Elasticity of Supply

Calculate the supply elasticity at any point using the calculus method. (Linear equation)

Suppose you're given the following question: Demand is Q = 100 - 3C - 4C2, where Q is the amount of the good supplied, and C is the production cost of the good. What is the price elasticity of supply when our per unit cost is $2? We saw that we can calculate any elasticity by the formula: Elasticity of Z with respect to Y = (dZ / dY)*(Y/Z) In the case of price elasticity of supply, we are interested in the elasticity of quantity supplied with respect to our unit cost C. Thus we can use the following equation: Price elasticity of supply = (dQ / dC)*(C/Q) In order to use this equation, we must have quantity alone on the left-hand side, and the right-hand side be some function of cost. That is the case in our demand equation of Q = 400 - 3C - 2C2. Thus we differentiate with respect to C and get: dQ/dC = -3-4C So we substitute dQ/dC = -3-4C and Q = 400 - 3C - 2C2 into our price elasticity of supply equation: Price elasticity of supply = (dQ / dC)*(C/Q)Price elasticity of supply = (-3-4C)*(C/(400 - 3C - 2C2)) We're interested in finding what the price elasticity of supply is at C = 2, so we substitute these into our price elasticity of supply equation: Price elasticity of supply = (-3-4C)*(C/(100 - 3C - 2C2))Price elasticity of supply = (-3-8)*(2/(100 - 6 - 8))Price elasticity of supply = (-11)*(2/(100 - 6 - 8))Price elasticity of supply = (-11)*(2/86)Price elasticity of supply = -0.256 Thus our price elasticity of supply is -0.256. Since it is less than 1 in absolute terms, we say that goods are substitutes.

Elasticity of supply changes with time

The more time a producer has to respond to price changes the more elastic the supply. If the supply is elastic, producers can increase output without a rise in cost or a time delay; If the supply is inelastic, firms find it hard to change production in a given time period.

Value to decide what type of elasticity a good is

The supply curve is elastic if... Elasticity > 1 The supply curve is inelastic if... Elasticity < 1 The supply curve has unit elasticity if... Elasticity = 0

Elasticity of Supply

a measure used in economics to show the responsiveness, or elasticity, of the quantity supplied of a good or service to a change in its price.