Consider the problem of a household that will earn $I during its working life – the present – and values consumption goods both in the present (Cp) and during its retirement years – the future – (Cf). Suppose the real after-tax interest rate between the two periods is “r”.
(a) Write out the equation for the household’s budget line and illustrate it in a diagram with Cp on the horizontal axis and Cf on the vertical axis. Identify the intercepts. What is the relative price (opportunity cost) of Cp? Identify it on your diagram.
(b) Suppose the household’s preferences are such tha tit chooses positive consumption in each period. Illustrate this choice with an indifference curve and identify the level of saving in your diagram. Comment on the household’s consumption pattern over time versus its income-earning pattern.