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

• P_i is initial price
• P_f is final price
• S_i is initial supply
• S_f is final supply
• D_i is initial demand
• D_f is final demand
• r_i is initial interest
• r_f is final interest
• I_i is initial investment
• I_f is final investment
• S_i is initial savings
• S_f is final savings

Price elasticity of demand

$= \frac{ %change in D }{ %change in P } = \frac{ \frac{ D_f - D_i }{ ( D_f + D_i ) / 2 } }{ \frac{ P_f - P_i }{ ( P_f + P_i ) / 2 } }$

Price elasticity of supply

$= \frac{ %change in S }{ %change in P } = \frac{ \frac{ S_f - S_i }{ ( S_f + S_i ) / 2 } }{ \frac{ P_f - P_i }{ ( P_f + P_i ) / 2 } }$

Interest elasticity of investment

$= \frac{ %change in I }{ %change in r } = \frac{ \frac{ I_f - I_i }{ ( I_f + I_i ) / 2 } }{ \frac{ r_f - r_i }{ ( r_f + r_i ) / 2 } }$

Interest elasticity of savings

$= \frac{ %change in S }{ %change in r } = \frac{ \frac{ S_f - S_i }{ ( S_f + S_i ) / 2 } }{ \frac{ r_f - r_i }{ ( r_f + r_i ) / 2 } }$

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.