Rationing Under Concave Preferences

We study the behaviour of prices and quantities in a model of bilateral trade with coordination frictions, capacity constraints, and risk aversion in small and large markets. The equilibrium markup over the expected return to the asset depends on the ratio of buyers to sellers and the level of buyer risk aversion. Sellers ration buyers in equilibrium and the level of rationing depends negatively on the buyer-seller ratio and positively on the concavity of the buyer's utility function. Coordination between buyers intensifies rationing, increases prices and reduces buyer welfare. We then compare our results to a model of random search and find that the latter can produce too much or too little seller entry depending on which the side of the Hosios condition is analyzed