Suppose that Shelly's preferences for consumption and leisure can be expressed as u(c ,l)=(c-200)×(l-80).
a) Calculate her utility, u0 , if she consumes c = $360 and enjoys l = 110 hours of leisure per week.
b) Evaluate her marginal utilities of consumption and leisure at this point and use them to determine the slope of her indifference curve at this point. [Hint:Using calculus, it can be shown that for any given level of utility u, MUc = l – 80 and that MUl = c – 200.]
c) Marginal utilities are important because they can be used to calculate the change in utility, ?u, that results from changing c and l by the small amounts ?c and ?l. The induced change in utility is approximately (?): ?u ? MUl ??l + MUc ? ?c. Based on your answers for (b), what happens to her utility if her consumption increases by ?c = $5 and her leisure declines by ?l = 1 hour?
d) Now compute her utility when c = $365 and she enjoys l = 111 hours of leisure. How close is your (approximate) calculation in part (c) to the exact calculation you just did?