In this chapter, we showed an example in which the consumer has preferences for consumption with the perfect complements property. Suppose, alternatively, that leisure and consumption goods are perfect substitutes. In this case, an indifference curve is described by the equation
i = al + bC,
where a and b are positive constants, and u is the level of utility. That is, a given indifference curve has a particular value for u, with higher indifference curves having higher values for u.
(a) Show what the consumer’s indifference curves look like when consumption and leisure are perfect substitutes, and determine graphically and algebraically what consumption bundle the consumer chooses. Show that the consumption bundle the consumer chooses depends on the relationship between a/b and w, and explain why.
(b) Do you think it likely that any consumer would treat consumption goods and leisure as perfect substitutes?
(c) Given perfect substitutes, is more preferred to less? Do preferences satisfy the diminishing marginal rate of substitution property?