Question 2 [15 marks]
Mary lives for two periods. In the first period she gets a real wage 𝑌1 of £5,000 and in the second period a real wage 𝑌2 of £6,000. She knows with certainty what her second–period wage will be and obeys her intertemporal borrowing constraint.
(a) Mary chooses to consume £5,400 in period 1 and £5,540 in period 2. Find the real interest rate, 𝑟. Draw Mary’s intertemporal budget constraint, making sure that you show the slope and both intercepts of the constraint.
(b) Assume that the real interest rate changes to 10% and that Mary still consumes £5,540 in period 2. Graphically, numerically, and verbally discuss the effects of the interest rate change on Mary’s consumption in both periods.
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(c) Instead assume that Mary’s wages remain unchanged (i.e., 𝑌1 = £5,000, 𝑌2 = £6,000) and that the real interest rate is 10%, but Mary also receives an inheritance of £500 at the start of period 1 and will leave £500 to future
generations (i.e., will have £500 left at the end of period 2). What is the maximum Mary could consume in period 1 (i.e., 𝐶1 𝑀𝐴𝑋)?
(d) George obeys his intertemporal budget constraint and lives for three periods with real income as summarised in the table below. George can borrow and save at the real interest rate that is 10%.
i. What is the maximum George can consume in period 1?
ii. What is the maximum George can consume in period 2?
iii. What is the maximum George can consume in period 3?
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