1

IV. Elasticities

A. Show the responsiveness of quantity supplied or

quantity demanded to a change in another variable

1. Good´s own price

a) Price elasticity of supply

b) Price elasticity of demand

2. Income-income elasticity of demand

3. Price of a related good (in consumption)-cross

elasticity of demand.

4. An elasticity is expressed as a ratio of two

percentages

a) Suppose a price increase of 20% leads to a

12% decrease in quantity demanded. The price

elasticity of demand is −.12

.20

= −.6

b) Suppose a price decrease of 10% causes a 25%

decrease in quantity supplies .25

.10

= 2.5

c) Suppose a 5% increase in income causes a 5%

reduction in demand for the good −.05

.05

= −1

(1) What does this say about the type of good?

(2) Inferior good

B. Price elasticity of demand-3 methods to calculate

1. Return to pizza example.

a) 3 of the price quantity combinations

(1) 40 KD 10 pizzas

(2) 30 KD 25 pizzas

(3) 20 KD 50 pizzas

2

b) Use the first two combinations to start-price

drops from 40 KD to 30 KD

(1) Percentage change in the quantity of pizza

25−10

25+10( ) /2

=

15

17.5

=

30

35

=.86

(2) Percentage change in the price of pizza

30−40

30+40( ) /2

= −

10

35

= −.29

(3) Price elasticity of demand εd = −

.86

.29

= −3

c) Use the second and third-price drops from 30

KD to 20 KD

(1) Percentage change in the quantity of pizza

50−25

50+25( ) /2

=

50

75

=.67

(2) Percentage change in the price of pizza

20−30

20+30( ) /2

= −

10

25

= −.4

(3) Price elasticity of demand εd = −

.67

.4

= −1.7

d) Notice that putting the average in the

denominator of each percentage change means that

the elasticity will be the same whether price falls or

price rises.

e) This manner of calculating the elasticity (with

the average percentage change in the denominator)

is called arc elasticity. Arc because it is between two

points.

2. Another way to calculate the price elasticity of

demand

a) This manner gives point elasticity, meaning the

elasticity at a specific point. Since we need to use the

slope of the demand curve in the calculation we will

only use this method for a demand schedule that is a

straight line.

3

b) ExampleQd = 200−2P

(1) Draw graph showing extreme points.

(2) We can use any two points on the demand

to find the line slope. Slope is -½.

(3) Inverse of slope is -2

(4) Now take any P,Q combination that satisfies

the demand equation and the elasticity is

!

!”!”#

!

!

= 𝜀!

(a) Example-1 50 KD, 100 pizzas

−𝟐 𝟓𝟎

𝟏𝟎𝟎

= −𝟏

(b) Example-2 75 KD, 50 pizzas

−𝟐 𝟕𝟓

𝟓𝟎

= −𝟑

(c) Example-3 25 KD,150 pizzas

−𝟐 𝟐𝟓

𝟏𝟓𝟎

= − 𝟏

𝟑

(5) In talking about price elasticity of demand

the negative sign is frequently ignored since we all

know the actual elasticity must be negative due to

the law of demand.

(a) If εd = -1, unit or unitary

elasticity of demand (with respect to

price). Example 1

(b) If εd < -1, elastic demand. Example 2

(c) If 0 > εd > -1, inelastic demand.

Example 3

3. Yet another way

a) If you understand calculus the following form

might make more sense to you. Otherwise you need

not worry about the following.

b) 𝜺𝒅 =

𝒅𝑸𝒅

𝒅𝑷

𝑷

𝑸

4. Extreme cases

a) Perfectly inelastic demand

4

(1) Demand schedule is a vertical line

(2) 𝜀! = 0

(3) An example might be certain drugs, insulin

for example, that must be taken in the prescribed

dosage to maintain health. Demand for the drug

does not fluctuate with price.

b) Perfectly elastic demand

(1) Demand schedule is a horizontal line

(2) 𝜀! = −∞

(3) We will see this case when we talk about a

firm in a perfectly competitive market (to be

defined later in the course).

5. Factors affecting the price elasticity of demand

a) Availability of substitutes

(1) A good that has few substitutes tends to have

inelastic demand (0 > εd > -1), quantity demanded

is not very responsive to price.

(a) Cigarettes

(b) Drug like insulin

(c) Oil

(2) A good that has many substitutes tends to

have elastic demand (εd < -1), quantity demanded
is very responsive to price.

(a) Pizza

(b) Soft drinks

b) Unimportance of the good in one’s budget

(1) Tend not to respond much to price changes

of goods that are a very small share of one’s

budget.

(2) That is the good tends to be inelastic.

(3) Examples

5

(a) Salt

(b) Detergent

c) Time

(1) Over short time horizons demand for a

good tends to be inelastic. Oil in 1973-price

increased

(a) Difficult to quickly adjust driving

habits when price rises

(b) Difficult to switch to smaller cars,

alternative transport when price rises.

(c) Electricity prices increased.

(2) Over longer time horizons, demand is more

elastic.

(a) Adjust driving habits

(b) Switch to smaller and more fuel

efficient vehicles

(c) Replace older appliances with

those that use less electricity

C. Price elasticity of supply

1. Return to pizza example

a) 3 of the price quantity combinations

(1) 40 KD 80 pizzas

(2) 30 KD 70 pizzas

(3) 20 KD 50 pizzas

b) Use the first two to start-price drops from 40

KD to 30 KD

(1) Percentage change in the quantity of pizza

70−80

70+80( ) /2

= −

10

75

= −

2

15

= −.13

(2) Percentage change in the price of pizza

30−40

30+40( ) /2

= −

10

35

= −.29

6

(3) Price elasticity of supply 𝜀! =

.!”

.!”

= .45

c) Use the second and third-price drops from 30

KD to 20 KD

(1) Percentage change in the quantity of pizza

50−70

50+70( ) /2

= −

20

60

= −.33

(2) Percentage change in the price of pizza

20−30

20+30( ) /2

= −

10

25

= −.4

(3) Price elasticity of supply 𝜀! =

.!!

.!

= .83

d) Notice that putting the average in the

denominator of each percentage change means that

the elasticity will be the same whether price falls or

price rises.

e) Again, an elasticity calculated in this manner

(with the average in the denominator) is called arc

elasticity. Arc because it is between two points.

2. Another way to calculate elasticity if we have a

straight line supply schedule.

a) This manner gives point elasticity, elasticity at

a specific point.

b) Straight line like 𝑸𝒔 = 𝟓𝑷 − 𝟖𝟎

(1) Graph showing vertical axis intercept at 16

KD

(2) Slope is !

!

. Inverse of the slope is 5

(3) Take any P,Q combination that satisfies the

equation then elasticity is

!

!”#$%

!

!

= 𝜀!

(a) Example-1 20 KD, 20

𝟓𝟐𝟎

𝟐𝟎

= 𝟓

(b) Example-2 40 KD, 120

7

𝟓

𝟒𝟎

𝟏𝟐𝟎

=

𝟓

𝟑

= 𝟏.𝟔𝟔

(c) Example-3 100 KD, 420

𝟓𝟏𝟎𝟎

𝟒𝟐𝟎

= 𝟏.𝟐

(4) Size of the price elasticity of supply

(a) If εs = 1, unit or unitary elasticity

of supply (with respect to price)

(b) If εs > 1, elastic supply

(c) If εs < 1, inelastic supply

3. Yet another way

a) If you understand calculus

b) εs =

dQs

dP

P

Q

4. Extreme cases

a) Perfectly inelastic supply

(1) Supply schedule is a vertical line

(2) 𝜀! = 0

(3) Example would be a good for which supply

cannot be changed in the short run. Supply of fish

in the market cannot vary day to day. Supply of

apartments cannot be changed over the short run.

b) Perfectly elastic supply

(1) Supply schedule is a horizontal line

(2) 𝜀! = +∞

D. Income elasticity of demand

1. Measure of the responsiveness of demand for a

good to changes in income.

2. Ratio of two percentages

8

a) Suppose income increases 5% and demand

increases 12% then εy =

12

5

= 2.4 Note this must be a

normal good

b) Suppose income decreases 10% and demand

increases 6% then εy = −

6

10

= −.6 Note this must be an

inferior good.

3. Again we use an arc elasticity measure.

a) Suppose income in the United States as

measured by gross domestic product increases from

9.5 trillion to 10.5 trillion. By the arc measure, the

percent change in income is 10.5−9.5

10.5+9.5( ) /2

=.1 or 10%.

b) Suppose that the quantity demanded of cars

goes from 4.5 million to 5.5 million 5.5−4.5

5.5+4.5( ) /2

=.2 or

20%

c) Income elasticity of demand is .2

.1

= 2 . Why can

we conclude that cars are a normal good?

(1) A normal good is one whose demand

increases (D shifts right) when income increases

and vice versa. . Thus 𝜀! > 0

(a) Thus either demand rises

(positive percentage change) when

income rises (positive percentage

change) or

(b) demand falls (negative

percentage change) when income falls

(negative percentage change)

(c) The income elasticity of demand

is either the ratio of two positive

percentage changes or two negative

percentage changes thus always

positive for a normal good.

(2) An inferior good is one whose demand

increases (D shifts right) when income decreases

and vice versa. Thus 𝜀! < 0

9

(a) Thus either demand rises

(positive percentage change) when

income falls (negative percentage

change) or

(b) demand falls (negative

percentage change) when income rises

(positive percentage change)

(c) The income elasticity of demand

is the ratio of a positive percentage

changes and a negative percentage

change thus always negative for an

inferior good.

E. Cross elasticity of demand

1. Ratio of the percentage change in the quantity

demanded caused by a percentage change in the price of

another good. Goods A and B 𝜀! =

%!!!

!

%!!!

2. Cross elasticity values

a) εc = 0

(1) Goods must be unrelated.

(2) A price change in one has no effect on the

quantity demanded of the other.

b) εc > 0

(1) A price increase (decrease) in one increases

(decreases) the quantity demanded of the other.

(2) The goods are substitutes

(3) Example: the price of tea increases causing

the demand for coffee to increase.

c) εc < 0

(1) A price increase (decrease) in one decreases

(increases) the quantity demanded of the other.

(2) The goods are complements

(3) Example: the price of tea increases causing

the demand for sugar to decrease.

1

VI. Production

A. Definition-process of converting inputs to outputs

1. Inputs-land (raw materials), labor, capital

2. Output-whatever the firm produces

B. Firm’s decisions

1. Determine how much should be produced-depends on

a) Price of output

b) Costs of production

2. Select the technology (production function) to use

3. Determine the amount of inputs

4. These are not really independent decisions but made together.

a) In this part assume the firm selects output level

b) Our focus on technology and inputs

c) Firm seeks to minimize costs for a given level

of output

C. Production function

1. Mathematical relation showing how inputs converted to output.

𝑞 = 𝑓(𝑘,𝑙), which just tells us that output, q, depends on the firm’s

capital (k) and labor (l).

2. Assumptions about production function

a) More k or more l means more q. More

inputs means more output

b) As additional units of capital are added to

a fixed amount of labor the increments to output

get smaller. Diminishing marginal product of

capital

2

c) As additional units of labor are added to a

fixed amount of capita; the increments to output

get smaller. Diminishing marginal product of

labor. Draw graph

3. Marginal Product of Labor Example-Price of good is 2 KD-

a) Value of the MPL is the price of what is

produced times MPL. This represents the amount

added to revenue by the additional worker.

b) Suppose wage rate is KWD 15

Labor Output Average product of labor

Marginal

product of labor

Value of marginal

product of labor

0 0 — —

1 40 40 40 80 KD

2 70 35 30 60

3 90 30 20 40

4 100 25 10 20

5 105 21 5 10

c) Should the 1st worker be hired? Yes, value of

what each produces (the value of the MPL) exceeds the

wage.

d) Should the 2ndworker be hired?

e) Should the 5th worker be hired? No, the 5th worker

produces goods worth 10 KWD but costs 15 KWD.

4. Short run production function-in short run one input, capital, is

fixed and the other factor, labor, is variable.

5. Long run production function-all inputs are variable

6. Long run example-suppose there are five different technologies for

producing 100 pizzas, these are shown in the table below.

3

Technology Capital Labor

A 2 9

B 3 8

C 4 4

D 6 3

E 10 2

a) What is the best combination (lowest cost) for

producing 100 pizzas? Don’t know without

information on prices of labor and capital.

Technology Capital Labor PK=10, PL=7 PK=10, PL=1

A 2 9 83 29

B 3 8 86 38

C 4 4 68 44

D 6 3 81 63

E 10 2 114 102

b) If the price of labor is low (last column) use

technology that uses little capital and much labor.

Option A, lowest cost of the 5 technologies given

labor price of 1 and capital price of 10.

c) If the price of labor is KWD 7 then the lowest

cost technology is C.

PERFECT

COMPETITION

ECONOMICS 1

0

1-PROFESSOR WALLACE

SPRING 2020

ASSUMPTIONS – PERFECT COMPETITION

• Many small firms. No firm is large enough to affect market price. Firms are

price takers.

• Firms produce identical product.

• There are no barriers to market entry and exit in the industry in the long

run. Barriers such as patents and ownership of a scarce resource are not

present. Free (unrestricted) entry and exit.

• Perfect information about market.

CHARACTERISTICS OF IMPERFECT COMPETITION

• Firms produce a differentiated product.

• Actions of a firm affect market price of the good.

• Types of imperfect competition

• Monopolistic Competition – many small firms selling differentiated products.

Free entry and exit in the long run. Barber shops, restaurants.

• Oligopoly – few large firms with average costs declining at high levels of

output. Thus restricted entry and exit in the long run. Cell phones

• Monopoly – One firm in the industry. Good has no close substitutes.

Barriers prevent long run entry. Electric utility, oil company in many places.

PERFECT VS. IMPERFECT COMPETITION

• Key distinguishing feature is the demand schedule of the firm.

• Perfect competition – firms are price takers so the firm’s demand is

horizontal line at the market price of the good.

• Imperfect competition – actions of a firm affect market price so the firm’s

demand schedule has a negative slope.

REVENUE

• Revenue concepts

• Total revenue (TR) is price of the good times quantity sold, 𝑃×𝑞

• Marginal revenue (MR) is the change in TR caused by the change in output,

MR =

∆”#

∆$

PERFECT COMPETITION AND SHORT-RUN PROFIT

MAXIMIZATION

• In the short run there is no entry or exit because quantity of a firm’s

capital is fixed. The firm cannot obtain the capital needed to enter the

market. Cannot reduce capital to exit a market.

• Rule to maximize profits

• All firms (perfect and imperfect competition) produce where MR = MC

• Only perfectly competitive firms – produce where P* = MC because P* = MR

in perfect competition since the firm is a price taker.

• Exception: if P* < AVC, the firm will shutdown.

P = 8 KD. Since the firm is a price taker, the level of output does not affect P.

Thus TR = P ✕ q = 8 ✕ q . What are total fixed costs in this example?

Output Total Cost Marginal Cost

0 7 —

1 12 5

2 18 6

3 26 8

4

36 10

HOW MUCH SHOULD THE FIRM PRODUCE?

• Should the firm produce the first unit of output? YES Since P* > MC

(8 > 5), producing this unit will add more to TR than it adds to TC, thus

profits rise (loss falls).

• Should the firm produce the second unit of output? YES Since P* > MC

(8 > 6), TR increases more than TC, thus profits rise (loss falls).

• Should the firm produce the fourth unit of output? NO Since P* < MC (8 < 10), TR increases less than TC, thus profits fall (loss increases).

• Firm should produce 3 units of output where P* (MR) = MC.

KD Perfect Competition in the Short Run

P Firm is a Price Taker. Assume P >

AVC

q*

q

MC

P* MR=d

D S

Q*

If P* > MC

Produce more

If P* < MC Produce less

Condensed Perfect Competition

ANALYSIS WITH THE GRAPHICAL MODEL

• We have seen that a perfectly competitive firm will produce

where P* = MC, provided P > AVC.

• Now we will look at four cases. In the first three the firm

produces where P* = MC. In the fourth, the firm shuts down

because P* < AVC.

• We will include the AC, AVC curves in the graph.

CASE 1-FIRM MAKES ECONOMIC PROFIT IN THE

SHORT RUN

• Total revenue is P* ✕ q*

• Total cost is AC ✕ q*

• Economic profit is TR – TC = (P* – AC) ✕ q* > 0

• Note that P* = MC > AC

KD Perfect Competition-Short Run

Economic Profit. P* >

AC

q* q

MC AC

AVC

P*

AC

Area of economic profits

MR = d

0

KD Perfect Competition-Short Run

Economic Profit. P* > AC

q* q

P*

TR

MR = d

0

KD Perfect Competition-Short Run

Economic Profit. P* > AC

q* q

P*

AC

TCTR

MR = d

0

KD Perfect Competition-Short Run

Economic Profit. P* > AC

q* q

P*

AC

Area of economic profits

0

CASE 2-FIRM MAKES ZERO PROFIT IN THE SHORT

RUN

• Total revenue is P* ✕ q*

• Total cost is AC ✕ q*

• 0 = TR – TC = (P* – AC) ✕ q*

• Note that P* = MC = AC

KD Perfect Competition-Short Run

Zero Economic Profit P* = MC = AC

q* q

MC AC

AVC

P* MR = d

CASE 3-FIRM HAS AN ECONOMIC LOSS IN THE

SHORT RUN

• Total revenue is P* ✕ q*

• Total cost is AC ✕ q*

• TR – TC = (P* – AC) ✕ q* < 0

• Note that P* = MC < AC

KD Perfect Competition-Short Run

Economic Losses-Firm Continues

to Produce. AVC < P* < AC

q* q

MC AC

AVC

P*

AC

Area of economic losses

WHY DOES THE FIRM PRODUCE IF IT HAS A LOSS?

• Note that AVC < P* < AC

• TR – TC = (P* – AC) ✕ q* = (P* – AVC – AFC) ✕ q*

• Price is high enough that it can cover the AVC of the output and pay part

of AFC.

• Numerical example: Let q* = 50, P* = 6 KD, AC = 10 KD, and

AVC = 4 KD. TR = 300, TC = 500 profit (loss) = -200.

• AFC = 10 – 4 = 6, TFC = 300. Shutdown loss would be -300.

CASE 4: P < AVC FIRM HAS A SMALLER ECONOMIC LOSS IF IT SHUTS DOWN

• Note that P* < AVC < AC

• TR – TC = (P* – AC) ✕ q* = (P* – AVC – AFC) ✕ q*

• Price is not high enough to cover the AVC.

• Firm shuts down production in the short run if P* falls below the

minimum AVC (shutdown point).

CASE 4 CONTINUED:

P < AVC

NUMERICAL EXAMPLE

• Price is not high enough to pay the AVC,

• Numerical example: Let q* = 50, P* = 6 KD, AC = 10 KD, and

AVC = 7 KD. TR = 300, TC = 500 profit = -200.

• AFC = 10 – 7 = 3, TFC = 150. Shutdown loss would be -150, smaller than

if the firm produces where P* = MC. Remember TVC is 0 if q = 0.

KD Perfect Competition-Short Run

Economic Losses-Firm Shuts Down

P < AVC q MC AC AVC P*

0 = q*

Shutdown Point

MR = d

NUMERICAL EXAMPLE – ECONOMIC PROFIT

• P* = 10, AC = 7, q* = 50

• TR = 10 ✕ 50 = 500

• TC = 7 ✕ 50 = 350

• Economic profit = TR – TC = 150 or (10 – 7) ✕ 50

KD Perfect Competition-Short Run

Economic Profit. P* > AC

50 q

MC AC

AVC

10

7

Area of economic profits

NUMERICAL EXAMPLE – ECONOMIC LOSS, P* > AC

• P* = 10, AC = 12, q* = 50

• TR = 10 ✕ 50 = 500

• TC = 12 ✕ 50 = 600

• Economic loss = TR – TC = -100 or (10 – 12) ✕ 50

• Suppose AVC = 9 then AFC = 3 and TFC = 3 ✕ 50 = -150, economic loss

if the firm produced nothing.

KD Perfect Competition-Short Run

Economic Losses-Firm Continues

to Produce. AVC < P* < AC

50 q

MC AC

AVC

10

12 Area of economic losses

SAMPLE QUESTIONS

• Look at the graph in the next slide.

• How much does the firm produce?

• What is total revenue?

• What is total cost?

• How much is the firm’s economic profit or loss (which is it)?

• Price would have to fall to ___ or less for the firm to shut down.

$ Short Run Costs, Demand of a Wheat Farm

6 9 12 16 17 q

MC AC

AVC

15

7

d=MR

13

11

4

MARKET ENTRY IN THE LONG RUN

• Long run is a period of time sufficient for firms to change the amount of

capital (fixed in the short run).

• In the long run, market entrants (new firms) can acquire the capital

needed to compete in a perfectly competitive market.

• What attracts market entrants? Economic profits.

• New entrants cause the market supply to shift right and price falls.

• When price falls to minimum of the long run average costs, economic profits are

zero and entry stops.

KD Perfect Competition-Long Run

P P* > LRAC New firms enter market

q** q* q

LRAC

P*

P**

D S

S´

Q* Q**

LRMC

MARKET EXIT IN THE LONG RUN

• Long run is a period of time sufficient for firms to change the amount of

capital (fixed in the short run).

• In the long run, existing firms can dispose of capital and leave the market.

• What drives firms out of a market? Economic losses.

• Market exit causes the market supply to shift left and price rises.

• When price rises to minimum of the long run average costs, economic losses are

zero and exit stops.

KD Perfect Competition-Long Run

P Existing firms leave market

q* q** q

LRAC

P**

P*

D S´

S

Q** Q*

Market Entry and Exit in the Long Run