Asymmetric Information and Middleman Margins: An Experiment with Indian Potato Farmers

Proof of Proposition 1: The off-equilibrium path beliefs imply that any price offer below M(w) is definitely rejected, and any price offer above M(w̄) is definitely accepted. Any price offer v between M(w) and M(w̄) leads F to believe that w = M−1(v), and he is indifferent between accepting and rejecting it, making it optimal for him to randomize his acceptance decision. Finally, when the randomization satisfies condition (3), it is optimal for V T in state w to offer price M(w) rather than any other price in the interval [M(w),M(w̄)], for the following reason. Selecting a price M(ŵ) would lead V T to earn an expected profit of α(ŵ)[w −M(ŵ)]q(M(ŵ). (3) is the first-order condition corresponding to the condition that ŵ = w is locally optimal. Standard arguments ensure that it is also globally optimal under the assumptions imposed above. This completes the proof.