Elasticity

Motivating illustration:

Q: Why does the government tax cigarettes?

• Tax revenue

• Discourage people (especially teenagers) from smoking

We can use the concept of elasticity to explain this government policy.

Elasticity= measure of responsiveness

In general, says how much quantity will change given

• a change in price of that good

• a change in price of other goods

• a change in income

Elastic= very responsive

Inelastic= not very responsive

(think rubberband!)

4 types of elasticity:

1) Price elasticity of demand (E^d)

2) Price elasticity of supply (E^s)

3) Income elasticity (E^I)

4) Cross price elasticity (E^xy)

Each type of elasticity answers a certain question

Price elasticity of demand (E^d)

Q: How much does Qd change if the price of that good changes?

Application: By calculating E^d, government can determine how responsive groups of individuals will be to a price change (through a change in tax) and how much the tax change will affect cigarette tax revenue.

Interpret elasticity question into a mathematical formula.

E^d =

Note: DO NOT MEMORIZE these formulas - understand them!!

By law of demand,

Level of responsiveness:

• Very responsive: small change in price leads to a big change in Qd

 Ex) E^d for cigarettes by teenagers in 1 study (1996)=1.313

Interpretation: teenage demand for cigarettes is elastic

A 10% increase in price of cigarettes would cause approximately a 13% decrease in Qd of cigarettes

• Unresponsive: small change in price leads to an even smaller change in Qd

 Ex) E^d for all smokers is between 0.3 and 0.5

Interpretation: A 10% increase in the price of cigarettes causes Qd of cigarettes to fall by 3%-5%.

• Equal response:

Perfectly elastic vs perfectly inelastic

• Perfectly inelastic – no matter how much the price changes, Qd doesn’t change

Demand is vertical

• Perfectly elastic – any change in price will have an infinite response

Demand is horizontal

Think about the elasticity of demand for cigarettes. What types of things might affect E^d?

Given a price change, what type of things might determine whether Qd decreases by a lot or a little?

• price of chewing tobacco, cigars

• income

• necessity (addicts)

Price elasticity of demand affected by:

1. Presence of substitutes

More substitutes – more elastic

If there are many goods that you think are equivalent, then an increase in price of one of these goods will make you more likely to switch to a substitute

Qd of good with P increase will fall a lot

That is why firms try to do “branding” – convince you that there aren’t substitutes

2) Necessity vs luxury

3) Temporary vs permanent price change

5) Time (Short-run vs long-run)

Given a longer time frame, you can find substitutes

Ex) Suppose you went to the same café for coffee every morning. One morning they increase price by $0.50. Running late, buy anyhow. Next day, with more time, check out another café.

Good	Ed in short run	Ed in long run
Jewelry	0.44	0.78
Electricity	0.13	1.89
Gasoline	0.15	0.78

Long run will be more elastic than short-run

Ranking Exercise:Rank the following from least elastic to most elastic

• Soft drinks

• Coca-Cola

• Foreign Travel

• Food

• Rental Housing

E^d:Midpoint formula

There are different ways to calculate elasticity (can use different bases to calculate % change). We will use the midpoint formula.

Ex) Price of pizza increases from $4 to $5. Qd of pizza falls from 200 to 180. Calculate and interpret the elasticity.

Ex) Suppose that as the price of product H falls from $5 to $4, the quantity of H demanded increases from 2000 to 6000 units. In this case, what is the elasticity of demand, using the midpoint formula?

Ex) Suppose the US government wants to decrease teenage smoking by 50%. We know that E^d~=1.3. By what percentage would the government have to increase the price of a pack of cigarettes (through imposition of a tax) in order to cut teenage smoking by 50%? (Note, as we'll learn later, this question is not the same as saying what size tax would the government have to impose.)

E^d:Elasticity along a linear demand curve

Elasticity along a linear demand curve isn't constant.

Intuition:

Suppose you have a high Qd -- implies a low price. If you decrease Qd by 1 unit, the % change in Qd will be very small and the % change in price will be very large. Therefore, Ed must be a very small number.

Suppose you have a low Qd -- implies a high price. If you decrease Qd by 1 unit, the % change in Qd will be very large and the % change in price will be very small. Therefore, Ed must be a very large number.

Note: Even though this is the case, we typically draw inelastic as steep and elastic as flat.

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Why: if allowed curves to be non-linear, have constant elasticity/

E^d:Revenue and elasticity

Revenue=money that comes in (P*Q)

Elastic – price changes a little, quantity changes a lot

Intuition: you decrease price a little – people are very responsive to price change and buy a lot – even though selling at lower price, quantity increases so much that revenue increases

Inelastic: price changes a little, quantity changes even less

Intuition: you decrease price a little but barely anyone responds – quantity doesn’t incrase enough to make up for the fact that selling at lower price – revenue decreases

Comparative Statics

 A shock in a market will have different results on equilibrium P and Q, depending on elasticities of S and D (how responsive producers and consumers are to price change)

Illustrate an elastic and inelastic D curve

Want to compare effect of a decrease in supply when D elastic and inelastic. We know P increases and Q decreases.

If D is inelastic: P increases a lot, Q decreases a little

Why? People aren’t responsive to P changes that much – Q will fall only a little, even as P increases a lot

If D is elastic: P increases by less and Q decreases by more

People are very responsive to price change

Even just a small price change causes Q to fall a lot

Price elasticity of supply (E^s)

Q: How much does Qs change if the price of the good changes?

Tells us the ability of an industry to increase output in response to a price change

E^s =

Note: E^s is always positive by law of supply

 Note: All the forms of elasticity follow the same basic form for the midpoint formula. Rewrite E^s in the midpoint formula.

E^S affected by:

1. Cost of producing additional unit of good

 Higher cost – more inelastic

 Lower cost – more elastic

2. Time

When we study firm structure, we’ll discuss the idea of SR vs LR

In SR, there are fixed number of firms in industry each with fixed plant size

Can’t change Qs that much in response to price change (can work overtime)

In LR, firms can enter or firms can change size of plant

In LR, S is more elastic. Over a longer time frame, can change Qs more in response to P change

 Comparative statics: Same idea if S is elastic vs inelastic (Show on own)

Ex) Drug Market

Suppose originally the demand for drugs in the US is Qd=100-0.1P and the supply of drugs is Qs=40+0.5P. The government has two possible policy options if its goal is to decrease the quantity of drugs in the market:

• decrease supply by putting drug dealers in jails ("war on drugs")

• decrease demand by offering drug rehabilitation treatment.

Suppose if the government institutes a rehabilitation program, demand decreases to Qd'=88-0.1P. If the government institutes a "war on drugs", supply falls to Qs'=20+0.5P.

Which program is more effective if the goal is to decrease the amount of drugs sold? Explain why using E^d and E^s.

Income elasticity (E^I)

Note: Both Ed and Es refer to elasticity along a curve (describing D and S curves)

E^I and E^xy talk about relationship between Qd and a variable that shifts the curve

Q: If income changes, how much does Qd change at any particular price? (ie, how much does D shift?)

Midpoint formula

Good	EI
Margarine	-0.2
Food	0.51
Hospital care	0.69
New cars	2.45
Recreation/Entertainment	1.57

Cross-Price Elasticity(E^xy)

Q: How does Qd of good X change at any particular price if the price of good Y changes?

Midpoint formula:

Magnitude of E^xy tells you how closely related two goods are

Elasticity table

Ex) It is estimated that in Indonesia, a 10% increase in the price of kerosene decreases Qd of kerosene by 2.2%. A 10% increase in the price of electricity increases Qd of kerosene by 1.6%. What conclusions can you draw?

In a few sentences, summarize the main points of this section.