Elasticity

Coffee Question Suppose two partners are arguing about a coffeeshop that is losing money. One of the partner thinks they need to raise prices - that way they will make more money on each cup of coffee they sell. The other partner thinks that if the lower prices they will make more money because they will sell a lot more cups of coffee. Who was right?

Coffee Question The answer is - it depends. On what? If you lower the price - will the new sales offset the loss in revenue on each coffee? If you raise your price - will the loss in sales be offset by the increase in price of coffee? In other words, how much will the quantity demanded change when price changes?

Demand We want to know just how much will quantity demanded change when price changes? That is what elasticity of demand measures.

Elasticity of Demand Elasticity of Demand (Ed) measures the responsiveness of Qd of a good to a changein its P. Ed = % in Qd % in P Note that  means “change” Also note that the law of demand implies Ed is negative. We will ignore the negative sign.

Price Elasticity of Demand

Calculating Elasticity of Demand There are two methods for calculating elasticity - point and arc methods. First, we will examine the point method.

Point Elasticity …and let’s say we want to find the Elasticity of Demand as we move from point A to Point B... P A 6 B 5 D Qd 2 3 6 7

Point Elasticity We know Ed = % in Qd % in P %can be calculated as the change divided by starting point

Point Elasticity Demand is Elastic The Elasticity of Demand (or Ed) is 1/2 divided by -1/6 which equals -3. But we ignore the sign and call it 3. Ed = % in Qd = 1/2 = 0.5 = - 3 or 3 % in P -1/6 -1.67 Demand is Elastic Let’s try that again moving from point C to D on the same curve

Point Elasticity P 6 5 C 2 D 1 Qd 2 3 7 8

Point Elasticity Demand is Inelastic The Elasticity of Demand (or Ed) is 1/7 divided by -1/2 which equals - 0.286 But we ignore the sign and call it 0.286 Ed = % in Qd = 1/7 = 0.143 = - 0.286 % in P -1/2 -0.50 Demand is Inelastic

Point Elasticity Note that Ed is different at different places along the curve. Specifically, it gets smaller as you move down the curve Note that elasticity and slope are NOT the same thing. One last calculation - let’s find the elasticity of demand going from point D to point C

Point Elasticity P 6 5 C 2 D 1 Qd 2 3 7 8

Point Elasticity Demand is Inelastic The Elasticity of Demand (or Ed) is -1/8 divided by 1 which equals -0.125 But we ignore the sign and call it 0.125 Ed = % in Qd = -1/8 = -0.125 = - 0.125 % in P 1/1 1 Demand is Inelastic But this is a different value than before!

Point Elasticity Note that we get a different elasticity depending on which point we call the starting point. A solution to this is by using the Arc Method for finding the Elasticity of Demand.

. Ed = Refinement: Midpoint Formula Change in quantity Sum of Quantities/2 price prices/2 .

Calculating Ed - Arc Elasticity Ed = % in Qd % in P % in Qd = Qd2 - Qd1 = Qd ____ (Qd1 + Qd2)/2 Average Qd % in P = P2 - P1 = P___ (P1 + P2)/2 Average P

Arc Elasticity The arc elasticity of demand is ED = .133/.667 = .2 As you can see from the equations, it doesn’t matter which is the starting point you will get the same number for the elasticity. Using points C and D we get % in Q = (1/(7+8)/2) = 1/7.5 = 0.133 % in P = (-1/(1+2)/2) = -1/1.5 = 0.667 The arc elasticity of demand is ED = .133/.667 = .2

Price Elasticity of Demand along a Demand Curve

How Do We Interpret Elasticity? If Ed = 2, means the ratio of %  Q to the %  P is 2 to 1 or: a 1% change in price will cause a 2% change in quantity demanded. a 2% change in price will cause a 4% change in quantity demanded, and so on.

Degrees of Ed Inelastic Ed = % in Qd % in P Ed < 1 For every 1% change in P, Qd changes by less than 1%

Degrees of Ed Unitary Elastic For every 1% change in P, Ed = % in Qd % in P Ed = 1 % in Qd = 1 % in P Ed = 1 For every 1% change in P, Qd changes by 1% (in opposite direction)

Degrees of Ed Elastic Ed = % in Qd % in P Ed > 1 For every 1% change in P, Qd changes by more than 1% (in opposite direction)

Degrees of Ed Perfectly Elastic Ed = % in Qd % in P Ed = % in Qd 0 The price of the good never changes, no matter how much consumers purchase of the good.

Elasticity P Perfectly Elastic Qd

Elasticity P Perfectly Inelastic Qd

Generalizing about Elasticity Notice that the vertical D curve has an elasticity of zero and the flat D curve has an elasticity of infinity. As the demand curve goes from vertical to horizontal the elasticity is going from 0 to infinity In other words, the flatter the demand curve, the greater the elasticity

Elasticity P Relatively Elastic Qd

Elasticity Relatively Inelastic P Relatively Elastic Qd

The Coffee Problem Back to the Coffeehouse question - should they raise or lower price? We said that depended on how much sales will change when they change price In other words, it depends on the elasticity

Total Revenue Total Revenue = P x Q The coffeehouse is interested in how TR (total revenue) changes as p and q change

Total Revenue Calculation - Example Price $1 Qd = 100 TR = $100 Price $2 Qd = 70 TR = $140

Total Revenue and Elasticity Let’s say demand is inelastic. Then if the coffeehouse raises prices 10%, the sales will drop by less than 10% In other words, the gain in revenue from higher prices is greater than the loss in revenue from lost sales.Therefore, Total Revenue will rise

Total Revenue and Elasticity If they lowered prices, though, the loss of revenue from higher prices would be greater than the gain from increased sales, so Total Revenue will fall

Elasticity and Total Revenue P Loss in Revenue Gain in Revenue Relatively Inelastic Qd

Total Revenue Test If P and TR or P and TR Demand is Inelastic

Total Revenue and Elasticity Let’s say demand is elastic. Then if the coffeehouse raises prices 10%, the sales will drop by more than 10% In other words, the gain in revenue from higher prices is less than the loss in revenue from lost sales.Therefore, Total Revenue will fall

Total Revenue and Elasticity If they lowered prices, though, the loss of revenue from higher prices would be less than the gain in revenue from increased sales, so Total Revenue will rise

Elasticity and Total Revenue P P TR Loss in Revenue Relatively Elastic Gain in Revenue Qd

Total Revenue Test If P and TR or P and TR Demand is Elastic

Total Revenue and Elasticity Unitary Inelastic

Total Revenue and Demand Elastic $ Elasticity = 1 Inelastic Demand Q $ Total Revenue Q

Elasticity and Total Revenue P Loss in Revenue Gain in Revenue Unitary Elastic Qd

Total Revenue Test If P and TR is unchanged Demand is Unitary

Elasticity and Total Revenue Inelastic Unitary

Determinants of Ed Availability of Substitutes Example: As there are more substitutes, demand is more elastic (and vice versa) Example: Insulin has no substitutes if diabetic and demand is very inelastic. Wal-Mart Brand Cola has many substitutes and hence, demand is very elastic

Determinants of Ed Amount of Consumers Budget Example: The less expensive a good is as a fraction of our total budget, the more inelastic the demand for the good is (and vice versa). Example: Price of cars go up 10% (from $20,000 to $22,000) Price of soda goes up 10% (from $0.50 to $0.55) Demand is more effected by the price of cars increasing.

Determinants of Ed Time Example - Price of Gasoline Increases The longer the time frame is, the more elastic the demand for a good is (and vice versa). Example - Price of Gasoline Increases Immediately: can’t do much, still need to get to work, school, etc. Short-run: find a car pool, ride bike, etc. Long-run: next car you buy uses less gas.

Determinants of Ed Necessities vs. Luxuries Example: Insulin The more necessary a good is, the more inelastic the demand for the good (and vice versa). Example: Insulin

Income Elasticity of Demand Income Elasticity of Demand (Ey) - measures the responsiveness of quantity demanded to changes in income. Ey = % in Qd % in Y Note that the sign IS important!

Ey = Income Elasticity of Demand Normal Goods - Positive Sign Percentage change in quantity demanded Ey = Percentage change in income Normal Goods - Positive Sign Inferior Goods - Negative Sign

Normal Goods Typically, if our income rises, we buy more and visa versa. These types of goods are called normal goods. Ey > 0 - normal good Normal Goods can be split into two categories: Luxury and Necessity Goods

Inferior Goods There are some good we buy less of as our income grows and more of as our income falls. For instance, in college you probably eat Macaroni & Cheese. But when you get a good job (as all SMSU-WP grads do) you will probably buy less Mac and Cheese. If a goods elasticity is Ey < 0 it is an inferior good

Cross Price Elasticity of Demand Another type of elasticity is the Cross Price Elasticity. This gets at how changes in price of one good can effect the demand of another Cross Price Elasticity of Demand (Ex,y) - measures the responsiveness of quantity demanded of good one when the price of good 2 changes.

Cross Price Elasticity of Demand Ex,y = % in Qd of Good X %  in P of Good Y Note that the sign DOES matter for this elasticity also!

Percentage change in quantity Cross Price Elasticity of Demand Percentage change in quantity demanded of good X Exy = Percentage change in the price of good y Substitute Goods - Positive Sign Complementary Goods - Negative Sign Independent Goods - Zero or near-zero value

Substitute Goods Consider Coke and Pepsi. If the price of Coke goes up, what would you expect to happen to the quantity demanded of Pepsi? It will rise, since people will buy less Coke and more Pepsi. Thus the Demand for Pepsi will rise. So the bottom of the elasticity fraction is positive and top of the elasticity fraction is positive.

This relationship is called substitutes and can be seen when Substitute Goods This relationship is called substitutes and can be seen when Ex,y > 0.

Complement goods Consider Washing Machines and Dryers. If the price of Washing Machines goes up, what would you expect to happen to the quantity demanded of Dryers? It will fall, since people will buy less washers at the new price, they will need less dryers. So the bottom of the elasticity fraction is positive and top of the elasticity fraction is negative.

Complement Goods This relationship is called complements and can be seen when Ex,y < 0

Elasticity of Supply This one is just same as price elasticity of demand, except we substitute the word supply for demand. It is measured the same and is inelastic, elastic, and unit elastic. Elasticity of Supply (Es) - measures the responsiveness of quantity supplied to changes in price of the good.

Elasticity of Supply Es = % in Qs % in P Law of Supply tells us this number is generally positive.

Determinants of Elasticity of Supply If supply is getting more (or less) elastic, we are saying that the firms can change supply in larger (or smaller) quantities when price changes. Generally, anything that can effect a firms ability to change production easily will effect the elasticity of supply.

Determinants of Elasticity of Supply For instance: more time specific difficulties of increasing output how cost changes at the firm increases Q To consider: what would the supply curve of Picasso paintings look like?

Elasticity of Supply P Picasso paintings Es = % in Qs Qd Perfectly Inelastic Supply Picasso paintings Es = % in Qs % in P = 0 Qd

Elasticity of Supply P Es = % in Qs < 1 Qd Relatively Inelastic Supply Es = % in Qs < 1 % in P Qd

Elasticity of Supply P Es = % in Qs > 1 Qd Highly Elastic Supply % in P Qd

Elasticity of Supply Immediate market period SM P An increase in demand without enough time to change supply causes only P to increase Po D2 D1 Q

Elasticity of Supply Short run SSR P An increase in demand with no expansion of capital use causes only a small Qs Po D2 D1 Q Qo

Elasticity of Supply Long run SLR An increase in P demand in the long run allows greater Qs P SLR Po D2 D1 Q Qo

KEY TERMS price elasticity of demand elastic demand inelastic demand unitary elasticity perfectly inelastic demand perfectly elastic demand point elasticity arc elasticity total revenue total-revenue test cross-price elasticity of demand income elasticity of demand elasticity of supply market period short run long run