# Principles of Economics/Elasticity

Elasticity refers to the degree to which one value changes when another does. Supply and demand change with respect to price; investment and savings change with respect to interest rate. The name is "X elasticity of Y" where a change in X causes a change of magnitude (the elasticity * Y):

where

• ${\displaystyle P_{i}}$ is initial price
• ${\displaystyle P_{f}}$ is final price
• ${\displaystyle S_{i}}$ is initial supply
• ${\displaystyle S_{f}}$ is final supply
• ${\displaystyle D_{i}}$ is initial demand
• ${\displaystyle D_{f}}$ is final demand
• ${\displaystyle r_{i}}$ is initial interest
• ${\displaystyle r_{f}}$ is final interest
• ${\displaystyle I_{i}}$ is initial investment
• ${\displaystyle I_{f}}$ is final investment
• ${\displaystyle S_{i}}$ is initial savings
• ${\displaystyle S_{f}}$ is final savings

Price elasticity of demand

${\displaystyle ={\frac {\%changeinD}{\%changeinP}}={\frac {\frac {D_{f}-D_{i}}{(D_{f}+D_{i})/2}}{\frac {P_{f}-P_{i}}{(P_{f}+P_{i})/2}}}}$

Price elasticity of supply

${\displaystyle ={\frac {\%changeinS}{\%changeinP}}={\frac {\frac {S_{f}-S_{i}}{(S_{f}+S_{i})/2}}{\frac {P_{f}-P_{i}}{(P_{f}+P_{i})/2}}}}$

Interest elasticity of investment

${\displaystyle ={\frac {\%changeinI}{\%changeinr}}={\frac {\frac {I_{f}-I_{i}}{(I_{f}+I_{i})/2}}{\frac {r_{f}-r_{i}}{(r_{f}+r_{i})/2}}}}$

Interest elasticity of savings

${\displaystyle ={\frac {\%changeinS}{\%changeinr}}={\frac {\frac {S_{f}-S_{i}}{(S_{f}+S_{i})/2}}{\frac {r_{f}-r_{i}}{(r_{f}+r_{i})/2}}}}$

## Cross elasticities

The elasticities mentioned above refer to one object. Cross elasticities refer to the effects of something's price, interest, etc. on something else. This comes into play with substitute and complementary goods and services for the consumer