Consider the following two-period problem in an endowment:

1. Find the IBC and provide a brief interpretation.
2. Find the consumer's optimality condition by first finding the slope of an indifference curve, then the slope of the IBC, and finally setting them equal. Provide a careful interpretation of the optimality condition.
3. Find the demand functions for the current consumption good and the future consumption good.
4. Now use the following parameter values r = 0.05 and ? = 1/(1+r) to calculate current-period consumption demand and savings for values of the endowment (y, y?) = (100, 105), (105, 105), (110, 105). Also, government expenditures equal zero. Briefly explain your results.