I'd say it's a 5$, but it's difficult. Actually i have changed my decision several times while writing this...
The Duration effect is strictly better than Warehouse, so 3$ is no option.
The instant effect is worse than Warehouse. So it basically plays a card at least worth 4$ and one worth less than an existing 3$ - an existing, good 3$.
Merchant Ship is basically two Woodcutters, worth 3$, and costs 5$, but also Merchant ship is stackable. Here the duration stacks more than the instant effect, but still the avarage "cost" of the two cards you'd usually play to get there is about 3$. Also this is easier play several times than Merchant Ship, and so it's easier to stack the part where stacking matters.
Durations usually have a "discount" from what they would be worth when played as one (Caravan would be a Lab when played as one), and this would add up to + 1 Action, + 4 Cards, Discard 4 Cards. This is not only clearly better than Warehouse, but probably also above 5$, when compared to Embassy. So with the discount we give for splitting it, it would be a 5$ again.
Those are two different argumentations, the second being a bit rough. But they come to the same conclusion, so yeah, at the end of this post i feel quite good about saying it should be 5$.