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This paper analyzes a bilateral trade model where the buyer's valuation for the object is uncertain and she can privately purchase any signal about her valuation. The seller makes a take-it-or-leave-it offer to the buyer. The cost of a signal is smooth and increasing in informativeness. We characterize the set of equilibria when learning is free and show that they are strongly Pareto ranked. Our main result is that, when learning is costly but the cost of information goes to zero, equilibria converge to the worst free-learning equilibrium.