Elasticity

This is Unit Four of Principles of Microeconomics, part one of two: elasticity, the number that says how much quantity responds when a price moves. Carry one idea. The laws of demand and supply give a direction; elasticity gives the size, and the size decides what a price change does to revenue and how a cost change divides between buyers and sellers. This part builds the measure, learns to read it off a line, and puts it to work on revenue. By the end you will be able to compute price elasticity of demand by the midpoint method and classify it. To tell elasticity from slope and locate the elastic and inelastic ranges on a straight line. To name the two extremes and what makes demand elastic. To use the total revenue test and predict who gains from a cost change. And to compute the elasticity of supply.

Four entries on the measure: what elasticity is, the price elasticity of demand, the midpoint method, and a full computation.

What elasticity measures.

MIC 0301 Elasticity Measures Responsiveness

Elasticity measures how much one variable responds to a change in another, as a ratio of percentage changes. The laws of demand and supply give the direction; elasticity gives the size. A ten percent fare rise might cut ridership by three percent or by fifteen. Percentages, not units, so the answer is the same whether quantity is in pounds or tons.

The most used elasticity.

MIC 0302 Price Elasticity of Demand

Price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price. The two move oppositely, so the ratio is negative, and the course reports the absolute value. A ten percent price rise cutting quantity twenty percent gives elasticity two. It measures a movement along one demand curve; shifts have their own elasticities, in part two.

How to compute the percentages.

MIC 0303 The Midpoint Method

The midpoint method divides each change by the average of the two values, not the starting value, so the elasticity between two points is the same in either direction. From forty to sixty the change is twenty over fifty, forty percent, either way. It is also called arc elasticity; the starting-value method gives a different answer for a rise than for a fall.

A full computation.

MIC 0304 Computing a Price Elasticity of Demand

Four steps. The change in quantity divided by the average quantity, times one hundred. The change in price divided by the average price, times one hundred. Divide the first percentage by the second. Drop the sign and classify: above one elastic, below one inelastic, exactly one unitary. At twelve dollars a museum sells eight hundred tickets a day and at ten dollars one thousand: the quantity change is two hundred over an average of nine hundred, about twenty-two percent; the price change is two dollars over an average of eleven, about eighteen percent; twenty-two over eighteen is about one point two two, elastic. Dividing by the starting value instead gives one point five, a direction-dependent number, and work both changes in the same direction.

Four entries on reading the number: the three classes, elasticity against slope, how it changes along a line, and locating a point.

The three classes.

MIC 0305 Elastic, Inelastic and Unitary

Demand is elastic when quantity changes by a larger percentage than price, inelastic when by a smaller one, and unit elastic when the two percentages match. Restaurant meals tend to be elastic; electricity tends to be inelastic. Inelastic does not mean unresponsive: quantity still falls when price rises, only by less than the price rose.

The number elasticity is mistaken for.

MIC 0306 Elasticity Is Not Slope

Slope is the change in price over the change in quantity, in units; elasticity is a ratio of percentages. On a straight line slope is constant and elasticity is not: a one-dollar cut is a big percentage at a low price and small at a high one. A steep curve is not always inelastic, since steepness depends on the units chosen and elasticity does not.

How elasticity changes along a line.

MIC 0307 Elasticity Along a Straight-Line Demand Curve

On a straight-line demand curve, demand is elastic in the upper half, unit elastic at the midpoint, and inelastic in the lower half. Near the top, price is high and quantity small, so a fixed step is a small price percentage and a large quantity one. Calling a whole straight demand curve elastic is an error; the question is where the market sits.

Locating a point on the line.

MIC 0308 Reading Elasticity off a Line

To classify a point on a straight-line demand curve, find the line's midpoint, halfway along from each intercept. Points above and to the left are elastic, the midpoint is unitary, and points below and to the right are inelastic. A line from a price intercept of twenty dollars to a quantity intercept of one thousand has its midpoint at ten dollars and five hundred units. At sixteen dollars and two hundred units demand is elastic, confirmed by a step to fourteen and three hundred, near three. At four dollars and eight hundred it is inelastic, confirmed by a step to two and nine hundred, about zero point two. The line's midpoint is set by the intercepts, not by the observed prices, and two lines through one point with different slopes differ there.

Four entries on the extremes and what makes demand elastic, including time.

The two extremes.

MIC 0309 Perfectly Elastic and Perfectly Inelastic

A horizontal curve is perfectly elastic: any quantity at one price, none at a higher one. A vertical curve is perfectly inelastic: the same quantity at any price. A single wheat farmer faces horizontal demand; a diabetic's insulin demand is nearly vertical. Perfectly inelastic is not inelastic: inelastic demand still slopes down, and only the vertical case does not respond at all.

The curve with elasticity one everywhere.

MIC 0310 Constant Unitary Elasticity

A unit-elastic curve has quantity change by the same percentage as price everywhere: for demand a curve, steep at the left and flat at the right; for supply a straight line through the origin. Halving the price doubles quantity anywhere on the demand version. Along a unit-elastic demand curve spending never changes, which is the total revenue test coming later in this part.

What makes demand elastic.

MIC 0311 What Makes Demand Elastic

Demand is more elastic when close substitutes exist, when the good takes a large budget share, when it is a luxury rather than a necessity, and when buyers have time to adjust. One brand of gasoline is elastic; gasoline as a whole is not. The narrower the good's definition, the more substitutes it has and the more elastic its demand.

The time dimension.

MIC 0312 Short Run Against Long Run

Elasticities are lower in the short run than the long run, for demand and supply alike: given time, buyers find substitutes and sellers build capacity. A higher electricity price changes little by tomorrow and much within a year. The same shift moves price a lot in the short run and quantity a lot in the long run, and both diagrams are right.

Three entries on revenue: what it is, the test that says which way it moves, and who gains from a cost change.

The number sellers watch.

MIC 0313 Total Revenue

Total revenue is price times quantity sold. On the diagram it is the rectangle under the point on the demand curve, and a price change reshapes that rectangle. Eight hundred tickets at twelve dollars is nine thousand six hundred dollars of revenue. A price rise always cuts quantity, so revenue can go either way, and which way depends on elasticity alone.

The test.

MIC 0314 The Total Revenue Test

Revenue moves with whichever variable changes by the larger percentage. If demand is elastic, quantity changes more, so a price cut raises revenue and a price rise lowers it. If demand is inelastic, price changes more, so a price rise raises revenue and a cut lowers it. The museum sells eight hundred tickets at twelve dollars, nine thousand six hundred, and one thousand at ten dollars, ten thousand: demand was elastic, so the cut raised revenue. A transit line sells forty thousand rides at two dollars, eighty thousand; a rise to two twenty cuts rides to thirty-eight thousand, eighty-three thousand six hundred: demand was inelastic, so the rise raised revenue. Revenue is not profit, since a price cut that raises revenue also raises output and its cost.

Who feels a cost change.

MIC 0315 Passing a Cost Change Through

When supply shifts, demand's elasticity decides how the change divides between price and quantity. Shift supply right against inelastic demand and the price falls a lot while quantity rises a little, so buyers capture most of the saving; against elastic demand, quantity rises a lot while the price falls a little. A bumper wheat harvest shifts supply right. With inelastic food demand, the price drops from six dollars to four while quantity rises from one million to one million one hundred thousand, and revenue falls from six million to four million four hundred thousand. The same shift in an elastic market, restaurant meals, cuts the price from twenty dollars to nineteen while quantity rises to one million two hundred thousand, and revenue rises from twenty million to twenty-two million eight hundred thousand. That is why a good harvest can hurt farmers as a group, and only elasticity says which way revenue goes.

Two entries on the supply side's own elasticity, and its computation.

The supply side's own elasticity.

MIC 0316 Price Elasticity of Supply

Price elasticity of supply is the percentage change in quantity supplied divided by the percentage change in price. It is positive, and the three classes apply: elastic above one, inelastic below, unitary at one. Pencils are elastic in supply; prime waterfront apartments are inelastic. Supply elasticity depends on how easily inputs are found and production expanded, not on what buyers want.

The computation.

MIC 0317 Computing a Price Elasticity of Supply

Midpoint method again: divide the change in quantity supplied by the average quantity, divide the change in price by the average price, and divide the first percentage by the second. The sign is positive and stays. A high number means a small price rise brings a large quantity response. At a rent of one thousand dollars landlords offer five thousand units, and at one thousand one hundred they offer five thousand five hundred: the quantity change is five hundred over an average of five thousand two hundred fifty, about nine point five percent; the price change is one hundred over an average of one thousand fifty, also about nine point five percent; the elasticity is about one, unit elastic. Do not reuse a demand elasticity for the supply side, and state the horizon with the number, since years give a larger number than months.

Look at what you can now do. You can compute price elasticity of demand by dividing each change by the average, and classify it as elastic above one, inelastic below, unitary at one. You can tell elasticity from slope, units against percentages, and place a point on a straight line: elastic above the midpoint, inelastic below. You can name the extremes, horizontal and vertical, and say that substitutes, budget share, luxury and time make demand elastic. You can run the total revenue test, revenue following the larger percentage change, and predict that a cost saving reaches buyers where demand is inelastic and raises sellers' revenue where it is elastic. And you can compute supply elasticity with the same method and a positive sign. Part two turns to time, the two elasticities read by their sign, and a tax, where elasticity decides who pays.