# Lagrangian Method With Two Sided No Commitment Consider The Model Of Kocher Lakota W 1946883

Lagrangian method with two-sided no commitment Consider the model of Kocher lakota with two-sided lack of commitment. Two consumers each have preferences where u is increasing, twice differentiable, and strictly concave, and where ci(t) is the consumption of consumer i. The good is not storable, and the consumption allocation must satisfy c1(t)+c2(t) ≤ 1. In period t, consumer 1 receives an endowment of yt ∈ [0, 1], and consumer 2 receives an endowment of 1−yt. Assume that yt is i.i.d. over time and is distributed according to the discrete distribution Prob(yt = ys)=Πs . At the start of each period, after the realization of ys but before consumption has occurred, each consumer is free to walk away from the loan contract.

a. Find expressions for the expected value of autarky, before the state ys is revealed, for consumers of each type. (Note: These need not be equal.)

b. Using the Lagrangian method, formulate the contract design problem of finding an optimal allocation that for each history respects feasibility and the participation constraints of the two types of consumers.

c. Use the Lagrangian method to characterize the optimal contract as completely as you can.