Brian is about to take early retirement at the age of 45. His current wealth is $2 million and he plans to use this wealth to fund his consumption over the remaining three periods of his life.1 Any money that he does not spend on consumption in period 0 can be put in the bank where it will earn interest at the rate of 100% per period. That is, r = 1, so if chooses not to consume an amount s of his $2 million in period 0 he will have s (1 + r) = 2s available at the beginning of period 1. Similarly, any money he does not spend on consumption in period 1 can be put in the bank where it will also earn interest at the rate of r = 1.

(a) Explain why his intertemporal budget set B can be described as follows: B = { (c_0, c_1, c_2) (0, 0, 0) : c_0 + 1/2 c_1 + 1/4 c_2 2 }