Why absolute value in elasticities and marginal rate of substitution?

Question

This is a point I find very confusing and very hard to justify to students. Depending on the books, one finds many different conventions regarding the sign of elasticities and marginal rate of substitution (MRS). Some define them taking absolute value, some don't, and one sometimes finds inconsistencies inside a single book or set of notes. My questions are : - To your knowledge, what is the most conventional stance regarding the use of absolute value in the definition of - Own-price elasticity - Cross-price elasticity - MRS - Is it mere convention or is there somewhat of a rational for taking absolute value in some/all/none of the cases?

Answer 1

As a purist I never take absolute values as there is information the size. Absolute values are typically used in introductory textbooks for student that get confused by negative numbers . Own price elasticities will be negative when demand curves are downward sloping. Cross price elascticities will be positive for complements and negative for substitutes. Income elasticities will be negative for inferior goods and positive for normal or superior goods. The sign and magnitude will have implication for the impacts of price/income changes on budget shares. This is very important. The marginal rate of substitution is the ratio of Marginal utilities which is a positive number (except for perfect complements). It is the negative of the slope of the indifference curve (not the absolute value). You can have indifference curve where one good is "good" and one good is "bad". The most common example is the relationship between expected return and risk. Indifference curves are positively sloped and the direction of increasing utility is northwest and the MRS is Negative.

I hope this helps

Answer 2

My suggestion: include the sign in your calculations - the sign aids understanding.

By convention we drop the sign when reporting price elasticity of demand and price elasticity of supply.

You need the sign for income elasticity and cross-elasticity.