In the variable supply auction considered here, the seller decides how many customers with unit demand to serve after observing their bids. Bidders are uncertain about the seller's cost. We experimentally investigate whether a uniform or a discriminatory price auction is better for the seller in this setting. Exactly as predicted by theory, it turns out that the uniform price auction produces substantially higher bids, and consequently yields higher revenues and profits for the seller. Furthermore, again as predicted by theory, the uniform price auction yields a higher number of transactions, which makes it also the more efficient auction format.