1\" Consider an economy with a continuum [0,1] of two types of consumers, Their preferences are given by U.(c' ) = 25' log(c,'), and the endowments of each type of agent is given by: 1=n (e;,e|',e;,e_:,...)= (8.1.8.1....) (43:12:35,...)=(1,8,1,8,...) In addition there is one unit of trees that produce r :10 units of the good every period. Each consumer of type i owns 9", 2 O of such trees in period 0, 9,: +0: = l . Trees are traded and do not grow or decay. (a) Define an Arrow- Debreu equilibrium for this economy. lb) Find initial tree holdings 9,: and 9: such that in the Arrow-Debreu equilibrium 0" = 0,2, f=0.l.2,... (c) Suppose consumers can borrow and lend as much as they want (with appropriate Ponzi conditions) of a one-period bond. Define a sequential markets equilibrium, (d) Assume initial tree holdings are as you found in part lb). What can you say about the price of trees and bonds? (e) Now suppose consumers cannot borrow or lend. Define an equilibrium for this liquidity constrained economy if) Suppose now that there is borrowing and lending, but there is limited enforcement, i.e. contracts must satisty a no-default constraint. In this context default means that at any point in time agents can walk away from the contract and the punishment is that theirtrees are seized and they are prevented from horrowing~|ending in the future. Define an Arrow-Debreu equilibrium in this context