In end-of-chapter exercise 2.9, you illustrated my department’s budget constraint between “pages copied in units of 100” and “dollars spent on other goods” given the quantity discounts our local copy service gives the department. Assume the same budget constraint as the one described in 2.9A.
A. In this exercise, assume that my department’s tastes do not change with time (or with who happens to be department chair). When we ask below whether someone is “respecting the department’s tastes” we mean whether that person is using the department’s tastes to make optimal decisions for the department given the circumstances faced by the department. Assume throughout that my department’s tastes are convex.
(a) True or False: If copies and other expenditures are very substitutable for my department, then you should observe either very little or a great deal of photocopying by our department at the local copy shop.
(b) Suppose that I was department chair last year and had approximately 5,000 copies per month made. This year, I am on leave and an interim chair has taken my place. He has chosen to make 150,000 copies per month. Given that our department’s tastes are not changing over time, can you say that either I or the current interim chair is not respecting the department’s tastes?
(c) Now the interim chair has decided to go on vacation for a month— and an interim chair has been named for that month. He has decided to purchase 75,000 copies per month. If I was respecting the department’s tastes, is this interim chair necessarily violating them?
(d) If both I and the initial interim chair were respecting the department’s tastes, is the new interim chair necessarily violating them?
B. Consider the decisions made by the 3 chairs as described above.
(a) If I and the second interim chair (i.e. the interim chair) both respected the department’s tastes, can you approximate the elasticity of substitution of the department’s tastes?
(b) If the first and second interim chairs both respected the department’s tastes, can you approximate the elasticity of substitution for the department?
(c) Could the underlying tastes under which all three chairs respect the department’s tastes be represented by a CES utility function?