An Economist at the Museum

We saw a magnificent art exhibit, The Impressionists in Paris, at the Folkwang Museum in Essen, Germany. It contained paintings from all over the world, including the National Galleries in both Washington and London, that showed views of Paris. My wife asked how they organize these exhibits – do they trade paintings, or what?
I don’t know the answer, but I can’t imagine that they trade – surely our National Gallery would have much more on offer than smaller museums like the Folkwang. If trading was standard, I don’t think a market would exist. So I assume the exhibiting museum pays. But how? Perhaps a percent of its gross – admission was $12/person, and it was very crowded. A fixed fee, sufficient to cover insurance, shipping and some profit for the owner? I would assume the latter, but I wonder how this market works? Or is there no single pattern?