Consider a small economy can borrow/lend to rest of the world at a constant real interest rate. Under an assumption of incomplete capital markets, there is no access to contingent debt on the realization of output in the second period. 1, Show the budget constraints of the first (no uncertainty in period one) and second periods (second period flow will depend on the realization of output) of consumptions under this economy. 2, Show in Lagrange function the objective function and budget constraint. 3, If consumers choose consumptions in both period one and two to maximize their utility, show the first order condition for incomplete capital market.