Interest Rates and Utility Functions

Assume a two-period, riskless, pure-exchange economy by two people, both of whom have time preferences for consumption represented by a utility function:

u(C0 ,C1 ) = C0aC11-a

Where the Time Preference (aL / aR ) is 1 and the growth rate (g) is 0.00. Assume that aL = aR = 0.5 and E0 = E1 = 100. Samantha's endowment is e0 = 55, and e1 = 25.