# A Perfectly Elastic Problem

A regression is of linear form

y = bo + b1x1 + e

It denotes house prices (dependent) on square-feet (independent) which are graphed on Y and X axis' respectively.

Marginal effects measure a slope's gradient, or how much Y changes to X, but not the rate of change, which is where elasticity is useful and (in this example) defined as

e = (%changeiny/%changeinx) = (changeiny/changeinx)•x/y = b•(x/y), b = marginal effect.

I am having difficulty "seeing" the theoretical and algebraic reasoning for infinite elasticity when applied to independant/dependant variables. How can it be understood generally using this linear example? Is it only possible where y=0?

• Why do you want to understand elasticity as a linear regression? – BB King Dec 6 at 10:45
• A graph shows elasticity (y-axis) graphed against square-feet (x-axis) on a price-house size regression. It is perpendicular, vertical at the beginning and then flat. – Geoffrey Turner Dec 6 at 10:59
• Seems like you could Edit a lot more details about the data and what you are seeing into the question. – denesp Dec 6 at 11:39
• @denesp. The data is an example to demonstrate marginal effect and corresponding elasticity for house prices against square-feet (size). I don't understand how the relationship is perfectly elastic at any point either algebraically or theoretically? – Geoffrey Turner Dec 6 at 11:52
• Rather than posting these in the comments, could you please gather all relevant info and edit it into the question? If you could include an image of the graph, that would also be nice. – denesp Dec 6 at 19:15