Elasticities

Abstract

• 1. Elasticities are always independent of the unit of measurement.

• 2. The point elasticity and the arc elasticity of a linear demand function are always identical.

• 3. The value of the price elasticity of a demand function $x(p)=\frac{10}{p}$ always equals 10.

• 4. The price elasticity of a supply function is influenced by the production functions of the firms supplying in the market.

Market research has measured the following market demand function: $x(p)=1{,}000-300\,p$. The market supply function is $y(p)=\alpha+100\,p$, with $-\frac{1{,}000}{3}<\alpha<1{,}000$.

• 1. The price elasticity of demand is constant.

• 2. The market demand in equilibrium reacts inelastically to changes in the price

• 3. The market supply reacts inelastically to changes in the price if α > 0.

• 4. The market supply in equilibrium reacts elastically to changes in the price if α < 0.

Thilo wants to consistently spend half of his income on apparel.

• 1. The income elasticity of his demand for apparel is (in absolute terms) 0.5.

• 2. The price elasticity of his demand for apparel is 0.

Carl wants to spend a constant percentage of his income on apparel.

• 3. The income elasticity of his demand for apparel is (in absolute terms) 0.5.

• 4. The price elasticity of his demand for apparel is 0.