Science, Tech, Math › Social Sciences Using Calculus to Calculate Price Elasticity of Supply Using Calculus to Calculate Price Elasticity of Supply Share Flipboard Email Print Cohdra/Morguefile Social Sciences Economics U.S. Economy Employment Supply & Demand Psychology Sociology Archaeology Ergonomics Maritime By Mike Moffatt Professor of Business, Economics, and Public Policy Ph.D., Business Administration, Richard Ivey School of Business M.A., Economics, University of Rochester B.A., Economics and Political Science, University of Western Ontario Mike Moffatt, Ph.D., is an economist and professor. He teaches at the Richard Ivey School of Business and serves as a research fellow at the Lawrence National Centre for Policy and Management. our editorial process Mike Moffatt Updated April 04, 2018 In introductory economics courses, students are taught that elasticities are calculated as ratios of percent changes. Specifically, they are told that price elasticity of supply is equal to the percent change in quantity supposed divided by the percent change in price. While this is a helpful measure, it is an approximation to some degree, and it calculates what can (roughly) be thought of as an average elasticity over a range of prices and quantities. To calculate a more exact measure of elasticity at a particular point on a supply or demand curve, we need to think about infinitesimally small changes in price and, as a result, incorporate mathematical derivatives into our elasticity formulas. to see how this is done, let's take a look at an example. An Example 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. Other Price Elasticity Equations Using Calculus To Calculate Price Elasticity of Demand Using Calculus To Calculate Income Elasticity of Demand Using Calculus To Calculate Cross-Price Elasticity of Demand Cite this Article Format mla apa chicago Your Citation Moffatt, Mike. "Using Calculus to Calculate Price Elasticity of Supply." ThoughtCo, Aug. 26, 2020, thoughtco.com/calculate-price-elasticity-of-supply-1146250. Moffatt, Mike. (2020, August 26). Using Calculus to Calculate Price Elasticity of Supply. Retrieved from https://www.thoughtco.com/calculate-price-elasticity-of-supply-1146250 Moffatt, Mike. "Using Calculus to Calculate Price Elasticity of Supply." ThoughtCo. https://www.thoughtco.com/calculate-price-elasticity-of-supply-1146250 (accessed July 24, 2021). copy citation Watch Now: How Does Price Elasticity of Demand Work?