My best friend's son is taking Eco 100. While studying for his midterm exam, he encountered this question:
True or false: There is no difference between these two equilibrium equations in Eco 100 consumer theory as one equation can be transformed mathematically into the other (a) MUx/MUy=Px/Py (b) MUx/Px=MUy/Py.
What do you think? Is this statement true or false? Please vote here (only the first 200 answers will be recorded.)
I think this statement is true. Clearly the statements are mathematically equivalent.
However the "right" answer is false. I'm not sure exactly why. Perhaps because the interpretation of the conditions is different. MUx/MUy=Px/Py is generally interpreted as "the slope of the indifference curve is equal to the slope of the budget constraint." MUx/Px=MUy/Py, on the other hand, is generally interpreted as "the utility gained from the last dollar spent is the same for each commodity." But this seems a little obscure for an Eco 100 class. My friend's son's explanation was a little garbled, but seemed to have something to do with whether utility was ordinal or cardinal.
Currently the Ontario government is planning a more differentiated university system. Each university must define for itself a clear role within the Ontario system (see The Benefits of Greater Differentiation of Ontario's University Sector.)
My friend's son is at a university that regards itself as a leading educational institution. I suspect they will define themselves as a research intensive school. Which begs the question: how will they ensure their first year students receive a quality education? If they can't guarantee a quality education, should they be educating first year students in the first place?
But without thousands of first year students, how will they be able to pay for the graduate student teaching assistantships and "internationally competitive" salaries that are the basic prerequisites of a "research intensive" school?
Update: of the 27 people who have responded to the survey so far, 24, or 89 percent, have answered "True." The best justification for a false answer is given by ECON 1000 guru Nick Rowe, "If x is leisure, and y is milk, then MUx/MUy has the units litres/hour, so we don't need to talk about utils." But the units of MUx/Px are utils per dollar. The problem with this response is, as Nick points out, that it's the MRS that is measured in units of litres per hour, MUx/MUy is measured as utils per litre of milk/utils per hour.
Update #2: I've managed to obtain the "official" answer, which is: There is a difference! First line above [MUx/MUy=Px/Py] refers to Indifference Theory that does not require measureable utility; there are no units of measurement on the LHS or RHS of the equation. Second line [MUx/Px=MUy/Py] refers to Utility Theory which does require measurement of satisfaction.
There have now been 72 responses to the survey. 83.3% of respondents answered "true."