculated. is it based off a cost price. ie. PPV is $2.

suppose I entered a purchase price (item fast tab) as $10.5, would the PPV be $1.50?

It is dependent on Cost defined for the costing version. (You can test it)
The purchase price defined in item prices or trade agreements are used to calculate the purchase price (on purchase order line).

Moving to User forum (from developer forum). Please post in the relevant forum.

If you dont use the costing version you would have had a fallback principle of item configured on the version, which would mean the $10, which means the PPV would be $2 for the one received in at $12 and $0.5 for the one at $10.5 - the purchase cost is not related to the PPV calculation.
And no you do not need a trade agreement to get standard costing to work.