In 2005, the U.S. Congress passed a bill to extend daylight savings time earlier into the spring and later into the fall (beginning in
2007). The change was made as part of an Energy Bill, with some claiming that daylight savings time reduces energy use by extending sunlight to later in the day (which requires fewer hours of artificial light). Among the biggest advocates for daylight savings time, however, was the retail and restaurant industry that believes consumers will spend more time shopping and eating in malls for reasons explored here.
A. Consider a consumer who returns home from work at 6PM and goes to sleep at 10PM. In the month of March, the sun sets by 7PM in the absence of daylight savings time, but with daylight savings time, the sun does not set until 8PM. When the consumer comes home from work, she can either spend time (1) at home eating food from her refrigerator while e-mailing friends and surfing/ shopping on the internet or (2) at the local mall meeting friends for a bite to eat and strolling through stores to shop. Suppose this consumer gets utility from (1) and (2) (as defined here) but she also cares about x3 which is defined as the fraction of daylight hours after work.
(a) On a graph with “weekly hours at the mall” on the horizontal axis and “weekly hours at home” on the vertical, illustrate this consumer’s typical weekly after-work time constraint (with a total of 20 hours per week available — 4 hours on each of the 5 workdays). (For purposes of this problem, assume the consumer gets as much enjoyment from driving to the mall as she does being at the mall).
(b) Consider first the scenario of no daylight savings time in March. This implies only 1 hour of daylight in the 4 hours after work and before going to sleep; i.e. the fraction x3 of daylight hours after work is 1/4. Pick a bundle A on the budget constraint from (a) as the optimum for this consumer given this fraction of after-work of daylight hours.
(c) Now suppose daylight savings time is moved into March, thus raising the number of after work daylight hours to 2 per day. Suppose this changes the MRS at every bundle. If the retail and restaurant industry is right, which way does it change the MRS?
(d) Illustrate how, if the retail and restaurant industry is right, this results in more shopping and eating at malls every week.
(e) Explain the following statement: “While it appears in our 2-dimensional indifference maps that tastes have changed as a result of a change in daylight savings time, tastes really haven’t changed at all because we are simply graphing 2-dimensional slices of the same 3-dimensional indifference surfaces.”
(f) Businesses can lobby Congress to change the circumstances under which we make decisions, but Congress has no power to change our tastes. Explain how the change in daylight savings time illustrates this in light of your answer to (e).
(g) Some have argued that consumers must be irrational for shopping more just because daylight savings is introduced. Do you agree?
(h) If we consider not just energy required to produce light but also energy required to power cars that take people to shopping malls, is it still clear that the change in daylight savings time is necessarily energy saving?
B. Suppose a consumer’s tastes can be represented by the utility function u(x1,x2,x3) = 12x3 lnx1 + x2, where x1 represents weekly hours spent at the mall, x2 represents weekly after-work hours spent at home (not sleeping), and x3 represents the fraction of after-work (before-sleep) time that has daylight.
(a) Calculate the MRS of x2 for x1 for this utility function and check to see whether it has the property that retail and restaurant owners hypothesize.
(b)Which of the three things the consumer cares about — x1,x2 and x3 — are choice variables for the consumer?
(c) Given the overall number of weekly after-work hours our consumer has (i.e. 20), calculate the number of hours per week this consumer will spend in malls and restaurants as a function of x3.
(d) How much time per week will she spend in malls and restaurants in the absence of daily savings time? How does this change when daylight savings time is introduced?