fkirsten@uj.ac.za Dring 210
Chapter 4 Information
Topic: The business environment of a firm
E-Book: Page 62-174
Activity: 46-95
Outcome:
•
•
•
•
•
•
•
•
•
Linear demand function
Consumer sensitivity analyses
The rational consumer
Supply & market-clearing
Short-run production analysis
Concepts of returns to scale and input productivity efficiencies, net
efficiencies of inputs and elasticity of substitution.
Short- and long run cost analyses
Competitive environment of the firm
Selective pricing practices
Lecture 4.1
Market demand conditions (Linear
demand function, elasticities &
Rational consumer behavior A)
Market demand conditions
Linear demand function
-
Law of demand (negative relationship between price and quantity demanded
P = 170 -20Q
slope: ΔP/ ΔQ = 130-100/3.5-2 = -20
Q = 170/20-1/20 P thus Q = 8.5 – 1/20P
•
•
•
Price intercept when Q = zero and Quantity intercept when P = zero.
Slope remains unchanged on the same demand curve.
If demand is expressed when Q is the dependant variable then we are dealing with the
inverse of the slope.
Total revenue and marginal revenue
TR = PxQ = (170-20Q)Q = 170Q -20Q2
MR = Δ dTR/ ΔdQ = 170 – 40Q
Maximum sales revenue when MR = 0
Thus, MR = 170 - 40Q = 0; Therefore Q = 170/40 = 4.25 units and P = 170 – 20(4.25) =
R85.
TR = PxQ =85X4.25=361,25
Total revenue and marginal revenue
•
Both the demand and MR-functions have the same price-intercept but the slope of MRfunction is twice steeper as slope of the demand curve.
Change in own-price
Only a change in price, ceteris paribus, will result in a change in quantity demanded.
Shifts of demand curves.
Assumption: No change in own-price
Increase in demand: Whole demand curve will shift to the right at every price level.
Decrease in demand: Whole demand curve will shift to the left at every price level.
Normal versus inferior products
Normal product: Increase in income, ceteris paribus, will shift whole demand curve to the right
(increase in demand).
Inferior product: Increase in income, ceteris paribus, will shift demand curve to the left (decrease
in demand).
Substitute products
Dealing with products that can be used in the place of the other product. An increase in the price
of butter will firstly result in a decrease in the quantity demanded of butter. At the same time
those butter customers will buy more margarine (take note that the price of margarine did not
change). The demand curve for margarine will shift to the right (increase). The relationship
between substitutes are positive because an increase (+) in the price of butter resulted in an
increase (+) in the demand for margarine. Thus + times + = +.
Complementary products
Dealing with two products that are used together. The price of tennis racquets increase and the
result is a decrease in the number of tennis racquets demanded. Over time less tennis balls will
be sold because less tennis racquets are bought. The demand for tennis balls will shift to the left
at every price level (decrease). The relationship between complementary products is negative
because an increase (+) in the price of tennis racquets will result in a decrease (-) in the demand
of tennis balls. Thus + times - = -.
Change in consumer preferences: Negative change in consumer preference will result in a
decrease in demand but a positive change in consumer preference will result in an increase in
demand.
Other factors that will shift a demand curve:
1) Increase in total population and 2) expectations of future changes in the price of a product.
Consumer surplus: Difference between what the consumer is willing to pay and what he or she
is actually paying. Total amount willing to pay for 4 units is R10 (R4 + R3 + R2 + R1). Assume that
the current price is R1 per unit. The consumer will thus pay R4 (4 x R1). Consumer surplus (the
shaded area in figure (b) is thus R10 – R4 = R6.
Consumer sensitivity analysis
Own-price sensitivity (refer to example video in E-Book on page 73)
Refers to the relative change in quantity demanded due to the relative change in own price.
% Δ in quantity demanded / % Δ in own price
OR
Ed = P/Q x 1/slope (see derivation on p.70)
% Δ in quantity demanded / % Δ in own price
Observe that price-elasticity coefficients ranges from 0 to infinite. Sign will always be negative
(law of demand) but the interpretation is on the absolute value of the coefficient.
Interpretation: 1) when ed is < than 1 consumers are relatively price insensitive (inelastic) at
those price levels (thus the relative %Δ in quantity demanded is < than the relative %Δ in ownprice) , 2) when ed is > than 1 consumers are relatively price sensitive (elastic) at those price
levels (thus the relative %Δ in quantity demanded is > than the relative %Δ in own-price), 3) total
revenue will be maximised at price level where (ed = 1 is Unit elastic) respond the same
proportion.
Relative elastic versus inelastic demand curves.
A steeper sloped demand curve is in general indicative of a relative inelastic demand
(in general the relative %Δ in quantity demanded is < than the relative %Δ in ownprice).
A flatter sloped demand curve is in general indicative of a relatively elastic demand (in
general the relative %Δ in quantity demanded is > than the relative %Δ in own-price).
Perfect elastic versus perfect inelastic demand curves
A perfect elastic demand curve is horizontal and the slope is infinite. Any increases in price will
result in a total loss of consumers.
A perfect inelastic demand curve is vertical and the slope is zero. Any increases in price will have
no impact on the quantity demanded.
Price elasticity and total revenue
•
For ed > 1: % Δ in P < % Δ in Q; thus if P↑ then Q↓ and because of the above TR
(P x Q) will decrease. If P↓ then Q ↑ and because of the above TR (P x Q) will
increase .
•
For ed < 1: % Δ in P > % Δ in Q; thus if P↑ then Q↓ and because of the above TR
(PxQ) will increase. If P↓ then Q ↑ and because of the above TR (P x Q) will
decrease .
•
Max TR when ed = 1 and MR = 0.
Moral of the story: If the aim is to increase total revenue do not increase own-price for
price elastic price levels and for price inelastic levels you have scope to increase ownprice.
Refer to
video
example in
E-Book on
page 74
Income sensitivity (refer to video example in E-Book on page 75)
•
Income elasticity coefficient calculated as the %Δreal sales / %Δreal disposable
income
•
Sign & magnitude of income elasticity coefficient
i)
+ = normal product and + > 1 = luxury: + < 1 = necessity
ii) - = inferior product
(see table on page 75)
Related product price sensitivity (also referred to as cross-price sensitivity)
•
•
•
•
Related product price sensitivity calculated in order to determine the substitute or
complementary relationship (and the strength thereof) of two products.
%Δ in the quantity demanded of a product / %Δ in the price of another product
Substitute products: If the price of the one product increases the demand for the
other product increases. Thus relationship = + because when Pa↑ Db↑. Thus if
the sign of the coefficient is + we are dealing with a substitute relationship. If the
positive coefficient is > than 1 the products are strong substitutes but if the
positive coefficient is < than 1 the two products are weak substitutes.
Complementary products: If the price of the one product increases the demand
for the other product decreases. Thus relationship = - because when Px↑ Dy↓.
Thus if the sign of the coefficient is - we are dealing with a complement
relationship. If the negative coefficient in absolute terms is > than 1 the products
are strong complements but if the negative coefficient in absolute terms is < than
1 the two products are weak complements.
External variable price sensitivity
Aim is to determine the strength of the relationship between own-real sales and
changes in the value of an external variable.
%Δ in own-real sales / %Δ in value of the external variable
If the coefficient is positive and greater than 1, changes in the external variable will
have a strong impact on own-real sales but if the coefficient is positive and less than
1, changes in the external variable will have a weak impact on own-real sales.
As an example assume that a 25% increase in advertising resulted in a 50% increase in
sales. The coefficient is thus 50% / 25% = 2. Thus any increases in advertising will have
a strong increase in own-real sales.
Rational consumer behaviour
Underlying principles: 1) Consumer must choose between all possible options, 2) Consumer
preferences are transitive, 3) Consumer always chooses more rather than less of a product.
Concepts of utility (satisfaction derived from consumption), marginal utility (refer to example
video in E-Book on page 80) and the law of diminishing marginal utility.
Marginal utility is the additional utility per additional unit of the product (Δ in utility / Δ in units
of consumption). The law of diminishing marginal utility states that the marginal utility will
decrease as more units of a product is consumed.
A rational consumer strives for the optimal utilization of his or her budget. Weighted marginal
utility is the marginal utility / price of the product, thus for a product A it is MUa/P a. For a two
product scenario (A & B) a rational consumer will choose a combination such that the weighted
marginal utilities are equal, the MUa/Pa = MUb/Pb. This situation is illustrated in the two tables
below.
Indifference curve technique
Is a graphical representation of different combinations of two products that gives a consumer the
same level of satisfaction. Due to the law of diminishing marginal utility the indifference curve is
convex. A one unit decrease in one of the products requires increasing substitution of the other
product.
Properties of indifference curves
1) Consumer prefers indifference curves to the right (they represent higher utility levels).
2) Indifference curves never intersect.
In the next figure L is on the same indifference curves as N & K. Illogical because K is on another
indifference curve compared to N.
The slope of the indifference curve (that is convex) is negative and it is known as the marginal
rate of substitution (MRS). It means that a decrease in the consumption of one product must be
substituted with the consumption of the other product. It also measures the rate at which the
one product will be substituted by the other product in order to remain on the same indifference
curve.
3) The negative slope, convexity of the indifference curve and the law of diminishing marginal
utility are illustrated on the next two figures.
The following figure explains the negative slope of the indifference curve. Initial combination is
FoMo (point J). Keep A constant but increase B to M1 thus point K on a higher indifference curve.
To remain on the same indifference curve the consumption of A must decrease (F1). Clear that
slope is negative.
Refer to example video in E-Book on page 86
Observe that more and more units of product B are substituted for a one unit decrease in the
consumption of product A. The same reverse argument (not on the figure) can be made for more
and more substitution of product B for a one unit decrease in the consumption of product B. The
two ends of the indifference curve is the “flattening out”. Thus the convex shape of the
indifference curve.
The MRS is the slope of a tangent to a specific point on the indifference curve. In the following
figure ΔQa/ΔQb (change in vertical divided by change in horizontal).
The MRS is equal to the ratio of the marginal utilities. In order to remain on the same indifference
curve any change in utility created by a change in the consumption of one of the products must
be matched by the change in the utility created by the change in the consumption of the other
product. Thus ΔQa times MUa = ΔQb times MUb or ΔQa/ΔQb = MUb/MUa = MRS
Lecture 4.2
Market demand conditions (Rational
consumer behavior B) & Cost and
supply/capacity conditions (Linear supply
function, market-clearing, simultaneous shifts
of demand & supply curves, maximum &
minimum prices, deadweight losses)
Budget line
It indicates the different combinations of products which a consumer can afford. Thus, Qa and Qb
= f(Pa, Pb and I). The intercepts are Qa = I/Pa and Qb = I/Pb.
The maximum amount that can be spend on the two products is QaPa + QbPb = I. The slope of the
budget line is the vertical intercept divided by the horizontal intercept I/Pa ÷ I/Pb.
Thus I/Pa x Pb/I = Pb/Pa. The slope of the budget line is negative and is the price ratio of the two
products. The equation for the budget line (Qa is the dependant variable) is thus
Qa = I/Pa – Pb/Pa Qb.
A change in the income of the consumer, ceteris paribus, will result in a parallel shift of the
budget line (the slope remains unchanged). An increase in income, ceteris paribus, will shift the
budget line outwards (more maximum of both products can be afforded) but a decrease in
income, ceteris paribus, will shift the budget line to the left (less maximum of both products can
be afforded).
A change in the price of one of the products will change the slope of the budget line. An increase
in the price of a product indicates that less maximum of that product can be afforded. The
intercept of that product will decrease.
A change in the price of one of the products (B) will change the slope of the budget line. An
increase in the price of a product (B) indicates that less maximum of that product can be
afforded. The intercept of that product will decrease (Y2). A decrease in the price of a product
indicates that more maximum of that product can be afforded. The intercept of that product will
increase (Y1).
Assume that Pa and Pb were originally R2 each. The original slope of the budget line is Pb/Pa =
2/2 = 1. Assume that Pb increases to R4. The slope of the budget line Pb/Pa is now 4/2 = 2 (XY2).
Thus the slope increased (steeper). But if Pb decreases to R1 the slope is Pb/Pa = ½ (XY1). The
slope decreases (flatter).
Consumer equilibrium.
Consumer equilibrium (most optimal combination) will when the highest possible indifference
curve is tangent to the budget line. At this point the slope of the indifference curve (MRS) is
equal to the slope of the budget line (price ratio).
Refer to example video in E-Book on page 94
Indifference curve I1 is not affordable. Indifference curve I3 is affordable but inferior to I2.
Indifference curve I2 represent the highest attainable level of satisfaction that can be afforded if
combination e is consumed. At point e MRS = Pb/Pa and the weighted marginal utilities are
equal (MUa/Pa = MUb/Pb)(consult the proof on p.94).
Cost & supply/capacity conditions
Law of supply: A positive relationship between own-price and quantity supplied. Higher ownprices will result in higher quantities supplied.
Quantity supplied is a function of own-price prices of production factors and level of technology,
thus Qs = f (Px, Pf, Ty). Assume that Pf and Ty is assumed fixed then Qs = f(Px).
Observe the positive relationship between own-price and quantity supplied, ceteris paribus. Also
note that the price intercept (10) will occur when quantity supplied is 0.
The slope of the supply curve is ΔP/ΔQ = 90-50/10-5 = 8 (thus a positive slope).
The supply equation when P is the dependent variable is expressed as P = 10 + 8Qs. If Qs is the
dependent variable the slope of supply will be Qs = -10/8 + 1/8P thus Qs = -1.25 + 1/8P. Observe
that 1/8 is the inverse of the slope.
A change in own-price, ceteris paribus, will result in a movement along the same supply curve.
Changes in any of the other independent variables (excluding own-price) will result in a shift of
the supply curve. An increase in supply is illustrated by a rightward shift of the supply curve (S1)
and a decrease in supply is illustrated by a leftward shift of the supply curve (S2).
Producer surplus: difference between the amount that a producer is receiving in excess of a
minimum required price for production (R12 willing to receive for 3 units but receive R15).
Market-clearing prices & quantities.
The market will clear when Demand = Supply.
Thus 8.5 – 1/20P = -1.25 + 1/8P, thus P = 55.71 & Q =5.7145 (see p. 99 for full calculation)
The impact of simultaneous shifts of demand and supply curves on market-clearing prices &
quantities.
Rule 1: Increase in demand, ceteris paribus, will result in an increase in equilibrium price &
quantity while a decrease in demand, ceteris paribus, will result in a decrease in equilibrium
price & quantity.
Rule 2: Increase in supply will result in a decrease in equilibrium price but an increase in
equilibrium quantity. A decrease in supply will result in an increase in equilibrium price but a
decrease in equilibrium quantity.
Case 1: Simultaneous increase in supply & demand. Increase in supply = ↓Pe & ↑Qe. Increase in
demand = ↑ Pe & ↑Qe. Thus Qe will definitely ↑ but impact on Pe is indeterminate. If the
relative % increase in demand is greater than relative % increase in supply Pe will ↑ but if relative
% increase in supply is greater than the relative % increase in demand Pe will ↓.
Case 2: Simultaneous decrease in supply & demand. Decrease in supply = ↑Pe & ↓Qe. Decrease
in demand = ↓ Pe & ↓Qe. Thus Qe will definitely ↓ but impact on Pe is indeterminate. If the
relative % decrease in demand is greater than relative % decrease in supply Pe will ↓ but if
relative % decrease in supply is greater than the relative % decrease in demand Pe will ↑.
Case 3: Simultaneous decrease in supply and increase in demand. Decrease in supply = ↑Pe &
↓Qe. Increase in demand = ↑ Pe & ↑Qe. Thus Pe will definitely ↑ but impact on Qe is
indeterminate. If the relative % decrease in supply is greater than relative % increase in demand
Qe will ↓ but if relative % increase in demand is greater than the relative % decrease in supply Qe
will ↑.
Case 4: Simultaneous increase in supply and decrease in demand. Increase in supply = ↓Pe &
↑Qe. Decrease in demand = ↓ Pe & ↓Qe. Thus Pe will definitely ↓ but impact on Qe is
indeterminate. If the relative % increase in supply is greater than relative % decrease in demand
Qe will ↑ but if relative % decrease in demand is greater than the relative % increase in supply Qe
will ↓.
Maximum & minimum prices
Maximum prices is normally set to protect consumers. In order to be effective a maximum price
must be set lower that the market-clearing price. The consequence is the creation of a deficit on
the market (fg in the following figure).
At Pmax producers will produce at f but the demand from consumers will be at g.
Minimum prices are set to protect producers. In order to be effective the minimum price must
be set higher than the market-clearing price. The consequence of the setting of a minimum price
is the creation of a surplus on the market (hi in the following figure).
At the minimum price Pmin producers are willing to supply i to the market but the demand will
only be h.
Deadweight losses of minimum & maximum prices.
Remember that consumer surplus is the area B and producer surplus is area A in the case of the
market-clearing price Pm.
Total maximum surplus is thus the combination of areas A & B at the market-clearing price Pm.
The deadweight losses created by the setting of a maximum price. (refer to example video in EBook on page 103)
For a maximum price of Pmax the following will happen: consumer surplus will ↑ by area F minus
area C. Producer surplus will ↓ by area F plus area D. The total net loss is areas C & D =
deadweight loss created by the setting of a maximum price.
The deadweight losses created by the setting of a minimum price.
For a minimum price of Pmin the following will happen: consumer surplus will ↓ by area I & H.
Producer surplus will ↑ by area I minus area G. The total net loss is areas G & H
Deadweight loss created by the setting of a minimum price. Deadweight loss in terms of
consumer surplus (area G) will be greater when demand is more inelastic (steeper D-curve).
Lecture 4.3
Cost and supply/capacity conditions
(Input efficiencies in the short run)
Production & input efficiencies
•
•
Fixed versus variable inputs
Production function = defined as the relationship between quantities of inputs and
maximum physical output that can be produced during a given time-period.
Observe that total output increases with a one unit increase of labour but that output decreases
when the 8th unit of labour is employed = reason is the law of diminishing marginal output.
Thus, total output increases, reaches a maximum and then decreases as illustrated in the
following figure.
• Average & marginal output efficiencies.
Average output = total output ÷ unit of variable input (TO/N)
Marginal output = change in output as a result of a change in the variable input (MO = ΔTO/ΔN).
From the next table observe that both AO & MO increases, reaches a maximum and then
decreases = reason = law of diminishing marginal returns.
Also observe from the table that initially marginal output increases faster than average output. At
an input level of 4 workers AO = MO. From then onwards marginal output decreases faster than
average output. These relationship are graphically illustrated in the following figure.
•
Graphical derivation of the MO-curve
TO/N = AO = slope of a ray to any point on the TO-curve. Observe that the slopes of successive
ray’s increase until the maximum slope is reached at point H. After this point the slopes of
successive ray’s to the TO-curve will decrease. Thus, the AO-curve increases, reaches a maximum
and then decrease.
•
Derivation of the MO-curve.
MO = ΔTO/ΔN = slope of a tangent to any point on the TO – curve. Marginal output at point P is
the slope of tangent RR’. The slopes of successive tangents increases, reaches a maximum,
decrease and will be equal to zero at point S.
Combined derivation of average & marginal output curves from the total output curve.
C
•
Point R is the inflexion point. At this point the slope of a tangent to the TO-curve is at a
maximum = maximum point on MO-curve = point U.
• At point S the slope of a ray to the TO-curve will be at a maximum = maximum of AO-curve =
point V. At the same point S the slope of a tangent will be equal to the slope of a ray. Thus
MO = AO at point V.
• At point T the slope of a tangent is equal to zero = point W.
• Also keep in mind that initially MO increases faster the AO, they intersect at point V after
which MO will decrease faster than AO.
Technological improvements
gg
•
Technological improvements
Fig (a) = Same input levels produces higher output.
Fig (b) = Same output levels can be produced by a smaller input base.
Lecture 4.4
Cost and supply/capacity
conditions (Input efficiencies in
the long run: the isoquant
technique)
Production in the long-run: The isoquant technique
Isoquant = the same output that can be produced with different input combinations. Due to the
law of diminishing returns the isoquant is convex = a successive one unit decrease in an input
must be substituted by ever increasing units of the other variable.
Higher isoquants represents higher output levels & isoquants cannot intersect.
Curves F & G = two isoquants = convex. Lines A & B = production lines (indicate the same ratio of
inputs that is used). Movement from point b to b1 = The ratio of the input combination remain
the same while output increases.
Slope of isoquant = marginal rate of technical substitution (MRTS) = negative = -ΔC/ΔL = also
refers to the rate at which one input has to be substituted for the other input in order to remain
on the same isoquant. Assume C3L1 to C2L2 = thus –ΔC. MOc = +ΔL.MOL = ΔC/ΔL = MOL/MOC =
MRTSLC (see the rest of the prove on p. 115).
In practical terms it means that the rate at which substitution will occur is driven by the marginal
efficiency ratios of the two inputs. If the marginal efficiency of labour is greater that the marginal
efficiency of capital, the firm will substitute labour for capital (thus more labour will be used).
When more units of labour is substituted for capital MOL will decrease and MOC will increase
(due to the law of diminishing returns). Thus MOL/MOC = MRTS = will decrease. But if capital is
substituted for labour MOL will increase and MOC will decrease (due to the law of diminishing
returns). Thus MOL/MOC = MRTS = will increase.
Economic region of production
Between points b and d MRTS is negative = substitution takes place. But from point b to point c
(as an example) more units of both capital and labour are used to employ the same output =
irrational, thus MRTS becomes positive!! The same applies to combinations beyond point d. At
point d MRTS = at its maximum = infinite = indicates the minimum units of capital required to
produce I1 output. At point b MRTS = zero = minimum units of labour required to produce I1
output. Lines R & S links all such point where MRTS = infinite or zero. The area between these
two lines is referred to as the economic region of production = rational combinations of the two
inputs are chosen in this area.
Rectangular isoquants
Production requires a fixed input ratio.
Isocost curves = reflects all affordable combinations of two inputs = PCC + PLL
The intercepts are calculated as the production budget ÷ price of the input (under the
assumption that zero units of the other input is used) = maximum units of that input that are
affordable. Thus B/PC = maximum affordable units of capital and B/PL = maximum affordable units
of labour. By linking these two intercepts the isocost line is derived. The slope of the isocost line
is negative = B/PC ÷ B/PL = B/PC x PL/B = - PL/PC. = will remain unchanged from point to point on the
same isocost curve. Assume that capital is the dependent variable, thus the equation for the
isocost line is C = B/PC – PL/PCL and if labour is the dependent variable the equation is L = B/PL –
PC/PLC.
Optimum combination of two production factors.
Isoquant I3 is preferable to the other two isoquant (gives highest output level) but I3 is not
affordable. The highest possible isoquant that can be affordable is I2 and the combination of
inputs that is affordable to produce I2 is the combination at point a. Points b and d on I2 requires
combinations of inputs that are not affordable.
At point a the slope of the isoquant is equal to the slope of the isocost line. Thus MRTS = PL/PC
and MOL/MOC = PL/PC and PL X MOC = PC X MOL. Dividing both sides by PC X PL will yield MOL/PL =
MOC/PC.
Expansion path of individual firm = all points of tangency between successive isoquants and
isocost lines are linked. Could provide an understanding on whether a firm is becoming more
capital or more labour intensive over time.
Fig (a) is indicative of a firm that is becoming more capital intensive over a certain period of time
while fig (c) is indicative of a firm that is becoming more labour intensive over time. Fig (b)
indicates a neutral expansive position.
Impact of a price change of an input
Price of labour increases (PL1 to PL2) = isocost line changes from A to B. At the new equilibrium
(point r) less of both input are employed to produce the smaller output I2.
Concept of returns to scale = shows the relationship between the relative percentage change in
input combinations and the relative percentage change in output.
In fig (a) the same relative percentage increase in the input combination is needed to produce the
same relative percentage increase in output (as an example: in order to increase output by 20%
input combination must also be increased by 20%) = constant returns to scale.
In fig (b) a smaller relative percentage increase in the input combination will produce a greater
relative percentage increase in output (as an example: in order to increase output with 20% only
a 15% increase in the input combination is required) = increasing returns to scale.
In fig (c) a higher relative percentage increase in the input combination will produce a smaller
relative percentage increase in output (as an example: in order to increase output with 20% a
25% increase in the input combination is required) = decreasing returns to scale.
Net efficiencies, elasticity of substitution and input productivity efficiencies
•
•
•
•
•
•
•
•
•
Net efficiencies of inputs: the lower the real cost the higher the net efficiencies and the
higher the real cost the lower the net efficiencies
Greater demand for input that has the lower real cost.
Elasticity of substitution: % Δ in capital/labour mix due to % Δ in the marginal efficiency of
the two inputs.
Marginal efficiency (ME) = the addition to production if an additional unit of an input is used.
Marginal efficiency ratio = % Δ in the ME labour / ME capital ratio. Normally, if the usage of one
input is reduced more of the other input will be used. Thus elasticity of substitution will be
positive.(see example on p.126).
Cases where inputs are perfect substitutes (sign of elasticity of substitution = infinite) or
where two inputs are used in fixed-proportions (sign of elasticity of substitution = 0). (see
examples in middle of p.126).
Optimal input mix: when the marginal efficiency ratio = relative cost ratio. Thus MElabour /
MEcapital = relative cost labour / relative cost capital.
If marginal efficiency ratio < than relative cost ratio firm is over-utilising labour. Thus firm
should use less labour and more capital.
If marginal efficiency ratio > than relative cost ratio firm is over-utilising capital. Thus firm
should use less capital and more labour.
(see example bottom of p.126)
Lecture 4.5
Cost and supply/capacity conditions (returns
to scale, cost efficiencies in the short & longrun)
Cost efficiency of the firm in the short- and long run
Total constant (TCC) = remain unchanged in the short run. Total variable cost (TVC) = increases
when output increases (due to more variable inputs that are used). Total cost = TCC + TVC.
Variable cost: Increases when output increases.
Observe that when output = zero total variable cost is also = zero.
Total cost = TCC + TVC
Observe that even if output is zero the constant cost must be incurred. From there onwards
TC = TCC + TVC.
Average cost & marginal cost concepts
ACC = TCC/Q; AVC = TVC/Q; ATC = TC/Q; MC = ΔTC/ΔQ
Observe that ACC decreases as output increases; AVC decreases, reaches a minimum and then
increase again; ATC decreases, reaches a minimum and then increase again. Marginal cost also
decreases, reaches a minimum and increase again.
The shape of the AVC, ATC and MC curves are due to the law of diminishing returns. This is where
the important link between input efficiencies and corresponding costs is established.
Link between average efficiency and average cost
•
The link between productivity and resultant cost structures are of the utmost importance for
firms. The next figure indicates that lower AO (lower average productivity) will result in
increasing AVC and that higher AO (higher average productivity) will result in decreasing AVC.
On p. 132 the important link is derived. AVC =
•
•
•
•
𝑃𝑟𝑖𝑐𝑒 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒 𝑖𝑛𝑝𝑢𝑡
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑜𝑢𝑡𝑝𝑢𝑡
Assume that the price of the input is fixed. Increases in average input efficiency (AO) will
result in a decrease of AVC and decreases in average input efficiency (AO) will result in an
increase of AVC. Lowest average cost will be attained when AO is at a minimum.
Observe from the next figure that increases in AO (higher average productivity) will result in a
decrease in AVC, decreases in AO (lower average productivity) will result in an increase in
AVC. Lowest AVC will be attained when AO is at a maximum level.
Thus, there is an inverse relationship between AO and AVC.
The same arguments can be applied when the average total cost curve (ATC) is analysed. The
only difference is that TCC is added.
Marginal efficiency & Marginal cost
•
Marginal costs(MC) = marginal addition to variable cost / marginal output. The aim of the
discussion is to illustrate that there is also an inverse relationship between MO and MC. Higher
additional productivity levels (MO) will result in a corresponding lower additional cost (MC) and
lower MO levels will result in higher MC levels.
𝑃 𝑜𝑓 𝑖𝑛𝑝𝑢𝑡
(see proof on p.135). Assume that PN is fixed.
𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑜𝑢𝑡𝑝𝑢𝑡
•
MC =
•
From the following figure it is cleat that when MO increases MC decrease and when MO decreases
MC will increase. The lowest MC level will be attained when MO is at a maximum.
MO & MC relationship (refer to example video in E-Book 136)
Graphical presentation of the short-run curves
Observe that the MC curve intersect the ATC & AVC curves in the minima (remember that the
AVC & MC curves are the true reflections of the AO & MO)
Cost efficiencies in the long run.
Aim is to determine whether a firm is still experiencing economies of scale or dis-economies of
scale. In order to do so a long-run average cost function (LAC) needs to be derived. Economies of
scale = long-run average cost is still decreasing when output increases (still cost efficient). Diseconomies of scale = long-run average cost increases when output increases (cost inefficient).
The 1st building block of the LAC-curve is the least-cost principle. If Q1 is the output the least-cost
function is SACs (AC1). If output increases to Q2 the least-cost function is SACm. If all these leastcost points over time are linked a LAC-curve is derived.
The LAC-curve has a U-shape. The decreasing part is due to economies of scale. Observe that for
the successive SAC’s production takes place to the left of the minimum points, thus average cost
is still decreasing as output increases. The increasing part is due to dis-economies of scale.
Further expansion in output will occur at higher real average cost. Observe that for successive
SAC’s production takes places to the right of the minimum points, thus average cost is increasing
as output increases. It might force a firm to introduce re-engineering = a total overall of all the
activities of the firm in order to reap the benefits of economies of scale again.
Applications of the cost concepts.
Real labour cost = % change in nominal labour cost deflated by the corresponding % change in
productivity levels.
Thus if % increase in real labour costs is positive = increase in nominal wages more than increase
in corresponding productivity levels = real cost of firm will increase thus having negative impact
on competitiveness and ultimately on capacity expansion.
Negative real labour cost changes = nominal wage increases are less than the % increase in
corresponding productivity levels = result in decrease in real labour cost levels = firm more
competitive.
Marginal revenue product (MRP) = applied to determine optimal usage of labour = additional
sales revenue generated by the utilisation of one more labour-hour. If MRP > real cost per labourhour = firm will employ more labour.
Real capital costs = deals with the relative supply of capital not only in physical quantities but in
technological qualities = keeping cost of real capital stock as low as possible. Real capital stock
will be purchased and not leased if the lease-rate > sum of interest and depreciation costs. Can
also use the MRP concept (additional sales revenue generated by the utilisation of one more
machine-hour = If MRP > than cost per machine hour = firm will invest in more real capital stock.
Concept of net present value (NPV) = future net sales revenue that might flow from investing in
capital stock is discounted into present values (PV) (see formula on p. 141 & example on p.142).
The higher the discount rate the lower the PV. If NPV is positive firm should proceed with
investing in capital stock but if NPV is negative it should not proceed will capital outlay.
Lecture 4.6
Competitive environment (concepts of
economic and normal profits, the highly
competitive business environment)
Competitive environment of the firm
• Concepts of economic costs, economic profit / loss and normal profit.
Economic cost = direct + indirect costs. If revenue > economic costs =
economic profit (also referred to as abnormal profits). If revenue =
economic cost = normal profit. If revenue < economic cost = economic
loss.
(see example on p. 143)
• Measurement of level of competition
Lerner index = P-MC / P = closer to 1 the less competition and closer to 0 the
higher the level of competition.
Four-firm concentration ratio = calculates market share of top four firms in an
industry = below 40% = monopolistic competition and greater than 60% =
oligopoly.
Herfindal-Hirschmen index = squaring market share of each firm in market
then summing resulting numbers = between 0 and 1 = higher values closer to
1= greater market concentration.
Highly competitive business environment
• Abundance of customers and firms.
• Easier entry into and exit market.
• No barriers to entry.
• Homogeneous product.
• Freer mobility of inputs.
• Very little control over own pricing policy = adopt
market-going price.
• Consumers highly price-sensitive.
• Can only control size of its business operations.
• Profitability depend to large extend on cost structures.
• Can realise economic profits/loss or normal profits in
short run but only normal profits in long run.
The individual firm = price-taker = has no control over the price = demand curve facing the
individual firm is perfect elastic. If firm increase price it will loose all its consumers and if it lowers
the price all the other firms will do the same (no win situation).
Price is determine in the open market (where demand is equal to supply). All firms must sell at
this price (P1). The individual firm can produce whatever it prefers at this price.
At the same time the price = average revenue (AR) = marginal revenue (MR).
The aim of the competitive firm is to determine an output level that will maximise its profit
position or at least minimise its loss position. In the next figure the cost structures (MC & ATC)
and the demand (revenue) curve are combined in the same figure. In the discussion ATC will be
compared to AR while MR will be compared to MC. The golden rules are 1) when AR > ATC the
firm will make economic profit, when AR = ATC the firm will make a normal profit and when AR <
ATC the firm will make an economic loss. 2) when MR > MC the firm makes an economic profit on
that additional unit, when MR = MC the firm is making a normal profit on that additional unit but
if MR < MC the firm is making an economic loss on that additional unit.
Refer to
example
video in
E-Book on
page 146
For quantities to the left of Q2 the firm will make an economic loss (ATC > AR). For quantity Q2
(point D) the firm makes a normal profit. Beyond Q2 the firm will now realise economic profit. At
the same time the MR per unit > MC per unit. At Q4 (point I) the firm is again making a normal
profit. Beyond Q4 the firm will make a economic loss per unit. From Q4 to Q5 the MC per unit
(point H) > MR per unit (point G). Thus the maximum “pool” of economic profit is = shaded area.
Conclusion = in order to maximise total economic profits the firm must produce a quantity such
that MR = MC = P. This will occur when Q4 (point I) is produced.
The upward part of the MC-curve starting at the intersection with the minimum point on the
AVC-curve represent the short-run supply curve of the firm.
Points such as B, C, D and E fulfils the equilibrium condition MR = MC = P (they all fall on the MCcurve). If the price falls below P4 the firm will not produce any quantity simply because of the fact
that it does not cover its variable and its constant costs. For price levels between B and D the firm
will cover its variable cost but not all of its constant costs. The firm will thus make an economic
loss (economic loss will be minimised if the equilibrium condition is applied). For price P2 (point
D) the firm will only realise a normal profit. For price levels higher than the minimum of the ATCcurve (such as P1) the firm will make economic profits.
Long-run equilibrium of the individual firm and the industry
Assume a price of P1 = the average individual firm will produce a quantity that corresponds to E1
= average individual firm is thus making an economic profit. This situation will attract new
entrants = increase supply in the industry (S1 – S2) = start to decrease the market price. At the
same the economic profits of the average individual firm will start to decrease (at the lower price
levels). New entry will stop once the average firm in the industry will only realise normal profits =
At P2 (D = S2) where the average firm produces quantity at E2 (minimum point of the LAC-curve).
Thus firms can only realise normal profit in the long run.
Derivation of the long-run supply curve for a constant cost industry
Assume initial position D1 = S1 = P1 = average firm make normal profit.
Assume demand shock that increases demand to D2 = price increases to P2 (D2 = S1) = average
firm makes an economic profit = new entry and supply begins to increase = LAC for average firm
remains unchanged = Equilibrium in industry will be restored at P1 (D2 = S2) and average firm only
makes normal profit. End result = more is produced in the industry but cost structure of average
firm and the price remains unchanged. Dealt with constant returns to scale situation. The longrun supply curve is horizontal.
Derivation of the long-run supply curve for a increasing cost industry
Assume initial position D1 = S1 = P1 (point c) = average firm make normal profit.
Assume demand shock that increases demand to D2 = price increases to P2 (D2 = S1) = average
firm makes an economic profit = new entry and supply begins to increase = LAC for average firm
at the same time starts to increase = Equilibrium in industry will be restored at P3 (D2 = S2 and
point d) and average firm only makes normal profit. End result = more is produced in the industry
but cost structure of average firm increased to LAC2 and the price is higher. Dealt with decreasing
returns to scale situation. The long-run supply curve has a positive slope and is upward-sloping.
Derivation of the long-run supply curve for a increasing cost industry
Assume initial position D1 = S1 = P3 (point e) = average firm make normal profit.
Assume demand shock that increases demand to D2 = price increases to P2 (D2 = S1) = average
firm makes an economic profit = new entry and supply begins to increase = LAC for average firm
at the same time starts to decrease = Equilibrium in industry will be restored at P1 (D2 = S2 and
point f) and average firm only makes normal profit. End result = more is produced in the industry
but cost structure of average firm decreased to LAC2 and the price is lower. Dealt with increasing
returns to scale situation. The long-run supply curve has a negative slope and is downwardsloping.
Conversion of prices: The Cobweb model
Basic argument is that QS = f(Pt – 1) = supply is based on prices in the previous period. QD = f(Pt) =
demand is based on the current price.
Assume Q1 = will only be purchased at P2 but Q2 will only be supplied at P3. This process will
continue until equilibrium price P4 and equilibrium quantity Q4 is reached (intersection of
demand & supply curves). Reason for convergence = slope of supply curve is steeper than slope
of demand curve. If slope of demand curve were to become steeper than slope of supply curve =
price and quantity will diverge.
Lecture 4.7
Competitive environment (monopolies,
monopolistic competition & oligopolies)
Monopoly or near-monopoly
• Pure monopoly = only one firm controls total market = very rare =
mostly state-controlled
• Barriers to entry = absolute = due to exclusive control over resources,
technology so advanced and expensive but market limited = only one
firm can survive, large financial investment required = only one big
firm, authorities put legal constraints in place such as patent rights and
licences.
• Absolute power over setting of price.
• Consumers less price sensitive = limited choice.
• Near monopolies = one single firm controls about 95% of market.
• Should realise economic profits both in short and long run
• Normally viewed as undesirable for efficient operation of market =
institute higher prices and limits capacity utilisation when compared to
more competitive market environment.
Demand function of the monopolist
The demand function of the monopolist is negative-sloping. The demand is still equal to AR = P
(AR = TR/Q = P.Q/Q = P) but not equal to MR (see table 4.15).
The relationship between marginal revenue, price, price and demand
At point B ed = 1 and for Q2 MR = 0. Thus for price levels higher than point B the ed > 1 and for
price levels lower than point B the ed < 1. The difference between price and marginal revenue
increases as ed decreases: MR = P[1-1/ed] = monopolist will only sell up to the point where the
elasticity of demand = 1. At price levels below point B MR is negative. Thus the monopolist will
not supply output greater than Q2 = Negative marginal revenue implies losses on additional sales.
Short-run equilibrium
If the monopolist applies the marginal rule (MR=MC at point A) it will produce Q 1 at a price of P1.
Total revenue is 0P1CQ1 and total cost is 0Q1BD. An economic profit of DP1CB will be realised.
Observe that MR is positive at this price & quantity.
Because there is no entry into the industry a monopolist should also generate economic profits in
the long run.
Comparison between monopolist and highly competitive situation
It is mostly argued that monopolies are not always in the interest of society. Remember that in
the following figure a monopolist is compared to a highly competitive industry and not an
individual firm (all the individual firms constitutes the total industry).
For the highly competitive industry price and output is determined by the intersection of the
demand and supply curves (MC), thus at point C P1 & Q1. For the monopolist MR = MC (point D),
thus P2 & Q2. It is clear that the monopolist charges the higher price and produces the lowest
output.
Efficiency of a monopolist
The perfect competitive solution: Pp/c & Qp/c (D=S). Thus consumer surplus = area aPp/cc and
producer surplus = area fPp/cce.
Monopolistic solution = Pmon & Qmon (MR=MC) = reduce consumer surplus but raise producer
surplus. Loss to consumer surplus = area Pp/cPmonbc (areas A + B). Gain area A but lose area C.
Thus gain in producer surplus is area A minus area C.
Conclusion: Total loss to society is areas B & C (neither consumers nor the producer gain these
two areas). = deadweight loss to society.
Sometimes argued that monopoly can improve welfare of society. 1) Monopoly can utilize
economies of scale with large-scale production, 2) Often in position to invest more in R&D and
utilize technological progress better, 3) Easier to obtain financing for development of new
innovative products, 4) Create better quality & design and 4) Can apply practice of price
discrimination in highly uncompetitive business environment.
Price discrimination (refer to example video in E-Book on page 162)
Market 1 = less price elastic (D1) and market 2 (D2) = more price sensitive. One MC curve for
monopolist and combined MR-curve = MR1+2. Equilibrium for monopolist (MC=MR1+2) = MCa &
Q1+2. Equate MCa to the individual MR-curves. Thus for market 1: P1 & Q1 and for market 2: P2 &
Q2. Conclusion = the more price sensitive market (market 2) pays the lower price while the less
price sensitive market 1 pays the higher price.
Monopolistic competition
Combination of competitive & monopolistic characteristics: i) unrestricted entry into market ii)
existence of product groups iii) product differentiation = each firm produces and sell own version
(brand names) of product = operating in a product group = in essence ‘small monopolies’ in their
own right = set their own price = constantly compete for market share = most instances based on
non-price competition variables (advertising, innovations, cost management, better packaging,
better distribution networks).
Can make economic profits in short run but only normal profits in the long run (due to free entry
& exit).
In previous figure MC = MR at point A, thus P1 & Q1. Economic profits = DP1CB. Given the free
entry characteristics new firms will enter with new innovations. Market shares of existing firms
decreases. Entry will end once economic profits are cleared in the industry. In the next figure LAC
is tangent to the demand curve at point C . Correspondent to LMC = MR (point A) and P1 & Q1.
Conclusion = firms only make normal profit in the long run.
Oligopoly
•
Small number of firms collectively control the majority of market share = level of
interdependence among firms = absolute size of firm not necessary a sign of oligopoly.
• Barriers to entry = important = aim is to limit entry of new competitors = consumer
preferences towards existing brands, cost advantages of existing firms, patent rights,
exclusive arrangements with suppliers, economies of scale.
• Homogeneous (pure) oligopoly = cement industry and differentiated oligopoly = motor
vehicle industry.
• Firms = powerful and temptation to collude on price and capacity = new firm must either
come in with lower prices and higher advertising costs = not sustainable.
• Exiting firms = compete on basis of non-price variables = tend to avoid price wars = adopt
price-leadership model in most cases = dominant firm sets price and allow other firms to sell
whatever they can at that price.
• Economic profits possible in both short and long run.
There is not one single universal theory that explains oligopoly formation exclusively. A number of
different theories are developed around oligopoly formation. Three models will be discussed
namely 1) rigid pricing (model of Sweezy), 2) dominant price-leadership model and 3) cartel
formation.
Rigid price model of Sweezy
Sweezy hypothesized that when an oligopolist lowers its price, other firms will follow suite but if
oligopolist were to raise price, competitors would probably keep price unchanged. Consequence
= kinked demand curve = one part that is relatively elastic in respect of price increases (DL) and
one part that is relatively inelastic to price increase (LD’). MR-curve = two parts RA & BR1. Thus
for all three MC-curves (MC1, MC2, MC3) equilibrium price & output will be P1 & Q1. Given these
circumstances, it would appear that prices in an oligopoly market situation could be rigid.
Dominant firm price-leadership model
Assumptions = 1) One firm dominates the industry and rest of market share belongs to a number
of small suppliers, 2) Dominant firm sets the price and allows smaller firms to sell what they can
at this price.
DD’ = total market demand; Ssmaller firms = supply of rest of firms at every price level; ARd = market
curve of dominant firm (DD’ minus Ssmaller firms); MCd &MRd = respectively marginal cost and
marginal revenue of dominant firm. Dominant firm maximises profit at P1&Q1 (MCd = MRd). Total
combined supply of the other firms is Q2. Total market thus Q3 (Q1 + Q2). Some of the other firms
might also make economic profits.
Cartel formation
Formal collusion takes places = attempt to manipulate output & price levels.
Fig c: Total demand for cartel & MCtotal = combined MC of the members. Price determined by the
cartel = P1 & total cartel output = Qe (MCtotal = MR).
Figures a & b: Members must sell at P1 and the qouta for each member = based on the equation
of the equilibrium MR1 to the individual MC-curves. Thus Qe = Q1 + Q2. The member with the
lowest cost structure (AC1) will make the highest profit.
Cartel formation seem to be characterised by instability. 1) Located in existence of different
marginal cost curves among members of cartel. Division of output not attainable in practice
because a political process is normally involved in negotiations. 2) Negotiating process can be
very slow and 4) Always temptation for individual members to increase their profits by either
openly leaving the cartel or secretly offering price concessions to certain buyers = thus incentive
to cheat.
Assume that cartel price is Po and that the member above decides to maximise its own position
(MC1 = MR) and sets a price of P1 and sells Q1. Thus revenue now much higher under the cartel
price.
Regulation of uncompetitive firm behaviour (competition legislation)
•
•
•
•
•
•
Competition act of 1998 = aim = promote higher levels of competition and minimum anticompetitive behaviour = i) defining public interest with respect to both competitiveness and
development ii)make SA economy more competitive iii) address socio-economic backlogs iv)
integrated with overall national policy framework iv) prohibiting anti-competitive conduct,
abuse of dominant market position v) administrated by an autonomous authority vi) enhance
reform of corporate structure with specific focus on consumer interest and BEE vii)
importance of property rights, greater economic efficiency, optimal allocation of resources.
Competition authorities = Competition commission & Competition tribunal = aims for
effective regulation and supervision of markets
Economy experiencing greater level of vertical re-bundling = big firms operating in various
sectors in order to control cost and competition in their supply chain = result = higher levels
of concentration in the economy and less competition = must prevent collusion and price
fixing.
Law prohibits anti-competitive agreements between businesses = firms must not agree to fix
prices or terms of trade, limit firms production in order to reduce competition, carve up
markets or customers, discriminate between customers.
Examples of abuse of dominant market position = unfair trading terms such as exclusivity,
excessive, predatory or discriminating pricing, refusal to supply or provide access to essential
facilities and practice of tying (stipulating that a buyer wishing to purchase one product must
also purchase all or some of his requirements for a second product).
Competition authorities evaluate impact of merger or acquisition before it can give
permission & cartel formation banned in SA = most serious form of anti-competitive
behaviour.
Pricing practices
•
Role of pricing infrastructure = NB = in order to set correct pricing points so that firms can
increase real sales revenue and profitability = pricing function of pivotal importance when
overall business strategy are determined = requires implementation of an effective set of
pricing metrics ( market and firm pricing data, market conditions, consumer data, profit
margins, financial data, operational cost & production data).
Optimal pricing
• Focussed on attainment of highest possible rate of return given the average pricing points in
market = pricing points can be lower, higher or the same than the average pricing points in
the market = aim not to chase market share but to attain highest profitability for the firm.
(See example on p. 173)
Revenue maximisation
• Aim = set price to capture maximum market share market share defined in terms of sales
volume = profitability secondary = apply concept of marginal revenue in order to establish a
maximum revenue pricing point = maximum sales revenue at price level where marginal
revenue = 0
(see example on p.173)
Pricing based on set profit margins
• Normally based on the mark-up principle = demand conditions not explicitly included in
determination of price = firms comfortable with their own estimation of sales volumes.
• Costs = important when pricing points are determined = firm must cover cost plus add set
margin on top of costs.
• Thus calculates average variable cost per sales unit & gross profit margin per sales unit
(average fixed cost + net profit margin. Increase in costs will result in higher pricing points.
(see the example on p. 174)