Comparitive statics.md

#flashcards/micro #review

Comparitive Statics

The change in one variable relative to another after a change in an external factor (exogenous variable)

Income elasticity of demand

The coefficient of the income elasticity of demand is the % change in the amount of good purchased resulting from a given percentage change in income.

Coefficient of income elasticity of demand ($\eta$) of good 1::$$\eta_1=\frac{\Delta x_1}{\Delta m}\frac{m}{x_1}$$

When it comes to optimised values, the income elasticity is :: $$\eta_1=\frac{m}{x_1}\frac{\partial \hat{x}(p_1,p_2,m)}{\partial m}$$

Implications:

• $\eta<0$ ::inferior [[Goods|good]]

• $\eta \ge 0$ ::normal good

• $\eta>1$ :: luxury good

Price elasticity of demand

The coefficient of the price elasticity of demand is the % change in the amount of good purchased resulting from a given percentage change in the price of the good. Coefficient of price elasticity of demand ($\epsilon$) of good 1::$$\epsilon_1=\frac{\Delta x_1}{\Delta p_1}\frac{p_1}{x_1}$$

When it comes to optimised values, the price elasticity is :: $$\epsilon_1=\frac{p_1}{x_1}\frac{\partial \hat{x}(p_1,p_2,m)}{\partial p_1}$$

Implications:

• $\epsilon>0$ ::Giffen good

• $\epsilon \le 0$ :: ordinary good

Cross elasticity of demand

The coefficient of the cross elasticity of demand of good 1 with respect to good 2 is the % change in the amount of good 1 purchased resulting from a given percentage change in the price of good 2. (change in demand relative to the price of the other good) Coefficient of cross elasticity of demand (e) ::$$e_{x_1x_2}=\frac{\Delta x_1}{\Delta p_2}\frac{p_2}{x_1}$$

When it comes to optimised values, the cross price elasticity is :: $$e_1=\frac{p_2}{x_1}\frac{\partial \hat{x}(p_1,p_2,m)}{\partial p_2}$$

Implications:

• $e>0$ ::Substitutes

• $e<0$ ::Complements