Let us consider a world with only one consumer good that can be consumed in two time periods: this year and next year. Anton has an income of $1,500 this year and he expects an income of $1,100 next year. He can borrow and lend money at an interest rate of 10% per annum, compounded annually. Consumption goods cost $1 per unit this year and next year. Suppose that Anton has the following utility function: U(C 1 , C 2 ) = C 1 C 2 Where: C 1 and C 2 represent the amount of consumption this year and next year, respectively. a) What is the present value of his income? Anton is trying to figure out the optimal amount of consumption for this year and next year that will maximise his utility, given his budget constraint. Note that the present value of his consumption cannot exceed the present value of his income. b) Formulate the budget constraint. c) Formulate the Lagrangian function for this problem. d) To maximise Anton's utility subject to his budget constraint, the amount of consumption next year must be 110% of his current consumption. True or False? e) Calculate the optimal amount of consumption