We showed an example in which the consumer has preferences forconsumption with the perfect complement property. Suppose,alternatively, that leisure and consumption goods are perfectsubstitutes. In this case, an indifference curve is described bythe equation:
u=al+bC
where a and b are positive constants and u is the level ofutility. That is, a given indifference curve has a particular valuefor u, with higher indifference curves having higher values foru.
a) Show what the consumer’s indifference curveslook like when consumption and leisure are perfect substitutes, anddetermine graphically and algebraically what consumption bundle theconsumer will choose. Show that the consumption bundle the consumerchooses depends on the relationship between a/b andw, and explain why.
b) Do you think it likely that any consumerwould treat consumption goods and leisure as perfectsubstitutes?
c) Given perfect substitutes, is more preferredto less? Do preferences satisfy thediminishing-marginal-rate-of-substitution property?
