Consider my tastes for consumption and leisure.
A: Begin by assuming that my tastes over consumption and leisure satisfy our 5 basic assumptions.
(a) On a graph with leisure hours per week on the horizontal axis and consumption dollars per week on the vertical, give an example of three indifference curves (with associated utility numbers) from an indifference map that satisfies our assumptions.
(b) Now redefine the good on the horizontal axis as “labor hours” rather than “leisure hours”. How would the same tastes look in this graph?
(c) How would both of your graphs change if tastes over leisure and consumption were non-convex— i.e. if averages were worse than extremes.
B: Suppose your tastes over consumption and leisure could be described by the utility function u(ℓ,c)= ℓ1/2c1/2.
(a) Do these tastes satisfy our 5 basic assumptions?
(b) Can you find a utility function that would describe the same tastes when the second good is defined as labor hours instead of leisure hours?
(c) What is the marginal rate of substitution for the function you just derived? How does that relate to the sign of the slopes of indifference curves you graphed in part A(b)?
(d) Do the tastes represented by the utility function in part (b) satisfy our 5 basic assumptions?