Question

4. Mountain Dew, which (fun fact) was invented in east Tennessee, is sold in 6 and 12-packs (a 6 pack contains 6 cans of Mountain Dew in a single package, and a 12 pack contains 12 cans of Mountain Dew in a single package). In this exercise we are going to explore how the MRS for Mountain Dew and pretzels might be affected by the units of measurement for Mountain Dew.
a. Suppose Mountain Dew is only sold in 6-packs. On a graph with Mountain Dew on the horizontal axis (measured in number of 6-packs) and pretzels (measured in pounds) on the vertical axis, draw three indifference curves. Assume preferences for both goods are rational, and satisfy the continuity, monotonicity, and convexity assumptions.
b. Now suppose that Mountain Dew no longer offer 6-packs, and only offers Mountain Dew in 12-packs. What happens to the MRS at each consumption bundle in the graph from part (a) if 1 unit of Mountain Dew now includes 12 cans of Mountain Dew instead of 6 cans.

c. In another graph, draw one of the indifference curves from part (a). Pick a consumption bundle on that indifference curve and then draw the indifference curve through that consumption bundle for an indifference curve where Mountain Dew is measured in 12 packs. Does the fact that these indifference curves cross imply that preferences have changed?

d. Let x1=Mountain Dew and x2=pretzels. When x1 is measured in units of 6-packs, preferences are captured by the utility function U(x_1,x_2 )=x_1 x_2
What is the MRS of pretzels for beer?

e. What does the MRS have to be if x1 is measured in units of 12-packs?

f. Give a utility function that represents your preferences when x1 is measured in 12-packs. Make sure to check that the MRS matches your answer in part (e)

g. Use this example to explain why it might be useful to compare the substitutability between different goods using percentages terms rather than relying on the MRS alone?

the price remain the same

Answer 1