Consider a consumer who lives for two periods. His utility is a function of consumption levels in periods 1 and 2 and is given by (1, 1 ) = (1 ) + (2 ). His income in periods 1 and 2 are given by 1and 2, respectively. The market interest rate is equal to r. (a) Do you agree with the following statements? Carefully explain your reasoning and, where relevant, use graphs to support your answer.

(i) "If the interest rate is equal to zero a rational consumer will never save in period 1." (5 points)

(ii) "In the context of the two-period consumption model, if a consumer can borrow or lend funds, we say that this consumer can access the capital market. It is true that having access to the capital market will always make a (rational) agent strictly better off." (5 points)

(b) Suppose that consumer's utility function is given by (1, 1 ) = 0.5(1 ) + 0.5(2 ) and that 1 = 200, 2 = 110 and r = 0.1. Set up and solve the constrained optimisation problem to find the optimal consumption profile. (10 points)