Beer comes in six and twelve-packs. In this exercise we will see how your model of tastes for beer and other consumption might be affected by the units in which we measure beer.
A: Suppose initially that your favorite beer is only sold in six-packs.
(a) On a graph with beer on the horizontal axis and other consumption (in dollars) on the vertical, depict three indifference curves that satisfy our usual five assumptions assuming that the units in which beer is measured is six-packs.
(b) Now suppose the beer company eliminates six-packs and sells all its beer in twelve-packs in- stead. What happens to the MRS at each bundle in your graph if 1 unit of beer now represents a twelve-pack instead of a six-pack.
(c) In a second graph, illustrate one of the indifference curves you drew in part (a). Pick a bundle on that indifference curve and then draw the indifference curve through that bundle assuming we are measuring beer in twelve-packs instead. Which indifference curve would you rather be on?
(d) Does the fact that these indifference curves cross imply that tastes for beer change when the beer company switches from 6-packs to 12-packs?
B: Let x1 represent beer and let x2 represent dollars of other consumption. Suppose that, when x1 is measured in units of six-packs, your tastes are captured by the utility function u(x1, x2) = x1 x2.
(a) What is the MRS of other goods for beer?
(b) What does the MRS have to be if x1 is measured in units of 12-packs?
(c) Give a utility function that represents your tastes when x1 is measured in 12-packs and check to make sure it has the MRS you concluded it must have.
(d) Can you use this example to explain why it is useful to measure the substitutability between different goods using percentage terms (as in the equation for the elasticity of substitution) rather than basing it simply on the absolute value of slopes at different bundles?