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Price elasticity of demand

Chapter 5

Elasticity

How does a Change in Supply Affect Price & Quantity? Want a quantitative answer. Suppose new safety regulations increase the

cost of producing toasters. How much does price increase?

How much does quantity decrease?

P

How much do P & Q change?

Depends on:

– shape of D curve

– where you are on the D curve.

D

SS’

Q

P

Q

Price Elasticity of Demand

How responsive the quantity demanded is to changes in price.

Availability of Substitutes

The more and better the substitutes, the higher the elasticity, since as the price rises consumers switch to other products easily.

Note: the more broadly one defines a good, the lower the elasticity.

Ex: citrus fruits v. fresh produce Ex: toothpaste v. Aim toothpaste

Proportion of Income Spent on the Good The higher the proportion, the higher the

elasticity. Ex: salt v. housing

Price Elasticity of Demand: Formula %QD = QD/ave. Q

% P P/ave. P

QD/ave. Q = Q0-Q1

(Q0+Q1)/2

P/ave. P= P0-P1

(P0+P1)/2

An Example

% QD =(7-3) (100)

(7+3)/2

% P =(5-7) (100)

(5+7)/2

=4/5

-2/6

= -2.4

D

SS’

Q

P

73

5

7

Interpreting the Answer

Negative sign: The price elasticity of D will always have a negative sign. (Why?)

By convention, we usually drop the negative sign & focus on the absolute value of.– Note: sign is still imp’t for other elasticities

we’ll study later.

Interpreting the Magnitude

= % QD/ % P = 2.4

The quantity demanded will fall by 2.4 % for every 1% increase in price.

Ex: If price rises 15%, then QD will fall by 36%.

Elastic Demand

We say that demand is elastic when > 1. % QD> % P

Total revenue (P x Q) moves in the same direction as QD.

If price rises, QD falls by a larger %, total revenue falls.

If price falls, QD rises by a larger %, total revenue rises.

Unit Elastic

We say that demand is unit elastic when = 1.

%QD= % P

Total revenue (P x Q) unchanged as price changes.

Inelastic

We say that demand is inelastic when < 1. %QD< % P

Total revenue (P x Q) moves in the same direction as price.

If price rises, QD falls by a smaller %, total revenue rises.

If price falls, QD rises by a smaller %, total revenue falls.

Relating Elasticity to the Shape of & Location on D curve

Straight-line demand curve: Elasticity falls as you move down the D curve.

See textbook for a numerical example.

D

Q

P

> 1

< 1

= 1

Revenue Maximization & Straight-Line Demand

When elastic, what happens to revenue as price falls?

When inelastic, what happen to revenue as price falls?

Where is revenue maximized?D

Q

P

> 1,elastic

< 1inelastic

= 1,unit elastic

Revenue Max. & Profit Max.

Are they the same thing?

Perfectly Inelastic Demand

= %QD/ % P

= 0

(Violates the Law of Demand)

Q

P D

Perfectly Elastic Demand

= % QD/ % P

= Violates the Law of

Demand

Q

P

D

Comparing 2 straight-line D curves

Begin at pt. C. Same P change. Change in Q very

different

Q

P

DBDA

pt. C

Comparing 2 straight-line D curves DA is steeper, less elastic (more inelastic)

compared to DB at the point where they cross.

Short Run versus Long Run

Short run (SR): the period after some change, but before adjustments to the change are complete.

Long run (LR): the period after some change, once all adjustments to the change have been made.

Elasticity in the SR & LR

Short Run– Quantity demanded has a limited response to

changes in price.– Demand is less elastic

Long Run – response to changes in price is complete.– Demand is more elastic.

Demand in the LR and SR

DLR represents complete adjustment to new P.

DSR shows initial response to P, given initial P.

Q

P

DLR

DSR

pt. B

DSR

DSR

pt. A

pt. C

Coming Up

Other demand elasticities. Price elasticity of supply.

Group Work

Problems on handout relating to price elasticity of demand.

Odd-numbered groups work 1 &3 first, even-numbered groups work 2 & 4 first.

1. Sale of Fresh Green BeansMonth Price/lb. Quantity in lbs.

June $0.80 125July $0.65 150

Calculate the price elasticity of demand using the data above. Show your work.

Is the demand for green beans price elastic, unit elastic, or price inelastic?

2. Price Elasticity

Suppose that = 1.25 and price falls from $7.00 to $5.00. By what percentage will the quantity demanded increase? Show your work.

Will revenue rise or fall as a result? How do you know?

3. Water authority wants usage to fall during drought There is a meeting to consider raising the price. One

person says, “You can increase the price of water, but since it is a necessity, people won’t cut back.” You, however, convince the water authority to raise prices by 30 percent, predicting a 25 percent reduction in consumption. One month after the new rates are implemented, the water company reports that consumption has fallen 3 percent, and water officials are greatly discouraged.

Water Problem, Cont’d.

What is price elasticity of demand did you use to make your prediction? Show your work.

What is the price elasticity of demand, as indicated by the experience of this water company so far? Show your work.

Were you necessarily wrong? [Hint: Will the situation be the same six months from now?]

4. Pricing parking spaces in a parking lot You think that if you reduce prices then you

will be able to fill more spots and therefore earn more money. Your friend says that you should raise prices and thereby increase revenue even if fewer people park there.

Suppose you find out that the elasticity of demand (at your current price) is equal to 0.80. How can this information settle your debate?