Section 2
Theory of the Firm
Section 2: Theory of the Firm
• A firm is any economic entity that produces goods and services.
• The production process involves converting input (factor of
production) into output.
– Input: anything used in the production process. e,g labor, capital, technology, land
entrepreneurial ability.
– Output: the end product of the production process
• Firms go into production with the main motive of earning
profits.
• Profit is the total revenue a firm receives from the sale of goods
and services minus all costs. Profits = Total Revenue-Total Costs.
• In maximizing profits, firms also strive to minimize costs.
• Not all firms are profit maximizers. E.g non-profit organizations
are not profit driven but they do aim to minimize costs.
Therefore, even though profit maximization implies cost
minimization, the reverse does not hold true.
Types of inputs
• Fixed inputs: a factor of production whose quantity does not
change as the output changes. For example, something like land
and machinery cannot be altered within a relatively short period of
time.
• Variable inputs: a factor of production whose quantity changes
with the level of production. For example, something like labor can
be changed within a relatively short period of time.
Short Run vs Long Run
• Short Run: A period of time during which some inputs cannot be
varied and therefore remain fixed (e.g capital). Changing these
input within such a short period of time would entail increasing
per unit cost of production. However, some inputs like labour can
be changed within this relatively short period of time at little or no
cost.
• Long Run: A period of time sufficiently long that all of the firm’s
inputs can be varied, even capital.
Why is it possible to take in more gym members in a
relatively short period of time than it is to construct
better roads to accommodate the increased traffic flow?
• Taking in more gym members involves hiring
more gym instructors and maybe renting a bigger
gym space. All these changes can take place in a
matter of months.
• By contrast, how long did it take to complete the
Tlokweng border gate road? Certainly not a few
months. Road construction requires lengthy
inspections, contractors and machinery. That is, it
is more capital intensive and capital cannot be
altered within a short period of time.
Short Run Production Function
• A production function shows the maximum output that
can be produced from a particular combination of
inputs. For example
Q  f ( K , L)
Where: K= fixed amounts of capital
L= variable amount of labour
Q= output
This means that in the short run, output depends on
capital and labor inputs. However, since K is fixed in the
short run, this means that output Q will only vary with the
level of labour
Properties of a short-run production function
1. The
SR production function passes through
the origin, implying that when L=0, output=0
2. As more of the variable input is employed
in production, K constant, initially, output
increases at an increasing rate.
3.Beyond a certain point, additional units of
the variable input results to smaller increases
in output. This is called the law of
diminishing returns
The Law of Diminishing Returns
The law states that: In the short run,
when at least one input is fixed,
successive increases in the input of a
variable factor eventually yield smaller
increments in output.
Total, Marginal and Average Products
• Total product (TP): the total output relative to the
variable input
• Marginal Product (MP): the change in TP due to a
one unit change in the variable input.
total product
Q
MPL 

labour input
L
• Average Product (AP): the total product divided by
the quantity of the variable input.
Total product
Q
APL 

Total labour input L
TP
MPL 
 slope of TP curve
L
Thus, the MPL at any point is the slope of the TP curve
at that point.
TP
TP
A •
∆TP
∆L
L
The Relationship Between TP, MP and AP
Labor input
0
1
2
3
4
5
6
7
8
TP
0
60
135
210
280
340
380
380
370
AP=TP/L
60
67.5
70
70
68
63.3
54.3
46.3
MP=
-
Figure 13: Total, Average and Marginal Product Curves
Features of the Diagram
i. As long as MP is positive, TP is rising. TP reaches a maximum when
MP=0 and begins to fall thereafter.
ii. When MPL is greater than APL, the AP is rising and the MP lies above
it.
iii. When MPL is less than APL, the AP is falling and the MP curve lies
below it.
iv. The MPL intersects the APL at the maximum point of the AP curve.
Thus, the two are equal at the maximum of the AP curve.
v. MPL is equal to zero when the TP is at a maximum.
vi. Point A lies on the line which is from the origin and tangent to the
TP curve. This point is the maximum of the MP curve.
vii. Where the AP curve is at a maximum, the corresponding point on
the TP curve, B is called the inflexion point. Point B is where
diminishing marginal returns set in, i.e. it is the point where the TP
curve switches from increasing at an increasing rate to increasing at a
decreasing rate.
Stages of Production
• Stage I: APL is rising; MPL rises, reaches a maximum and then begins
to fall. Since TP is increasing, MPL is positive.
• STAGE II: Both APL and MPL are declining, but since TP is rising, MPL is
still positive
• STAGE III: APL continues to decline; TP starts to decline and therefore
MPL becomes negative.
At which stage should firms produce?
•No firm would want to produce at Stage III. This is because at stage III,
further increments of the variable input leads to a decline in TP.
•At Stage I, there is still opportunity to increase TP by increasing the
variable input. Therefore, even though TP is still positive, producing at
this stage is not optimal because it is still possible to increase labor input
and in turn increase TP. TP is increasing at an increasing rate.
•Stage II is the most ideal stage of production. Even though TP is
increasing at a decreasing rate, it is still increasing, hence it is till
worthwhile to produce. This is known as the economic region of
production.
Long Run (LR) Production Function
•In the LR, the firm is able to undertake all its desired
adjustments, therefore, all inputs are variable in the LR. A
LR production function is expressed as follows:
Q  f ( K , L)
Where: K= variable amounts of capital
L= variable amount of labour
Q= output
•To produce a given output, a firm chooses different
combinations of K and L.
•A curve representing the different combinations of K and L
that a firm may use to produce a given amount of output is
called an ISOQUANT.
Isoquant
• Along the isoquant, output remains constant. That is, at
both points A and B, output is 100, however, different
combinations of K and L are employed.
• 18K+4L=100
• 12K+8L=100
K
18
•A
•B
12
4
8
Q=100
L
Properties of Isoquants
1.Isoquants are downwards sloping to the right, indicating that there is
diminishing marginal rate of technical substitution.
2.Isoquants further away from the origin represents higher levels of
output
3.Isoquants from the same isoquant map cannot intersect as this would
mean two different output amounts are the maximum attainable
from a give combination of resources.
An Isoquant Map
K
Q=120
Q=80
Q=40
L
Marginal Rate of Technical Substitution (MRTS)
The MRTS is the rate at which one input can be
exchanged for another, whilst still maintaining the
same level of output. MRTSLK = K   K  MPL
L
L MPK
K
∆K
∆L
Q0
L
Proof that
MRTS LK  
dK
MPL

dL
MPK
Given the following production function: Q= f(K,L).
Totally differentiating the production function
Q 
f
f
dK 
dL
K
L
By definition,
f
f
 FK , and
 FL
K
L
Therefore, by substitution: Q  FK dK  FL dL
Since output remains fixed along an isoquant, ∂Q=0. This
implies that, FK dK  FL dL  0
Re-arranging terms,
 FK dK  FL dL
Dividing both sides by FK:
FK
FL

dK 
dL
FK
FK
FL
 dK 
dL
FK
• Dividing both sides by dL
dK
FL


dL FK
Since MRTSLK =  dK
.
dL
and FL=MPL and FK = MPK,
MRTSLK =  dK  MPL
dL
MPK
Types of Isoquants
1. Convex isoquants: these have diminishing marginal
rate of technical substitution (MRTSLK)
K
Q3
Q2
Q1
L
2. Linear/negatively sloped Isoquants
• These reflect perfect substitution. For example, at
point A on the vertical axis, there is no labour
employed, only capital is used to produce output
Q2.
K
A
Q1
Q2
Q3
L
3. L-shaped Isoquants
These reflect that inputs must be used in fixed factor
proportions. The isoquants are right angles, indicating
that if one input (K) is changed (e,g, from A to B) while
the other is held constant, there is no increase in the
output rate.
K
•B
•A
Q3
Q2
Q1
L
Something to be mindful of
• Isoquants play the same kind of role in production
theory that an indifference curve plays in demand
theory.
• While an indifference curve shows the different
combinations of goods X and Y that provide the
same level of satisfaction to the consumer; an
isoquant shows the various combinations of inputs K
and L that the firm employs to produce the same
amount of output.
• Like indifference curves, isoquants are convex to the
origin and they cannot intersect.
Returns to Scale
Returns to scale tells us, if inputs are increased by a certain proportion,
what is the resulting proportionate change in output.
There are three types of returns to scale:
I. Increasing returns to scale (IRS)
II. Constant returns to scale (CRS)
III. Decreasing returns to scale (DRS)
Increasing Returns to Scale
A firm experiences IRS when increasing inputs by a given proportion
causes output to increase by a bigger proportion. E.g when doubling
inputs more than doubles output.
• Example, initially a firm employs 4 workers using 2 machines and produces 100 kg of
output.
• From Figure 13, when management decides to double the inputs, thus employing 8
workers, and 4 machines, this increases to output to 300 kg. If inputs double further to 16
workers and 8 machines output increases to 700. Doubling the inputs furthermore increases
output to 1600.
• In this scenario, doubling the inputs more than doubles the output: Increasing Returns to
Scale
Graphical Representation of IRS: Figure 13
In this case, moving out from the origin, successive isoquants
becomes closer and closer as inputs are increased
K
Ray
16
8
4
1600
700
300
2
100
4
8
16 32
L
Constant Returns to Scale (CRS): Figure 13(b)
A firm experiences CRS if a proportionate increase in input leads to a
proportionate increase in output. e.g when doubling inputs exactly
doubles output.
• Example, initially a firm employs 4 workers using 2 machines and produces 25 kg of output.
• In this case, when the inputs are doubled to 8 workers and 4 machines, then to 16 workers and
8 machines and finally to 32 workers and 16 machines, output also doubles to 50 kg, then to 100
kg and then to 200 kg, respectively.
• In this scenario, doubling inputs exactly doubles the output: Constant Returns to Scale
K
Ray
16
8
200
4
100
2
50
25
4 8
16
32
L
Decreasing Returns to Scale (DRS): Figure 13(c)
A firm experiences DRS if increasing inputs by a given proportion causes
output to increase by a smaller proportion. e.g when doubling inputs less
than doubles output.
In this case, when the inputs are doubled from 8 workers and 4 machines, then to 16 workers and 8 machines
and finally to 32 workers and 16 machines, output only increases to 38 kg, then to 58 kg and then to 88 kg,
respectively.
In this scenario, doubling inputs less than doubles the output: decreasing returns to scale. Successive
isoquants move further apart as inputs are increased
K
Ray
16
88
8
58
4
2
38
25
4 8
16
32
L
Factors which give rise to Increasing returns
to scale (IRS).
1. Specialization
2. Adoption of improved equipment and
technology
Factors which give rise to Decreasing returns
to scale (DRS).
1. Decreased efficiency
PEASE READ FURTHER
Something to be mindful of………
The difference between Diminishing Returns and
Decreasing Returns to Scale
• In the case of diminishing returns, we observe
the effect on output of leaving one of the inputs
fixed (K), while the other input varies (L).
• In the case of decreasing returns to scale, we
observe the effect on output of varying all inputs
(K and L).
Optimal Input Combination
Recall:
• The firm’s objective is to maximize profits, to do this, it will
either minimize the cost of producing, or maximize the output
derived from a given amount of costs faced by the firm.
• The resources available to the firm for production (K and L)
are represented by a production function or an isoquant.
• The next step is to determine what combinations of inputs (K
and L) a profit maximizing firm should use given the amount of
costs the firm faces.
• The optimal input combination is therefore the combination
of inputs which maximizes output given the costs faced by the
firm.
• To find the combination, we find the point where the firm’s
isoquant is tangent to the isocost curve.
Isocost Curve
• The isocost curve shows all combinations of
inputs (K and L) that cost the same.
• For a firm using K and L, the isocost curve is
presented as: TC = wL+ rK
(1)
Where:
TC= total cost
w=price of labour
r= price of capital
L= amount of labour employed
K= amount of capital employment
The slope of the isoquant curve can be derived as follows:
Solve for K from equation 1: TC  wL  rK
rK  TC  wL
TC
w
K
 L
r
r
w
Where, 
is the slope of the isocost curve
K
r
TC/r
TC/w
L
The optimal Combination of Inputs
• This occurs where the firm’s isoquant is tangent
to the isocost curve. This is at point A on the
graph below
K
Q3
•A
Q2
Q1
L
Characteristics of the Optimal Input Combination
1. The optimal combination occurs where the slope of
the isoquant is equal to the slope of the isocost
curve. i.e. where MRTSLK  wr
2. The marginal rate of technical substitution is equal
to the ratio of the marginal products, MRTSLK  MPL
therefore, at the optimal point,
MP
w
L
MRTS

and MRTS

LK r
LK MP
K
Rearranging,
MP
L w
r
MP
K
MP
MP
L
K
r
w
MP
K
Theory of Costs and Cost Functions
Short Run Production Costs
We know that when firms produce output, they
incur costs. Since in the short run, some resources
are fixed while some vary, it means that short run
costs can be classified ad either fixed or variable.
1. Total Fixed Costs (TFC or FC)
These are the costs that remain constant as output
either increases or decreases. Fixed costs cannot be
avoided in the short sun and are incurred even
when the firm’s output is zero, eg: rental payments,
interest on a firm’s debts.
2. Total Variable Costs (TVC or VC)
These are costs that vary as the output increases or
decreases. e.g labour costs, electricity and water costs.
3. Total Costs
These are the sum of fixed costs and variable costs,
that is, total costs include all the costs a firm uses in its
production
TC = TFC+ TVC
4. Average Total Costs
These are the total cost of producing output , divided
by the total output.
ATC= TC/Q
5. Average Fixed Costs (AFC)
The total fixed costs of producing output divided by the total output.
AFC= FC/Q
6. Average Variable Costs (AVC)
The total variable costs of producing output divided by the total
output.
AVC= TVC/Q
7. Marginal Costs (MC)
The change in total costs associated with producing each additional
unit of output
MC= ∆TC/∆Q
Since FC do not change in the short run, the change in TC is brought
about only by the changing variable costs. Therefore,
TC TFC  TVC TVC , since ∆TFC= 0


Q
Q
Q
You are thinking of buying a bakery at block 8 to add to the ones you
already manage.
• Using historical data from your other bakeries plus survey
information in block 8 on the demand for bread, you derive the
following data for what you believe relate to daily sales at your
new bakery.
Total Fixed Cost
Total Variable Cost
Quantity
(bread)
(TFC in Pula)
(TVC in Pula)
0
120
0
10
120
20
20
120
30
30
120
50
40
120
80
50
120
130
60
120
230
70
120
380
80
120
690
Note that the following assumptions are made:
1. The period under consideration is the short
run (the shop size, number of bread ovens is
fixed and not able to be changed in the near
future)
2. More bread loaves can only be baked by
employing more labor (where labor is the only
variable cost).
Complete the table by calculating the TC, TVC, TFC, AFC, AVC and
the MC for a firm (a perfectly competitive firm)
Quantity
(bread loaves)
A
TFC
B
TVC
C
0
120
0
10
120
20
20
120
30
30
120
50
40
120
80
50
120
130
60
120
230
70
120
380
80
120
690
TC
D=B+C
AFC
B/A
AVC
C/A
ATC
D/A
MC
∆D/∆A
-
-
-
-
Figure 14: Graphically, the costs curves can be shown as
follows
Characteristics of the graph
• AVC and ATC curves initially decline as output increases,
reach a minimum and thereafter increase as output
increases.
• The upward sloping part of the MC curve corresponds to the
region of diminishing returns
• The minimum of the AVC occurs before that of the ATC curve.
This is because since AFC decline continuously, the ATC
continues to fall even after the AVC has begun to rise.
• When the MC lies above the AVC and the ATC curves, the AC
curves are rising, and when the MC lies below the AVC and
the ATC curves, the AC curves are falling. Therefore, the MC
passes through the minimum of both the ATC and AVC curves.
• The distance between the ATC curve and the AVC is the AFC.
Why does it this distance smaller and smaller as output
increases?
Why do AFC continuously decline with rising output???
AFC continuously decline with rising output
because TFC do not vary with output. That is,
since the numerator doesn’t change as the
denominator increases, the whole ratio declines
TFC
 AFC 
Q
The relationship between cost functions and production
functions
1. Average cost (AC) and Average product (AP)
Recall that
TVC
Q
AVC 
and APL 
Q
L
Since TVC are costs on the variable input, i.e. labor, TVC= wL
AVC 
wL
L
 w
Q
Q
(1)
Q
1
L
Since APL  it means that

L
APL Q
By substituting (2) into (1):
AVC  w 
(2)
1
APL
Thus, the AP curve is the inverse of the AC curve
2. Marginal Cost and Marginal Product
Recall that
MPL 
Q
1
L
;

L
MPL
Q
TC
TVC
MC 

Q
Q
and TVC  wL, therefore, MC 
wL
Q
Equation (1) can be expressed as:
L
MC  w 
Q
1
L
1
since

, it means MC  w 
MPL
Q
MPL
Thus, the MC curve is the inverse of the MP curve
(1)
Figure 15: Graphical Representation of Cost and Product curves
•The assumption is that labor is the only variable
and that its price (w) is constant
•The MC and AC curves are mirror images of the
MP and AP curves, respectively.
•When the MP is rising, the MC is falling, and
when MP is falling, MC is rising.
•Similarly, when AP is rising, AVC is falling and
when AP is falling, AVC is rising
The Short-Run Supply curve
We have established that a firm will not produce below the
shutdown point, i.e. below the minimum of the AVC curve.
Therefore, since the supply curve shows the quantities of
goods and services supplied at different prices, the supply
curve is the area on the MC curve above the minimum AVC
curve.
LONG-RUN (LR) PRODUCTION COSTS
• The short run average cost curves (SAC) show
how output can be varied given some level of fixed
costs, i.e. the cost of capital. However, long-run
allows sufficient time for firms can make all desired
adjustment, e.g therefore, in the LR, all inputs are
variable and there are no fixed costs.
• The long-run average cost curve (LAC) is made up
of the points of tangency of many SAC curves.
• The LAC It is an outer envelope of a family of SAC
curves.
Up to Q*, the LAC is falling and this is called ECONOMIES OF SCALE
(similar to increasing returns to scale in production).
Beyond Q*, the LAC is rising and this is DISECONOMIES OF SCALE
ECONOMIES OF SCALE
Changes in the LAC where the average cost of production
declines as the amount of output increases. Economies of
scale are observed on the downward sloping segment of
the LAC curve.
Types of economies of scale
1. Technical Economies of Scale
2. Non-technical Economies of Scale
READ FURTHER……….
We know that generally, the main assumptions
made by firms is that their goal is to maximize
profits. We have also learnt that profits are defined
as the total revenue (TR) a firm receives from selling
its products minus the total costs (TC). That is,
Profits=TR-TC. By costs, what exactly are we
referring to? It is important to be clear in
understanding what economic profit is and how it is
calculated
Types of costs and types of profits
1. Explicit costs
These are costs the firm incurs on factors of
production, e,g costs on labour and capital
2. Implicit Costs
These are the value of next best opportunity
sacrificed by the firm when it use its resources in
the chosen industry it operates in, ie: implicit cost
is an opportunity cost.
Because we have these two types of costs, there
are different ways of calculation profits.
Understanding Profit Definitions
1. Economic profits
The difference between a firm’s total revenue and the sum of explicit
and implicit costs:
2. Accounting profits
The difference between a firm’s total revenue and its explicit costs
only.
In summary:
Economic profit= total revenue - (explicit costs + implicit costs)
Accounting profit = total revenue - explicit costs
Example: Consider a firm with
TR= P800; workers’ salary = P200 , cost of machinery =P100.
Suppose that if the firm had instead saved its money in a savings account, it could
have earned P100 as interest on savings.
i.
Calculate the firm’s Accounting profit
ii. Calculate the firm’s Economic profit
Normal Profits
• Note that accounting profits are greater than economic
profits by exactly the amount of the implicit costs.
Economic profit= total revenue - (explicit costs + implicit costs)
Accounting profit = total revenue - explicit costs
Economic profit= Accounting profit – implicit costs
(1)
Therefore,
Accounting profits > Economic profit, and this difference is equal to
the amount of implicit costs
Implicit costs are also referred to as the firm’s normal profit.
By definition from (1), when
Economic Profit = 0; Accounting profit = Implicit costs. Therefore,
Normal profit is the amount of accounting profit that a firm makes
when economic profits equal to zero.
SECTION 3: MARKET STRUCTURES
There are different markets under which firms
operate.
1. Perfect Competition: A market in which no
individual firm has any influence on the market
price of the product. Such a market is called a
perfectly competitive market
2. Imperfect Competition: A market in which
individual firms have some influence on the market
price of the product. These are
i. Monopolistic competition
ii. Oligopoly
iii. Monopoly
Section 3.0.Perfectly Competitive Markets: Characteristics
1.There are many buyers and sellers
Because these kinds of markets are easy to get into (i.e. the
start-up costs are relatively low), they consist of many sellers
and many buyers. Each seller sells only a small fraction of the
amount in the entire market.
2. The firms (sellers) are price takers
Because there are many sellers, no single firm is able to
influence the market price, each one takes the price as
determined in the market.
3. The firms sell standardized/homogenous products
This means that products sold by firms are the same, e.g.
when you go and buy lunch from the street vendors outside
UB, what kinds of food are you likely to find?
4. Resources are perfectly mobile and there is free
entry into and exit from the industry.
No real barriers to entry exist as resources can be easily
moved and firms are able to enter and leave the
industry. This means that if a potential seller identifies
an opportunity in the market (e.g profits), the seller will
be able to obtain the K, L, or other necessary resources
to enter the market. If on the other hand a seller who is
dissatisfied with the conditions in the market (e.g.
losses), they can choose to leave.
5. There is perfect information
Buyers and sellers know all there is to know about the
goods and services bought and sold in the market
Perfect Competition
Monopolistic Competition
Oligopoly
Many buyers and sellers
Many buyers and sellers
Many buyers, few sellers
Products are
homogeneous and are
close substitutes
Slightly differentiated
products (products are
substitutes)
Products are close
substitutes
Firms are price takers, no
influence over the price
Firms have some
influence over the price
Demand curve is
horizontal
Demand curve is
downward sloping
Street vendors
Petrol stations
Monopoly
A single seller and many
buyers
No close substitutes
Firms have some
influence over the price
The single firm sets the
price
Demand curve is
downward sloping
Demand curve is
downward sloping
Mascom and Orange
BPC, UB bar at UB
Can you think of more examples of firms that operate in PC
markets??
1. Street vendors outside UB
The Demand Curve for a Perfectly Competitive Firm
Since a PC firm has no control over the price, it takes the price as
given in the market and only decides how much output to produce at
the prevailing market price. Therefore, the demand curve for a PC
firm is perfectly elastic at the market price. The left panel of the
figure below shows the market demand and supply curves
intersecting to determine the market price of P*. The right panel
shows the demand curve for an individual firm in the market, a
horizontal line at the market price.
Short Run condition of profit maximization
• Recall the following prescription from the costbenefit rule: a firm should keep selling or producing as
long as MR>MC.
• What is the marginal revenue to a seller? It is equal
to the price. That is, MR=P. Why?
Assume a price of P5, and quantity of 5, it means
TR= P*Q= 5*5 = 25.
When quantity is 10: TR = P*Q = 10*5 = 50.
Since MR= ∆TR/ ∆Q
= 50-25/10-5 = 25/5 = 5
That is, MR=P, since P=5
• Using the cost-benefit prescription, it means a firm
should keep producing as long as the price is greater than
or equal to the marginal cost (P>=MC)
• That is, when a firm is producing where price is above
the marginal cost (P>MC), it should continue to increase
output.
• When a firm is producing where price is below the
marginal cost (P<MC), it should decrease its output.
Therefore, only when a firm is producing where
price is equal to the marginal cost (P=MC) will it
have reached its the profit maximizing point. In
other words, the profit maximizing point for a
perfectly competitive firm occurs where P=MC
• In the figure above, when the firm follows the profit maximizing
rule, it must produce 260 bottles per day, because this is the
quantity at P=MC. To prove that 260 is the profit maximizing
quantity:
Proof that 260 is the profit maximizing quantity:
– Suppose that the firm instead sells 200 bottles per day at the given price P2 per bottle.
Mind that when output is 200, the corresponding marginal cost is P1 and the MR is P2.
Therefore, if the firm increases output by one bottle it would increase revenue by P2
while costs will only increase by P1. Therefore, by selling the 201st bottle for P2, the
firm will increase its profit by P2-P1= P1 per day. That is, for any quantity where P>MC,
the firm can boost its profits by expanding output.
– Conversely, suppose that the firm sells more than 260 bottles per day, i.e. 300 bottles
at a price of P2 each. It can be seen from the figure that when the output is 300, MC is
P4 and MR is P2. This means that if the firm reduces output by one bottle, it will cut its
costs by P4 and only lose P2 in revenues, as a result, profit would grow by P4-P2 = P2.
Therefore, by reducing output by one bottle, the firm can reduce its losses by P2. That
is, for any quantity where P<MC, the firm can boost its profits by reducing output.
• We have therefore established that if the firm produces less
than 260 bottles per day (where P>MC), it should increase output
to increase profits. If it produces more than 260 bottles per day
(MC<P), it should reduce output to reduce losses.
• This means that, the PC firm maximizes profit by producing
output where P=MC, this is 260 bottles per day.
Formally: profit maximization for a PC firm is derived as follows:
Π  TR  TC
 P  Q  TC(Q)
The objective function of the firm is
Maximize Π  P  Q  TC(Q)
(1)
FOC for profit maximization :
Totally differentiating: dΠ  P  dQ  QdP - dTC(Q)
dΠ  P dQ  Q dP  dTC(Q)  0
dQ
dQ
dQ
dQ
P  Q dP  dTC(Q)  0
dQ
dQ
(2)
From equation (2) by definition:
MR  dTR(Q)  P  Q dP and,
dQ
dQ
MC  dTC(Q)
d(Q)
Substituting (3) and (4) into (2), it means
MR - MC  0, therefore,
MR  MC
(3)
(4)
(5)
Since in a perfectly competitive market the price is given, it means dP  0, therefore
dQ
MR  P  Q dP  P, since Q dP  0.
dQ
dQ
Therefore, substitutiong this result into equation (5)we obtain the profit maximizing rule for PC firm :
P  MC
Economic Profit in the Short-Run (SR)
In the SR, when a firm charges a price above the minimum of
the ATC curve (Pa>ATC), it is making profits and should continue
to operate(note: profits are made when TR>TC, therefore when
P>ATC, it is making profits. (How????? Insert proof from the
lecture). Profits equal the shaded area
Breakeven point in the SR
In the SR, when the firm charges a price equal to the
minimum ATC (Pa=ATC), it is breaking even and should
continue to operate. (note: breakeven is when TR=TC,
therefore when P=ATC, it is breaking even.(Insert proof from
the lecture).
Economic Losses in the Short Run
Economic losses: Firm continues to operate
In the SR, when the firm charges a price below the minimum of the ATC
(Pa<ATC), it is making losses (Insert proof from the lecture). However, if
the firm’s price is above the minimum of the AVC curve (Pa>AVCmin), it
should continue to operate. Thus AVCmin<Pa<ATC. This is because even
though the firm is operating at a loss it can still cover part of its fixed
costs and its variable costs. The losses are equal to the shaded area.
Shut Down Condition
• If the price of the firm is so low that the revenue
is less that the variable costs, i.e. P<AVCmin, the
firm should cease production and shut down.
Why?
• If P<AVCmin, it means that the firm cannot cover
both its fixed costs and its variable cost. That is, it
incurs losses on both its fixed costs and variable
costs. Therefore, by shutting down when P<AVCmin,
it incurs losses on only its fixed costs, which means
the losses are minimized.
Economic losses: Shut Down
In the SR, when the firm charges a price below the minimum of
the AVC curve (Pa<AVCmin), it is said to be making losses, but in
this case, the firm should shut down. By shutting down, it
minimizes losses to the size of its fixed costs. But by remaining
open, it would face even bigger losses.
Perfect Competition: Long-Run Equilibrium
• The Long-run competitive equilibrium is characterized by zero
economic profits. This is because:
• When firms in a perfectly competitive market are making economic
profits, profits act as an incentive for new firms to enter the market.
With the entry of new firms, supply increases and the supply curve shifts
to the right.
• The initial supply curve is S1, the entry of new firms into the market
increases supply and causes the supply curve to shift rightwards to, S2,
causing the market equilibrium price to fall from P1 to P2.
When do firms stop entering the market?
As the new entrants drive the price down, the profits for individual firms are
slowly eroded. Since it is positive economic profits that motivate firms to
enter the market, firms enter the market until all the profits are depleted
and there are zero economic profits. Profits are zero at Pequil , where P=ATC.
At this point, there is no more incentive for firms to enter the market since
existing firms will be making zero economic profits. This is the Long Run
position for the perfectly competitive firm.
MARKET
INDIVIDUAL FIRM
Economic Losses in the LR
• Conversely, when firms in a perfectly competitive market are making
economic losses, losses are an incentive for new firms to exit or leave the
market.
• As the firms exit, supply decreases and the supply curve shifts to the left from
S1 to S2, causing the market equilibrium price to rise.
• The market price will rise until eventually all the losses are elimimated and
the LR market equilibrium is restored where there are no economic losses nor
profits, this is where P=ATC.
Long Run Equilibrium under Perfect Competition:
Zero Economic Profits.
Graphically, the LR competitive equilibrium can be shown as
follows: where Q* is profit maximizing output in the market and
q* is the profit maximizing output for the individual firm.
Long Run Competitive Equilibrium
• Generally, when PC firms are in the LR
equilibrium, the firm makes neither economic
profits or losses and P=MC=MR.
• At this point, there is no incentive for existing
firms to exit or for new firms to enter the industry.
Section3.1 MONOPOLY
• A monopoly is a type of an imperfect market. It is a
market structure in which a single seller is the only
seller of a product for which there are no close
substitutes. In the market for telecommunications,
Botswana Telecoms is the sole provider of fixed line
services, therefore it has a monopoly in the provision
of fixed telephone line services. Furthermore, up
until 1996 when Mascom and Vista (now Orange)it
was the only provider of telecommunications
services in Botswana.
• Likewise, Botswana Power corporation is the sole
producer provider of electricity in Botswana, and the
UB bar is the only seller of alcohol on campus.
Characteristics of a Monopoly
1. There is a single seller.
Since there is only one seller, the single seller makes
up the entire market. Therefore, the demand curve for
the single firm is also the market demand curve.
2. Products have no close substitutes.
3. There are barriers to entry.
4. The monopolist sets the price. Therefore, contrast to
perfect competition, the monopolist is the price
maker/setter. Since a monopoly is able to influence the
price, it is said to have some market power and this is
reflected by a downward sloping demand curve.
Causes of a monopoly: What factors give rise to a
monopoly?
1. Exclusive control over important Inputs
A firm may have control over an input that is essential
to the production of a certain product.
2. Government created monopolies
By issuing things like patent rights, copyright
protection, franchises, licenses, governments give
the firm the exclusive right to produce a certain good.
For the life of the exclusive right, e.g. patent given to
a pharmaceutical company, copyright given to the
authors of movies, books or music, only the holder
can legally produce the good.
3. Economies of Scale
• Recall that economies of scale arise when the
average cost of production declines as the amount of
output increases. Imagine Telecoms when it began
operations in 1980, it had to invest in huge machinery,
set up an entire network of fiber optic cables in the
whole country etc. This means telecoms would have
had to incur large fixed costs to start its operations.
• Now imagine Telecoms now, 32 years later; Suppose
you have jut moved into a new house and want a fixed
line installed. How long would it take? Would telecoms
first have to install cables in order to connect your
landline phone?
The answer is no. And this is because Telecoms no longer faces those
large start up costs. As the number of customers increases, the
variable costs increase (e.g it may need to hire more technicians to
do the home installations), but the initial high start up costs do not
change. What’s he implication of this on overall costs?
TC  FC  VC (Q )
FC  VC (Q )
Q
FC
ATC 
 VC
Q
ATC 
• As Q increases, the fixed costs are being spread over and
therefore the ATC decrease.
• This is because, the monopolist faces high start up costs, but the
reproduction costs are low.
• Since the costs are low with increasing output, the firm is able to
set lower prices than other competing firms and still cover its total
costs. This derives competing firms out of business, forcing them to
exit. Economies of scale can therefore explain how a monopoly can
arise
Total Revenue (Perfect Competition vs Monopolist’s)
Total Revenue (TR) = P*Q
A perfectly competitive firm cannot change the price, only
the quantity, therefore, TR for a PC firm varies
proportionally (linearly) with changes in output.
Graphically
Monopolist’s Total Revenue
The ability to set prices means that the monopolist faces a
downward sloping demand curve. Also, since the monopolist is
able to change the price, TR does not vary proportionally with
output. TR passes through the origin implying that selling no
output generates no revenue. TR rises as output increases,
reaches a maximum and then declines. Graphically
P
Q
TR
TRmax
Q
Marginal Revenue for a Monopolist Firm
Recall that for a PC firm, profit maximization is
where P=MC, and since P=MR, P=MC=MR.
However, for a monopolist, P>MR. This is
P
because:
8
At P=6, Q=2; TR=12 6
5
At P=5, Q=3; TR=15 4
3
MR= P3
D
2
3
4
P3 is less than both P=6 and P=5
Therefore unlike a PC firm, P>MR
5
8
Q
The MR curve for a Monopolist
Suppose we have the following inverse
demand curve equation: P = 5 - 0.5Q. Plot
the demand curve and the marginal revenue
curve
The MR curve for a Monopolist
• The vertical intercept of the marginal revenue curve is
the same as that of the demand curve.
• The MR curve is twice as steep as the demand curve
• The MR revenue curve intercepts the horizontal axis at
exactly half way the intercept of the demand curve
P
5
D
5
10
MR
Q
Profit Maximization for a Monopolist
• Just like with perfect competition, the cost-benefit
rule prescribes that a monopolist should reduce
output when MR<MC
• Conversely, a monopolist should increase output
when MR>MC
• Thus a monopolist should continue to produce until
the point where MR=MC, this is the Profit maximizing
point.
• Since for a monopolist P>MR, it means the
monopolist maximizes profit where P>(MR=MC)
• Thus the price set by the a monopolist is higher than
that of a PC firm
Formally: profit maximization for a PC firm is derived as follows:
Π  TR  TC
.
Suppose the objective of the monopolist is to
Maximize Π  P Q  TC(Q)
(1)
FOC for profit maximization :
Totally differentiating : dΠ  P dQ  QdP - dTC(Q)
dΠ  P dQ  Q dP  dTC(Q)  0
dQ
dQ
dQ
dQ
P  Q dP  dTC(Q)  0
dQ
dQ
(2)
From equation (2) by definition:
MR  dTR(Q)  P  Q dP and,
dQ
dQ
MC  dTC(Q)
d(Q)
Substituting (3) and (4) into (2), it means
MR - MC  0, therefore,
MR  MC
(3)
(4)
(5)
Therefore, MR  MC is the profit maximizing position for the monopolist
Note the Difference
For a competitive firm, P = MR
For a monopolist P>MR
This means that:
For a competitive firm P =MR =MC
For a monopolist P> (MR = MC)
This shows that:
In both cases, both a perfectly competitive firm
and a monopolist maximize profit where MR = MC,
the only difference is that at the profit maximizing
point, a monopolist charges a higher price.
Steps to find the Profit maximizing point for a
Monopolist
1. Plot the demand, MR, ATC, and MC curves.
Find where MR = MC, and determine the
profit maximizing output quantity.
2. At this output level, find the corresponding
level on the Demand curve to determine
the price charged by a monopolist. Thus the
price the monopolist sets is where MR=MC
at the corresponding point on the demand
curve.
Graphical Presentation of Profit Maximization for a
Monopolist
P
MC
ATC
P*
D
Q*
MR
Q
Something worth a note
• MC is the supply curve, i.e. MC=S
• For a Perfectly competitive firm, P = MC,
since a PC firm cannot vary the price. Since
price is fixed, it means MC is fixed and
consequently Supply is fixed.
• Conversely for a monopolist, price is not
fixed since the monopolist can vary the
price. Since price is not fixed, the MC is also
not fixed and consequently supply is not
fixed.
Graphical Presentation of Profit Maximization for a
Monopolist: When MC is constant
P
ATC
P*
MC
D
Q*
Q
MR
Economic Profits by a Monopolist
A monopolist makes profits when P>ATC (just like a PC firm). Profit
maximization is where MR=MC, the corresponding output and price are Q*
and P*, respectively. Since P>ATC, the monopolist makes profits equal to
the shaded area.
P
MC
ATC
P*
ATC
D
Q*
Q
MR
Economic Losses by a Monopolist
A monopolist makes losses when P<ATC (just like a PC firm). Profit
maximization is where MR=MC, the corresponding output and price are Q*
and P*, respectively. Since P<ATC, the monopolist makes losses equal to the
shaded area.
P
MC
ATC
ATC
P*
D
Q*
Q
MR
Economic Profits in the Long-Run (LR)
• We know that in PC, firms make profits or losses
in the SR. However, because of the condition of
no barriers to entry, the profits (or losses)
disappear and zero economic profits prevail in the
LR.
• On the other hand, since barriers to entry exist in
the case of a monopoly, a monopolist can still
make profits in the LR. However, LR economic
losses will force a monopolist to leave the market.
Price Discrimination
• The market power monopolists have allow them
to charge different buyers different prices for the
same goods or service
• By price discriminating, a monopolist charges
each consumer their reservation price and
• Examples of price discrimination:
– Pay less at a night club if you get in before 9 pm
– Ladies free nights
– Discounted gym memberships for students
Socially Optimal Output and the Deadweight Loss
•The socially optimal/efficient level occurs where MR=MC.
•Under perfect competition, profit maximizing occurs where MR=MC; Price
is Pc and Q is Qc. This is the socially efficient output level
•Under Monopoly, profit maximization occurs where MR=MC; Price is Pm
and Quantity is Qm
•Thus, Pm > Pc and Qm < Qc. Under monopoly, the price charged is too high
and the quantity produced is too little. This results in a deadweight loss,
represented by the shaded triangle.
P
PM
PC
MC
D=MR
QM
QC
MR
Q
Perfect Competition vs Monopoly
Perfect Competition
Monopoly
Many sellers (competitors)
Price takers (Horizontal
demand curve)
Homogenous products
Single seller
Price maker (Downward
sloping demand curve)
Products have no close
substitutes
Entry is blocked
Profit maximization MR =
MC
At profit maximization P >
(MR= MC)
Entry is free
Profit maximization MR =
MC
At profit maximization P=
MR = MC