Consider a two-period model of intertemporal choice. In each period i=1,2, the consumer has income mi>0 and makes a consumption choice xi0. The price of the consumption good is 1 in both periods. The consumer can save her period 1 income or borrow against her period 2 income at interest rate r>0. The consumer's utility from consumption path (x1,x2) is x121+1+r1x221 (a) Write down the consumer's utility maximisation problem. (b) Argue that any optimal consumption path is such that xi>0 for all i=1,2. (c) Write down the Lagrangean of the consumer's utility maximisation problem and derive its first-order necessary conditions for an interior solution. Argue that these conditions are also sufficient. (d) Derive the consumer's demand functions for consumption in periods 1 and 2. (e) What happens to the consumer's consumption dynamics when the interest rate r increases? Interpret this result. Consider a two-period model of intertemporal choice. In each period i=1,2, the consumer has income mi>0 and makes a consumption choice xi0. The price of the consumption good is 1 in both periods. The consumer can save her period 1 income or borrow against her period 2 income at interest rate r>0. The consumer's utility from consumption path (x1,x2) is x121+1+r1x221 (a) Write down the consumer's utility maximisation problem. (b) Argue that any optimal consumption path is such that xi>0 for all i=1,2. (c) Write down the Lagrangean of the consumer's utility maximisation problem and derive its first-order necessary conditions for an interior solution. Argue that these conditions are also sufficient. (d) Derive the consumer's demand functions for consumption in periods 1 and 2. (e) What happens to the consumer's consumption dynamics when the interest rate r increases? Interpret this result