Consider an economy with one consumer in each generation. Each consumer has an endowment of one unit of the consumption good when young and nothing when old. There is no production and the consumption good cannot be stored.

a. What are the consumption levels in the two periods of life if there is no trade? If preferences are given by

what level of utility is achieved?

b. At any point in time, what are the feasible consumption allocations between the young and the old consumers who are alive at that point? Given the preferences, which allocation is optimal?

c. Can the optimal allocation be reached by trade?

d. Is the indecency in the production model a consequence of the existence of capital?