12. -Three types
Non-Price Discriminating
Price Discriminating
Natural Monopoly
-Then regulating monopolies
Short summary of what we will look at…
IV.) Monopoly
Market Structure
13. Characteristics Perfect
Competition
Monopolistic
Competition
Oligopoly Monopoly
# of sellers Many
(price takers)
Substitution of
Product sold
Only one
product type
from all sellers
Barriers to
entry into
market
No barriers to
enter/ exit
Pricing vs MC
and MR
P =MC=MR
Efficiently Efficient with
zero econ profit
P = AC
One
( no substitutes)
No Substitutes
Almost impossible
for others to
enter market
P > MR
P > MC
P > AC
big LR profits
14. IV.) Monopoly
-only one firm
-Very high barriers to enter market, almost
impossible to start a new business in this market
Price Maker - Can set its own price as high as
customers are willing to pay
15. IV.) Monopoly
Two types of Price Makers to examine side by side
- Charges every customer
the same price.
1.) Non- price
discriminating (normal)
2.) Price discriminating
- If it wants to increase
it’s output it must
decrease the price for
everyone
- Charges every customer
the highest possible price
- Will produce more then
a non-price discriminating
monopoly (normal)
MR ≠ P for this one MR = P for this one
16. (MR) Marginal Revenue
Profit Maximization
∆TR
∆Q
Profit-Maximizing Output: level at which (MR) marginal revenue
equals (MC) marginal cost
MR = MC
We assume all firms are profit maximizing, producing
at the point where their profits are at their highest
(MC) Marginal Cost
∆TC
∆Q
This is still the output answer
but the graph is a little harder
then perfect competition from
before.
17. P
Q
S
D
QQ1
P1
Market D + S
P
PC Firm Demand Curve
P=MR =AR =D
I.) Perfect Competition Demand
This point is a normal profit ( = zero economic profit)
- other firms won’t want to enter the market because there is no
economic (abnormal ) profits
- Output is productively and allocatively efficient
18. P
Q
D = P
Q
Monopoly Demand Curve
P
PC Firm Demand Curve
P=MR =AR =D
I.) Monopoly vs PC Demand
Price Maker
Since a Monopoly is the only firm in the market the demand line
for a monopoly is the entire market demand line.
This will determine the price (P), but this does not determine MR and
where on the line to produce at.
19. IV.) Monopoly Demand
Q
P
****The important thing to understand is that when a monopoly
wants to sell at a larger Q it must lower it’s price on every
single unit made, including ones already made
D = P
To sell a larger Q,
the firm must reduce P
on all units.
Thus, MR ≠ P.
20 40
10
6
20. IV.) Monopoly Demand
Q
P
****The important thing to understand is that when a monopoly
wants to sell at a larger Q it must lower it’s price on every single
unit made, including ones already made
D = P
To sell a larger Q,
the firm must reduce P
on all units.
Thus, MR ≠ P.
20 40
10
6
21. Q P TR AR MR
0 $4.50
1 4.00
2 3.50
3 3.00
4 2.50
5 2.00
6 1.50
n.a.
The table shows the
market demand for
coffee.
Fill in the missing
spaces of the table.
What is the relation
between P and AR?
Between P and MR?
IV.) Monopoly Demand example
22. Here, P = AR,
same as for a
competitive firm.
Here, MR < P,
whereas MR = P
for a competitive
firm.
1.506
2.005
2.504
3.003
3.502
1.50
2.00
2.50
3.00
3.50
$4.004.001
n.a.
9
10
10
9
7
4
$ 0$4.500
MRARTRPQ
–1
0
1
2
3
$4
IV.) Monopoly Demand example
23. Here, P = AR,
same as for a
competitive firm.
Here, MR < P,
whereas MR = P
for a competitive
firm.
1.506
2.005
2.504
3.003
3.502
1.50
2.00
2.50
3.00
3.50
$4.004.001
n.a.
9
10
10
9
7
4
$ 0$4.500
MRARTRPQ
–1
0
1
2
3
$4
IV.) Monopoly Demand example
27. IV.) Monopoly Demand
Q
P
D = P = AR
MR
Profit-Maximizing Q:
Where marginal revenue equals
marginal cost
MR = MC
MC
Step 1
28. IV.) Monopoly Demand
Q
P
D = P = AR
MR
Price:
Profit-Maximizing Q:
Where marginal revenue equals
marginal cost
MR = MC
D = P = AR
Where average revenue
meets the quantity produced
MC
Step 2
29. IV.) Monopoly Demand
Q
P
D = P = AR
To sell a larger Q,
the firm must reduce P
on all units.
Thus, MR ≠ P.
And will always be,
MR < P
MR
Price:
Profit-Maximizing Q:
Where marginal revenue equals
marginal cost
MR = MC
D = P = AR
Where average revenue
meets the quantity produced
MC
ALL old/new
products are at the
new low price
30. Increasing Q has two effects on revenue:
Output effect: higher output raises revenue
Price effect: lower price reduces revenue
To sell a larger Q, the monopolist must reduce the
price on all the units it sells.
Hence, MR < P
MR could even be negative if the price effect exceeds the
output effect
IV.) Monopoly Demand
31. P
Q
D
50
8
B
30
12
A
Demand for coffee
Point A
30 x 12 = 360
Point B
50 x 8 = 400
The total revenue is increased
from 360 to 400. So an increase in
price led to more revenue since
the demand is inelastic, you can
raise your price and make more
money, though less people buy it.
Example Total Revenue Test
Remember the output and
price effect with elasticity?
32. Q
P
D = AR
To sell a larger Q,
the firm must reduce P
on all units.
Thus, MR ≠ P.
And will always be,
MR < P
MR
Price:
P = D = AR
Where average revenue
meets the quantity produced
IV.) Monopoly Demand
34. Q
P
D = AR
MR
MC
Profit-Maximizing Level
Where marginal revenue equals
marginal cost
MR = MC
We assume all firms are profit maximizing, producing
at the point where their profits are at their highest.
IV.) Monopoly Price
Step 1
35. Q
P
D = AR
MR
MC
Profit-Maximizing Level
Where marginal revenue equals
marginal cost
MR = MC
Price:
P = D = AR
Where average revenue
meets the quantity produced
We assume all firms are profit maximizing, producing
at the point where their profits are at their highest.
IV.) Monopoly Price
Step 2
36. Q
P
D = AR
MR
MC
Profit-Maximizing Level
Where marginal revenue equals
marginal cost
MR = MC
Price:
P = D = AR
Where average revenue
meets the quantity produced
We assume all firms are profit maximizing, producing
at the point where their profits are at their highest.
IV.) Monopoly Price
38. Q
P
D = AR
MR
MC
ATC
Q = ATC
Cost:
Profit-Maximizing Level
Where marginal revenue equal
marginal cost
MR = MC
Price:
P = D = AR
Where average revenue
meets the quantity produced
This is a monopoly in the Short
Run and in the Long Run!
IV.) Monopoly Profit
Step 3
39. Q
P
D = AR
MR
MC
ATC
Difference between
AR and ATC
Profit Amount:
Q = ATC
Cost:
Profit-Maximizing Level
Where marginal revenue equal
marginal cost
MR = MC
Price:
P = D = AR
Where average revenue
meets the quantity produced
This is a monopoly in the Short
Run and in the Long Run!
IV.) Monopoly Profit
40. P
Q Q
P
Long RunShort Run
MC
ATC
AR=D
MR
MC
ATC
AR=D
MR
Since there are high barriers to enter the market,
other firms cannot enter the market to change it.
Since a monopoly is the only seller in the market, it
doesn’t have to change and can charge the highest
possible price all the time.
42. Q
P
D
MR
MC
Profit-Maximizing Level
MR = MC
Price
P = D at MR = MC
ATC
Difference between
AR and ATC
Profit Amount
Q = ATC
Cost
IV.) Monopoly Profit
Profit can be a lot
43. Q
P
D
MR
MC
Profit-Maximizing Level
MR = MC
Price
P = D at MR = MC
ATC
Difference between
AR and ATC
Profit Amount
Q = ATC
Cost
IV.) Monopoly Profit
Or a little
44. Q
P
D
MR
MC
Profit-Maximizing Level
MR = MC
Price
P = D at MR = MC
ATC
Difference between
AR and ATC
Profit Amount
Q = ATC
Cost
IV.) Monopoly Profit
Just connect the
dots!
45. P
Q Q
P
Long RunShort Run
MC
ATC
D
MR
MC
ATC
D
MR
Since there are high barriers to enter the market,
other firms cannot enter the market to change it.
Since a monopoly is the only seller in the market, it
doesn’t have to change and can charge the highest
possible price all the time.
47. Q
P
D
MR
MC
ATC
I will remove the ATC curve just to make this easier to read, to find allocative
efficiency since it is not a main curve used to figure out surpluses, just know
that it is there and makes this not all straight lines
Allocative efficiency
Most desirable outcome from
society’s perspective
IV.) Monopoly Welfare Analysis
48. Q
P
D = MB
MR
MC
Monopoly produces at
profit maximizing point
of MR = MC
Allocative efficiency is
MB = MC
So for society we make
MB = D = P = MC
Profit-Maximizing
MR = MC
Surplus-Maximizing
P = MC
IV.) Monopoly Welfare Analysis
These type of monopolies
don’t produce as much as the
market really wants
49. Q
P
D = MB
MR
MC
Monopoly produces at
profit maximizing point
of MR = MC
Allocative efficiency is
MB = MC
So for society we make
MB = D = P = MC
Profit-Maximizing
MR = MC
Surplus-Maximizing
P = MC
IV.) Monopoly Welfare Analysis
They only produce to here
50. Q
P
D = MB
MR
MC
Monopoly produces at
profit maximizing point
of MR = MC
Allocative efficiency is
MB = MC
So for society we make
MB = D = P = MC
Profit-Maximizing
MR = MC
Surplus-Maximizing
P = MC
Deadweight loss to
society
Difference of what production
society wants but Monopoly
actually makes
IV.) Monopoly Welfare Analysis
51. P
Q
S
D
QQ1
P1
Market D + S
P
Perfectly Competitive Firm
MC
MB = MC = max efficient
MC = S
MB = D
ATC
P=MR =AR =D
I.) Perfect Competition Welfare Analysis
MC = S
MB = D = P
P = MC = total
surplus is
maximizedThis is allocative
efficient
53. Q
P
D
MR
MC
Monopoly produces at
profit maximizing point
of MR = MC
Allocative efficiency is
MB = MC
So for society we make
MB = D = P = MC
Profit-Maximizing
MR = MC
Surplus-Maximizing
P = MC
Deadweight loss to
society
Difference of what production
society wants but Monopoly
actually makes
IV.) Monopoly Welfare Analysis
They only produce to here
54. Q
P
D
MR
MC
ATC
For productive efficiency I have to leave in the ATC curve because productive
efficiency is asking if the firm is producing the good or service at the most
efficient point for the firm in regards to society.
Productive efficiency
Producing at the most efficient
possible amount
IV.) Monopoly Welfare Analysis
55. Q
P
D
MR
MC
Monopoly produces at
profit maximizing point
of MR = MC
For society productive
efficiency is Q = min ATC
Profit-Maximizing
MR = MC
Surplus-Maximizing
Q = min ATC
ATC
Monopoly does not do this!
IV.) Monopoly Welfare Analysis
These type of monopolies
don’t produce at the cheapest
point
56. Q
P
D
MR
MC
Monopoly produces at
profit maximizing point
of MR = MC
For society productive
efficiency is Q = min ATC
Profit-Maximizing
MR = MC
Surplus-Maximizing
Q = min ATC
ATC
Monopoly does not do this!
IV.) Monopoly Welfare Analysis
Cost is where ATC = Q
57. Q
P
D
MR
MC
Monopoly produces at
profit maximizing point
of MR = MC
For society productive
efficiency is Q = min ATC
Profit-Maximizing
MR = MC
Surplus-Maximizing
Q = min ATC
Producer surplus
Higher for Monopoly
ATC
Monopoly does not do this!
Consumer surplus
Lower for Consumer
IV.) Monopoly Welfare Analysis
58. Q
P
D
MR
MC
ATC
Abnormal profit - YES
Productively - NO
Efficient
(Q = min ATC )
Allocatively - NO
Efficient ( P = MC )
IV.) Monopoly Welfare Analysis
Monopolies that are profit maximizing are not
producing enough from a society’s perspective
and they are charging too high of a price
59. 歧视 Discrimination: treating people
differently based on some characteristic, e.g.
race or gender.
The characteristic used in price discrimination
is willingness to pay (WTP):
A firm can increase profit by charging a higher
price to buyers with higher WTP.
IV.) Monopoly Power
Price Discrimination: selling the same good
at different prices to different
buyers.
It is sometimes possible for a monopoly to charge
different people difference prices
60. They can charge different prices
and different times when
elasticity is more inelastic like
during Chinese New Year
61. You will pay higher prices for
college then others because of
this price discrimination
62. What makes it possible:
No ability of resale
Lack of information by the
consumer
(asymmetric information)
Income Levels
IV.) Monopoly Power
Price Discrimination: selling the same good
at different prices to different buyers.
Otherwise that means there is no
monopoly of the market
Ignorance of choices though
government ownership,
geographical distance, etc
Richer people tend to have more
inelastic demand so the decision to
buy is less sensitive to price.
63. Willingness to Pay (WTP)
A buyer’s willingness to pay for a good is the
maximum amount the buyer will pay for that good.
WTP measures how much the buyer values the good.
name WTP
Peter 5250
Clara 4500
Wilson 3750
Key 3000
Example:
4 buyers’ WTP
for an iPad
Remember this?
64. WTP and the Demand Curve
At any Q,
the height of
the D curve is
the WTP of the
marginal buyer,
the buyer who
would leave the
market if P were
any higher.
Peters’s WTP
Clara’s WTP
Wilson’s WTP
Key’s WTP
0
750
1500
2250
3000
3750
4500
5250
6000
0 1 2 3 4
P
Q
65. About the Staircase Shape…
If we looked at a larger market with many
more buyers, each would be a step on this
curve
D = MB =P
0
750
1500
2250
3000
3750
4500
5250
6000
0 100200300400500
P
Q
Demand =
Marginal
Benefit
66. IV.) Monopoly Price Discrimination
Q
P
D = AR
MR
MC
ATC
Price discriminating monopoly
charges every single buyer the
highest possible price each will
pay
Profit-Maximizing
D = MC
A price discriminating monopoly will
charge everyone the highest possible
price they can!
4
Peter
Clara
Wilson
Key
321
MR = MC
MR = D
67. IV.) Monopoly Price Discrimination
Q
P
D =MR
MC
ATC
Price discriminating monopoly
charges every single buyer the
highest possible price each will
pay
Profit-Maximizing
MR = D = MC
Producer surplus
Monopoly takes all of it
Consumer surplus
Zero
68. IV.) Monopoly Price Discrimination
Q
P
D =MR
MC
ATC
Price discriminating monopoly
charges every single buyer the
highest possible price each will
pay
Profit-Maximizing
MR = D = MC
Producer surplus
Monopoly takes all of it
Consumer surplus
Zero
But look! These types of
monopolies are allocative
efficient!
69. IV.) Monopoly Power
Is Price Discrimination Bad?
A price discriminating monopoly will charge everyone the
highest possible price they can for each person.
Consumer surplus is zero, and monopolies take all of it.
However because of this they will also produce more output to MC = MB which, from a societies perspective is allocative efficient and everyone that wants
and values the good or service will get it, so there will no longer be a deadweight loss of not enough output.
70. IV.) Monopoly
Two types of Price Makers to examine side by side
- Charges every customer
the same price.
1.) Non- price
discriminating (normal)
2.) Price discriminating
- If it wants to increase
it’s output it must
decrease the price for
everyone
- Charges every customer
the highest possible price
- Will produce more then
a non-price discriminating
monopoly (normal)
MR ≠ P for this one MR = P for this one
71. IV.) Monopoly Welfare Analysis
Q
P
D
MR
MC
Monopoly produces at
profit maximizing point
of MR = MC
Allocative efficiency is
MB = MC
So for society we make
MB = D = P = MC
Profit-Maximizing
MR = MC
Surplus-Maximizing
P = MC
Deadweight loss to society
Difference of what production
society wants but Monopoly
actually makes
Deadweight loss
72. IV.) Monopoly
Two types of Price Makers to examine side by side
- Charges every customer
the same price.
1.) Non- price
discriminating (normal)
2.) Price discriminating
- If it wants to increase
it’s output it must
decrease the price for
everyone
- Charges every customer
the highest possible price
- Will produce more then
a non-price discriminating
monopoly (normal)
MR ≠ P for this one MR = P for this one
73. IV.) Monopoly Price Discrimination
Q
P
D =MR
MC
ATC
Price discriminating monopoly
charges every single buyer the
highest possible price each will
pay
Profit-Maximizing
MR = D = MC
Producer surplus
Monopoly takes all of it
Consumer surplus
Zero
No Deadweight loss!
74. IV.) Monopoly Price Discrimination
Q
P
D =MR
MC
ATC
Abnormal profit - YES
Productively - NO
Efficient
(Q = min ATC )
Allocatively - YES
Efficient ( P = MC )
75. IV.) Monopoly Power
Price Discrimination:
Another way monopolies price discriminate is with Elasticity, but this doesn’t
change the fact that it is an inefficient producer.
76. They charge different people
different prices, but this also
means it can make more money
to have more buses
77. They charge different people
different prices, but this also
means it can make more money
to have more flights
78. P
Q
D
Q
Off peak time
P
Peak demand (Chinese new year)
Another way monopolies price discriminate is with Elasticity.
IV.) Monopoly Price Discrimination
DMR MR
MC
ATC
MC
ATC
They sell the same good or service without any changes to the business itself, but can make an even larger profit due to
increased inelasticity of demand for the good or service
79. Price Discriminating summary:
Monopolies can charge the maximum price that
each different consumer is willing to pay which
also means a monopoly will produce more and
there is no longer a deadweight loss of not
enough output.
Monopolies can also charge a higher price to
everyone based on the elasticity of the demand.
80. Q
P
D
MR
MC
ATC
Abnormal profit - YES
Productively - NO
Efficient
(Q = min ATC )
Allocatively - NO
Efficient ( P = MC )
IV.) Monopoly Welfare Analysis
81. IV.) Monopoly Price Discrimination
Q
P
D =MR
MC
ATC
Abnormal profit - YES
Productively - NO
Efficient
(Q = min ATC )
Allocatively - YES
Efficient ( P = MC )
82. P
Q
D
Q
Off peak time
P
Peak demand (Chinese new year)
Another way monopolies price discriminate is with Elasticity.
IV.) Monopoly Price Discrimination
DMR MR
MC
ATC
MC
ATC
They sell the same good or service without any changes to the business itself, but can make an even larger profit due to
increased inelasticity of demand for the good or service
84. Public goods are in theory unlimited and in making them they
suffer from a problem of how much to make and who pays for
them since everyone gets to enjoy it.
Private
goods
Common
Resource
Natural
Monopolies
Public goods
Excludable Nonexcludable
Rival
Nonrival
IV.) Natural Monopolies
Remember
this?
87. - its use by one person does
not decrease the quantity
available to someone else.
CLASSIFYING GOODS AND RESOURCES
And this?
88. IV.) Natural Monopolies
- It occurs when one large business can supply
the entire market at a lower price than two or
more smaller ones
- A natural monopoly is a situation in which
there cannot be more than one efficient provider
of a good. In this situation, competition might
actually increase costs and prices
- The key point is that a natural monopoly is
characterized by increasing returns to scale at all
levels of output
92. HowHow ATCATC Changes asChanges as
the Scale of Production Changesthe Scale of Production Changes
Economies of scale:
ATC falls
as Q increases.
Constant returns to
scale: ATC stays the
same
as Q increases.
Diseconomies of scale:
ATC rises
as Q increases..
LRATC
Q
ATC
Other typical markets:
93. How ATC Changes as
the Scale of Production Changes
Economies of scale:
ATC falls
as Q increases.
Q
ATC
ATC1
ATC2 ATC3
IV.) Natural Monopolies
The bigger it get the costs
get cheaper at typically
continue to get cheaper
94. -Three types
Non-Price Discriminating
Price Discriminating
Natural Monopoly
-Then regulating monopolies
Short summary of what we will looked at…
IV.) Monopoly
Market Structure
95. P
Q Q
P
Long RunShort Run
MC
ATC
D
MR
MC
ATC
D
MR
Since there are high barriers to enter the market,
other firms cannot enter the market to change it.
Since a monopoly is the only seller in the market, it
doesn’t have to change and can charge the highest
possible price all the time.
96. Q
P
D
MR
MC
ATC
Abnormal profit - YES
Productively - NO
Efficient
(Q = min ATC )
Allocatively - NO
Efficient ( P = MC )
IV.) Monopoly Welfare Analysis
97. P
Q
D
Q
Off peak time
P
Peak demand (Chinese new year)
Another way monopolies price discriminate is with Elasticity.
IV.) Monopoly Price Discrimination
DMR MR
MC
ATC
MC
ATC
They sell the same good or service without any changes to the business itself, but can make an even larger profit due to
increased inelasticity of demand for the good or service
98. IV.) Monopoly Price Discrimination
Q
P
D =MR
MC
ATC
Abnormal profit - YES
Productively - NO
Efficient
(Q = min ATC )
Allocatively - YES
Efficient ( P = MC )
99. IV.) Natural Monopolies
- It occurs when one large business can supply
the entire market at a lower price than two or
more smaller ones
- A natural monopoly is a situation in which
there cannot be more than one efficient provider
of a good. In this situation, competition might
actually increase costs and prices
- The key point is that a natural monopoly is
characterized by increasing returns to scale at all
levels of output
100. Price Discrimination
- Bad for consumers and high prices
Not efficient from a society’s
perspective
- Does not produce as much as people want
Loses the Incentives to Innovate
-Monopoly might not innovate because it doesn’t
have to.
Downsides of a Monopoly
IV.) Monopoly summary
101. Price Discrimination
- Good for Society as more is produced
Capturing Economies of Scale
-Economies of scale can lead to natural monopoly.
-It is more efficient to regulate natural monopoly than to
break it up and make the industry competitive.
Strengthening the Incentives to Innovate
- Monopoly might be more innovative than competition.
-Innovation can create a monopoly.
Benefits of a Monopoly
IV.) Monopoly summary
When the AR column appears, note that AR = P at every quantity. This, of course, is a tautology.
When the MR column appears, note that MR is less than P. This is not as easy to see, because the MR numbers are offset from the rows of the table, just as if you were in an elevator stuck between two floors. But students can still see that MR &lt; P.
For example, in the range of output of Q=2 to Q=3, the price ranges from $3.50 to $3.00, but MR is only $2.
When the AR column appears, note that AR = P at every quantity. This, of course, is a tautology.
When the MR column appears, note that MR is less than P. This is not as easy to see, because the MR numbers are offset from the rows of the table, just as if you were in an elevator stuck between two floors. But students can still see that MR &lt; P.
For example, in the range of output of Q=2 to Q=3, the price ranges from $3.50 to $3.00, but MR is only $2.
The numbers in the table are from the preceding exercise. Students can see either from the table or the graph that, at any Q, MR &lt; P.
The numbers in the table are from the preceding exercise. Students can see either from the table or the graph that, at any Q, MR &lt; P.
The numbers in the table are from the preceding exercise. Students can see either from the table or the graph that, at any Q, MR &lt; P.
Note that a competitive firm has the output effect but not the price effect: the competitive firm does not need to reduce its price in order to sell a larger quantity, so, for the competitive firm, MR = P.
ing
FYI: The four guys in this example are the members of the Red Hot Chili Peppers. In the corresponding example from the textbook, Mankiw uses the Beatles.
When Q = 1, the height of the demand curve is $300, which is Flea’s willingness to pay, or how much he values an iPod. At any price higher than $300, Flea leaves the market; hence, at Q = 1, Flea is the marginal buyer.
When Q = 2, the height of the demand curve is $250, which is Anthony’s willingness to pay, or how much he values an iPod. At any price higher than $250, Anthony leaves the market; hence, at Q = 2, Anthony is the marginal buyer.
And so forth.
The lesson here is summarized in the text on the right side of the screen: At each Q, the height of the D curve tells you the marginal buyer’s willingness to pay, or how much that buyer values the good.
After the previous slide, most of your students will probably understand where this D curve comes from, but its staircase-like shape will seem quite odd to them.
Point out that it has 4 “steps,” one for each buyer. Suppose there were 10 buyers instead of 4; how many steps would it have? Ten, of course. If there were 20 buyers, this D “curve” would have 20 steps.
A perfectly competitive market has a huge number of buyers. Suppose there were 10,000 buyers in the market for iPods (a tiny fraction of the actual number of buyers!). Then, the number of steps would be 10,000. In relation to the graph, each step would be insignificantly small, and the D curve would look like a smooth curve rather than a staircase – even though it really is a staircase – one with 10,000 infinitesimally small steps.