Chapter 8: Managing in Competitive, Monopolistic, and Monopolistically Competitive Markets In this chapter we characterize the optimal price, output and advertising decisions of managers under three market structures: (1) perfect competition; (2) monopoly; and (3) monopolistic competition. PERFECT COMPETITION The key five assumptions for perfect competition are: 1. There are many small buyers and sellers in the market. 2. Firms’ products are homogeneous (identical or perfect substitues). 3. Buyers and sellers have perfect information of output, price and quality. 4. There are no transaction costs (traveling costs from one store to another). 5. In the long run there is free entry and exit in and from the market. The first four assumptions imply that single sellers are too small to have a perceptible influence on the price. Each seller is a price taker and the price or inverse demand equation for the firm is a constant. The second assumption implies that the products are perfect substitutes because they are identical. Since in the 4 th assumption there are no transaction costs (e.g.: cost of traveling to a store), then if one firm charges a higher price consumers would not shop at that firm. Assumption (5) implies if the industry experiences a positive profit, new firms will enter the market and the market price drops and the economic profit shrink until it becomes zero (profit pays the opportunity costs for the owner). Similarly, if there are sustaining losses in the market firms are free to leave and price would move up, losses shrink and the firms earn zero profit. This implies 1
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Chapter 8: Managing in Competitive, Monopolistic, and MonopolisticallyCompetitive Markets
In this chapter we characterize the optimal price, output and advertising decisions of managers under three market structures: (1) perfect competition; (2) monopoly; and (3) monopolistic competition.
PERFECT COMPETITION
The key five assumptions for perfect competition are:1. There are many small buyers and sellers in the market.2. Firms’ products are homogeneous (identical or perfect substitues).3. Buyers and sellers have perfect information of output, price and quality.4. There are no transaction costs (traveling costs from one store to another).5. In the long run there is free entry and exit in and from the market.
The first four assumptions imply that single sellers are too small to have a perceptible influence on the price. Each seller is a price taker and the price or inverse demand equation for the firm is a constant. The second assumption implies that the products are perfect substitutes because they are identical.Since in the 4th assumption there are no transaction costs (e.g.: cost of traveling to a store), then if one firm charges a higher price consumers would not shop at that firm. Assumption (5) implies if the industry experiences a positive profit, new firms will enter the market and the market price drops and the economic profit shrink until it becomes zero (profit pays the opportunity costs for the owner). Similarly, if there are sustaining losses in the market firms are free to leave and price would move up, losses shrink and the firms earn zero profit. This implies that in the long run the perfectively competitive firm earns zero or normal economic profit.
An example of perfect competition that fits the five assumptions above is agriculture (e.g.: corn, wheat, pork, beef, etc.). Another example is the catfish farm industry in the US. There are 2,000 small catfish farmers in the US. Another example is the T-shirt retailers in the US.
Demand at the Market and Firm Levels
The (output and demand) for the firm and the industry are represented by (Q, Df ) and
(Qm, D), respectively, as shown below:
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Market (industry) demand for corn shows how much corn all consumers will buy at each
possible price in the market. Market demand (for corn) is downward sloping because
consumers as a group buy more (corn) at each lower price.
The individual firm sells additional corn at the same price (i.e., it is a price taker and the
price is constant or the firm’s demand curve is a horizontal line).
Short run output decisions: (One decision)
To maximize profit in the short run, the manager must take fixed costs as given and use
the market price and variable cost to determine the optimal output level. (Q*). Perfect
competition is the easiest market structure for mangers to make decisions. They only
have to determine the optimal output level Q*, given the market-determined price.
Maximizing Profit in the Short-Run
This leads to determining the profit-maximizing output Q*. The plant size (K) is fixed and there is a fixed cost because this is the short run.
Let R be total revenue which is defined by P*Q where P is constant. Then profit is
Profit = R – TC (where TC = VC + FC) or
π = R – TC = total profit
The marginal profit per additional unit of output is:
∆π / ∆Q = (∆R/∆Q) – (∆TC/∆Q) = MR – MC
If MR > MC then firm should increase output (Q↑)
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(Typical FIRM) (Corn INDUSTRY)Q Qm
D
S
PP
Horizontal line
$4$4Df
If MR < MC then firm should decrease output (Q↓)
If MR = MC then there is no change in Q. This output is called equilibrium output (or
the profit-maximizing output) and will be referred to by Q*. This rule MR = MC is
called the first profit-maximizing rule (output choice Q*).
We can examine profit maximization under perfect competition using two approaches: the total approach and the marginal approach.
The total approachAs noted above, total profit is given byп = total revenues – total cost = P*Q – C(Q).
Fig 8-2 Revenue, Costs, and Profits for a Perfectly Competitive Firm
In Fig. 8-2, total revenue under perfect competition is a straight line originating from the
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origin because the price is constant (R= P-*Q). The cost function is generally a cubic
equation. In this figure, the profit or loss at any output level is the vertical difference
between sales revenues(R) and the cost function (C(Q)). The maximum vertical difference
or maximum profit is located where the slope of the cost function equals to the slope of
the total revenue or MR = MC (or slope of TR = Slope of C(Q)).
This profit maximization rule (output choice) determines the firm’s equilibrium level Q*
that maximizes profit. This is the 1st profit-maximization rule.
Under perfect competition, it can be rewritten as P = MC because total Revenue is linear.
That is, ∆R / ∆Q = ∆(P*Q)/ ∆Q = P*∆Q/ ∆Q = P.
The Marginal Approach
An alternative approach to the total approach is the marginal approach as depicted by
Fig. 8-3. This approach applies the same 1st profit maximization rule but also uses the
average and marginal costs instead of the total cost because in the short run part of the
cost is fixed and that does not influence optimal decisions. Under this approach we will
look at three cases of profit maximization.
Case 1: Firm earning a positive profit in S/R.
First draw the two average cost curves and the MC curve going through the minimums of
the averages. Then determine output Q* where MR = MC o
Fig. 8-3: Profit Maximization under Perfect Competition
S/R Profit Maximization Rule:
4
MC
Pe = AR
ATCAVC
d-Curve
AT*C
Pe
P
qQ*0
A
B
MC = MR but as mentioned before because MR = P then this rule can be rewritten as
MC = P
Pe A
π = rectangle =
ATC* B
This rectangle gives the maximum (total) profit. It is given by its base (Q*) times the
height [Pe –ATC*] which is the profit per unit, where ATC* = TC / Q* or C (Q*) / Q*.
That is, this profit area equals to
Q*[Pe - {(C (Q*) / Q*}] = Pe *Q* - C(Q*)= total revenue – total cost
Note again that [Pe – ATC] is the profit per unit of output.
TR = Pe A
0 Q* TC = ATC* B
0 Q*
Example 1: A watch-making firm. Suppose:
TC = 100 + Q2 → MC = ∆TC / ∆Q =0 + 2Q2-1 = 0 + 2Q = 2Q (MC is a straight line
starting from the origin). FC = $100 and VC = Q2 and AVC = Q2/Q = Q (AVC is also a
straight line but with a lower slope than MC). Note ATC = 100/Q + Q2/Q = 100/Q + Q
Pe = $60 (the firm is a price-taker working under perfect competition)
The General Case for Profit Maximization: The Marginal Approach
Here we skip the total approach for profit maximization to concentrate on the marginal
approach.
As mentioned above, for monopoly one sets
MR = MC
and solves for Qm.
Then it substitutes Qm into the inverse demand equation to solve for Pm.
In the graph below, total profit is: Output* unit profit
Profit = Qm *(Pm – ATCm)
where (Pm – ATCm ) = unit profit, or
Profit = TR – TC = Pm*Qm -TC
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Fig 8-15: Profit Maximization under Monopoly
Absence of Supply Curve under Monopoly
Monopoly does not have a supply curve because this curve is usually derived from
equilibrium points formed by equating P and MC. Under monopoly, equilibrium is
determined from having MR = MC and P > MR.
Monopolistic Competition
Examples: fast-food, toothpaste (see handout), soap, shampoo, cold medicine, etc.
Characteristics:
Monopolistic competition has three key characteristics:
1) Each firm competes by selling differentiated products. The differentiated products
are highly substitutable but are not perfect substitutes like under perfect
competition (i.e. the cross price elasticity of demand between the products of the
firms is positive and high but not infinite). Crest is different from Colgate, Aim,
and Close-up… etc. Therefore, because of differentiation there is consumer
loyalty on part of some consumers. Consumers are willing to pay 25¢ to 50¢
more (but may be not a 1$). Therefore, Proctor & Gamble has some but limited
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monopoly power. However, some of the customers may move to the substitutes.
Therefore, advertising is important under monopolistic competition.
2) The demand curve is downward sloping but is fairly price elastic. The demand
elasticity for crest is –7. Thus, because of its limited monopoly power, P&G
charges a price that is higher than marginal cost but not much higher.
3) There is free entry and exit. It’s easier and cheaper to introduce, new brands of
toothpaste than to start new models of cars. The latter requires large capital and
technology to realize economies of scale. The free entry and exit implies that
economic profit under monopolistic competition is zero (normal).
Equilibrium in the short run and the long run: Like in monopoly, firms under
monopolistic competition have monopoly power and, thus, they face a downward
sloping demand curve. Therefore, MR < P. The profit maximization rule is
MR = MC.
In the short run the firm can earn a positive economic profit as shown in Fig. 8-18.
Fig. 8-18: Profit Maximization under Monopolistic Competition
If there is a positive profit, there will be an entry into this market and prices should
drop. This will shift both demand and MR curves of the individual firm down, and
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Profit $
DSR
MR = MC
MRQ*SR
P*
ATC*
ATCMC
profit will shrink until it becomes zero ( TR= TC or P = ATC) as shown by the
tangency between the new inverse demand P and ATC curve (Fig. 8-19).
Fig. 8-19: Effect of Entry on Monopolistically Competitive Firm’s Demand
Like in perfect competition, because of free entry and exit firms under monopolistic
competition earn zero economic profit in the L/R. The point where MR=MC should
correspond to the point where the demand curve is tangent to the ATC curve to realize
zero profit.
The Long run
The positive profit will induce entry by other firms who introduce competing brands.
The incumbent firm will lose some market share and the demand curve will shift
down. ATC and MC may also shift when more firms enter the market. Assume no
shift in those cost curves. The DLR will shift down until it becomes tangent to the long
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run AC corresponding to where MR=MC. In this case the profit is zero. We have two
rules for the long run under monopolistic competition:
1. MR = MC (The 1st profit-max rule)
2. P = ATC > min ATC zero profit (because R = TC). See fig.8-20. This
condition is different from the long run condition for perfect competition P = min
ATC.
Fig. 8-20: Long-Run Equilibrium under Monopolistic Competition
Implication of Product Differentiation: Advertising
As mentioned above, monopolistically competitive firms differentiate their products in
order to have some control over the price. In this case, the products are not perfect
substitutes, and this makes the demand less than perfectly elastic. The implication of this
is that some consumer won’t switch when the prices go up within a limit, while others are
willing to switch. To keep the other consumers from switching to the substitutes, firms
under monopolistic competition spend a lot of money on advertising. There are two kinds
of advertising under monopolistic competition.
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ACLR = P*LR
Q*LR MRLR
DLR
ACMC
1) Comparative Advertising: This involves campaigns designed to differentiate a given
firm’s brand from brands sold by competing firms. Comparative advertising is common
in the fast–food industry, where firms such as McDonalds attempt to simulate demand for
their hamburgers by differentiating them from competing brands. This may induce
consumers to pay a premium for a particular brand. This additional value for a brand in
the price is called brand equity.
2) Niche Marketing: Firms under monopolistic competition frequently introduce new
products. The products could be totally “new” or “new improved”. Firms can also
advertise a product that fills special needs in the market. This advertising strategy targets
a special group of consumers. For example “green marketing” advertise “environmentally
friendly” products to target the segment of the society that is concerned with the
environment. The firm packages a product with materials that are recyclable.
These advertising strategies can bring positive profits in the short–run. In the long–run
other firms will mimic their strategy and reduce profits to zero.
Optimal Advertising Decisions
Optimal advertising is determined by the following formula
Formula: The profit maximizing advertising-to-sales ratio.
A/R = [(EQ, A) / - (EQ, P)] > 0,
where A is expenditure on advertising and R is sales revenue. Note: A/R is a positive
fraction because (EQ, P) is already negative and multiplied by a minus).
EQ, A = %ΔQ / %ΔA = (ΔQ / ΔA)*(A/Q)
is advertising elasticity of demand, and
EQ, P = %ΔQ / %ΔP = (ΔQ / ΔP)*(P / Q),
is the own–price direct elasticity of demand, which is negative.
If EQ, P = - ∞ (demand is perfectly price elastic under perfect competition), then
A/R = 0. That is, the optimal advertising-to-sales ratio is zero for the perfectly
competitive firm.
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The more elastic the demand with respect to own price (i.e., products are less
differentiated and more substitutable), the lower the optimal advertising-to-sales
ratio. This is a case of more competition than less, and there is not much need for
advertising.
The more elastic the demand with respect to advertising, the higher the optimal
advertising- to-sales ratio.
Demonstration 8-8
Suppose Corpus Industries operates under monopolistic competition and produces a
product at a constant MC. Suppose the demand for its product is estimated with a log
linear equation and the elasticities are:
EQ, P = - 1 (price elasticity of demand)
EQ, A = + 0.2 (advertising elasticity of demand)
To maximize revenue what portions of revenue should this firm spend on advertising?
Answer:
A/R = EQ, A / - EQ, P = [+0.2 / - (-1.0)] = (+0.2 / +1.0) = 0.2 = +20% of total sales.
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Chapter 9: Basic Oligopoly Models
This chapter discusses managers’ decisions under five different oligopolistic
market structures: Sweezy, Cournot, Stackelberg, Bertrand and Collusion. Comparison of
the outcomes in these different oligopolistic situations reveals the following. The highest
market output is produced under Bertrand oligopoly, followed by Stackelberg, then
Cournot, and finally collusion. Profits are highest for the Stackelberg leader and the
colluding firms, followed by Cournot, then the Stackelberg follower. Bertrand
oligopolists earn the lowest level of profits.
CONDITIONS FOR OLIGOPOLY
Examples of Oligopoly: Steel industry, airline industry and auto industry.
An Oligopoly is a market structure where there are few large firms in an industry. No
explicit number is required. However, the number is usually between two and ten firms.
If there are two firms, then the market structure is called duopoly. The product under
oligopoly can be homogeneous (steel) or differentiated (airlines travel). The manager has
a more difficult job in making decisions under oligopoly than under other market
structures. Under oligopoly there is firm rivalry and interdependence in decision making.
A manager, before it lowers the price of its product, it should consider the impact of the
lower price on the other firms in the industry.
THE ROLE OF BELIEFS AND STRATEGIC INTERACTIONS
The optimal decision whether to increase or decrease the price depends on how
the manager believes other managers in the industry will respond. If other managers
lower the price in reaction to this firm’s lowering the price, this firm will not increase its
sales much. In Figure 9.1, the reference point is B where the price is Po. The demand
curve D1 is the demand when other firms match any price change. If the manager of a
certain firm lowers his/her price, and the other firms in the market match this price
decrease, then the quantity will not increase much as given by D1. But if they don’t match
the price decrease then the manager can sell more as given by D2. Thus, the match D1 is
more inelastic than the no-match D2 , or D2 is more elastic than D1.
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If the manager increases the price and the other firms match, the firm’s sales will not
decline much. So the matching demand curve will be D1 .But if they do not match the
price increase, the firm will lose some market share and its demand will be the non-
matching D2. The only difficulty for the firm manager to make decisions is determining
whether or not rivals will match price changes.
Demonstration 9-2 (The kink Demand):
Thus if, for example, other firms match price reductions (D1) and do not match price
increases (D2) then the oligopoly effective demand is kinked as given by ABD1 as in Fig.
9-1. This assumption gives rise to what is known as the kinked demand curve ABD1.
Fig 9-1: A Firm’s Demand Depends on Actions of Rivals
Then the kinked demand is given by the two segments defined by A, B and D1.
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PROFIT MAXIMIZATION FOR OLIGOPOLY SETTINGS:
We will examine profit maximization under four alternative assumptions on how rivals
respond to price or output changes.
Sweezy Oligopoly:
An industry is characterized as Sweezy oligopoly if
1. There are few firms serving many customers.
2. The firms produce differentiated products.
3. *Each firm believes that rivals will respond to price reductions (effective D1) but
will not respond to price increases (effective D2) (ABD1 is kinked demand as in
Demonstration 9-2). This assumption represents the kinked demand curve.
4. Barriers to entry exist.
In Fig. 9-2, the kinked demand curve that fits assumption 3 is given by ABD1. If the price
is below P0 then the demand is the match demand D1, while if the price is above P0, then
the demand is the no-match D2. The corresponding MR to the kinked demand is ACEF.
The Kinked Demand Curve
P0
Price
Q0
B
Q
No Match
Match
D1
D2
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Fig 9-2: Sweezy Oligopoly
Profit maximization occurs when MR = MC. Let us for simplicity assume that MC is
linear (or straight line). If marginal cost is MC1 then profit maximization occurs at point
E and the price is P0. If MC is MC0 the profit maximization occurs at point C and the price
is P0. Note that if MC moves between points E and C (called the MR gap) there will be no
change in the equilibrium price P0. This model is good in explaining that firms avoid
price wars and thus prefer price stability by keeping the price at P0 even if MC changes
(however, within a limited range). This model is criticized for not explaining how the
firm arrived at point B in the first place. Nevertheless, the Sweezy model shows that
strategic interactions among firms in terms of prices and the managers’ beliefs on how
other firms would react to their price increases and decreases has a profound effect on
pricing decisions.
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The kinked demand is given by ABC and beyond as shown above. The corresponding gapped MR curve is depicted below. If the MC curve passes through the MR gap, modest shifts, upward or downward, in this curve will not change the industry price or the firms output. The Figure below (the cost cushion) shows the shifts in the MC1 curve to the MC2
and MC3 curves without a change in output or price (price stability). Recall, the 1st profit maximization rule requires thatMR = MC q* p*
Example: if the Match D1 is given by P1 = 15 – 2.5Q1 and the no match D2 is given by P2 = 10 –
0.5Q2, how do you determine the current or reference Q0 and P0 at point A of the Kink? Can you derive
MR1 and MR2? Can you calculate the MR gap ?
Answer: Set D1 = D2 and solve for the current or reference Q0 (=2.5) and P0 (=$8.75). Then substitute
Q0 in the respective marginal revenues (MR1 = 15 – 2*2.5Q1 (=$2.5?) and MR2 = 10 – 2*0.5Q2 (=$7.5)
to calculate the MR gap. Recall, the slope of the MR equation is twice the slope of the inverse demand
equation. To find MC in the gap and profit maximization point, substitute Q0 into the MC equation.
Cournot Oligopoly
An industry is a Cournot oligopoly if
1. There are few firms serving many customers.
2. The products are either differentiated (e.g. automobile) or homogenous (steel).
3. *Each firm believes that rivals will hold their outputs constant if it changes its
own output (naïve belief). Note that decision variables are outputs and not prices.
4. Barriers to entry exist.
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Thus, in contrast to Sweezy oligopoly which uses prices, the firm under Cournot
oligopoly believes that its output decisions have no effect on rivals output.
Reaction Functions in Cournot Oligopoly
To make matters easier suppose there are two firms. In this case, the market structure is a
duopoly. To determine the optimal output level, firm 1 will equate its MR1 to its MC1, and
firm 2 equate MR2to its MC2. The MR1 and MR2 equations are derived from the inverse
market demand equation.
P = a – b(Q1 + Q2)= a – bQ1 -b Q2 (note: output is homogenous there is one
P)
MR1 is derived by multiplying the slope b of Q1 by 2.
MR1 = a – 2*bQ1 - b Q2
Firm 1’s marginal revenue MR1 is affected by firm 2’s output (Q2), as well as by its own
Q1. The greater firm 2’s output, the lower is the marginal revenue of firm 1. In this case,
firm 1’s profit-maximizing output depends on firm 2’s output level Q2 and its Q1. Set MR1
= MC1 and solve for Q1 as a function of Q2. This relationship between firm 1’s profit-
maximization output Q1 and firm 2’s output Q2 is called a reaction function of firm 1.
The same applies to firm 2 setting MR2 = MC2 where
MR2= a – bQ1 – 2*b Q2
and deriving its reaction function which specifies Q2 as a function of Q1.
Therefore, a reaction function for firm 1 is its profit-maximizing output (Q1) as a function
of firm 2’s output (Q2). That is,
Q1 = r1(Q2),
where r1 is a “reaction function of”.
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Similarly, the reaction function of firm 2 is its profit- maximizing output as a function of
firm 1’s output. That is,
Q2 = r2(Q1).
Graphically, the reaction functions for a duopoly are given in Fig 9.3 where firm
1’s output is measured on the horizontal axis and firm 2’s output on the vertical axis.
Q1 = r1(Q2), and Q2 = r2(Q1).
Fig 9.3: Cournot Reaction Functions and Adjusting to Equilibrium
If firm 2 produces a zero output, then firm 1 is a monopoly and its profit- maximizing or
optimal output is Q1M. The greater firm 2’s output in Firm 1’ reaction function is, the
lower firm 1’s profit-maximizing output. For example, if the firm 2’s output is Q*2 then
the profit-maximizing output for firm 1 is Q*1.
Similarly, if firm 1’s output is zero, then firm 2 is a monopoly and its profit-
maximizing output is Q2M. Firm 2’s profit maximizing-output will go down if firm 1’s
output in firm 2’s reaction function increases. What is the firm 2’s profit maximizing
output when firm 1’s output is Q*1? It is Q*2.
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Equilibrium in Cournot Oligopoly
Graphically, we will describe how the duopoly reaches the equilibrium point (E)
based on movements along the two reaction functions. Suppose firm 1 produces Q1M.
Inserting this output into firm 2’s reaction function (by assumption 3), then this firm’s
profit-maximizing output corresponds to point A on the r2 reaction function.
On the other hand, given the positive output for firm 2 in the reaction function of
firm 1, then firm 1’s profit maximizing-output will correspond to point B. Given firm 1’s
output corresponding to point B in firm 2’s reaction function, then firm 2’s profit-
maximizing output will correspond to point C. Given this output in firm1’s reaction
function, firm 1’s output corresponds to point D. Then this will continue until it leads to
point E. where the two reaction functions intersect.
Therefore, equilibrium in Cournot oligopoly is determined by the intersection of the two
reaction functions which determine Q*1 and Q*2.
Formula: Marginal Revenues for Cournot Duopoly
Suppose for a Cournot duopoly with a homogenous product, inverse demand function is
P = a – b(Q1 + Q2)
(we sum up the two outputs because the product is assumed to be homogeneous).
Since the slope of MR is twice that of price then
MR1 = a – bQ2 – 2bQ1 (only slope of Q1 is doubled)
and
MR2 = a – bQ1 – 2bQ2 (only slope of Q1 is doubled)
Marginal products depend on own and the other firm’s outputs.
Formula: Reaction Functions for Cournot Duopoly
Suppose the inverse demand function is linear
P = a – b(Q1 + Q2),
and the cost functions with no fixed costs are
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C1(Q1) = c1*Q1 (the cost function is linear starting from the origin and c1 is MC1)
C2(Q2) = c2*Q2 (where c2 is MC2)
To derive the reaction function for firm 1, set MR1 = MC1 and solve for Q1 as a function
of Q2.
a – bQ2 – 2bQ1 = c1 (divide both sides by 2b and solve for Q1), we have
a/2b – 1/2Q2 – c1/2b = Q1.(combine the two constant terms a/2b and – c1/2b)
Q1 = r1(Q2) = (a - c1) / 2b – 1/2Q2 [please remember this formula]
Similarly for the reaction function of firm 2, set and solve for Q2 as a function of Q1.
MR2 = MC2.
a – bQ1 – 2bQ2 = c2 (divide both sides by 2b and solve for Q2)
Q2 = r2 (Q1) = (a - c2) / 2b – 1/2Q1 [please remember this formula]
To find the Cournot equilibrium (Q1*, Q2*) for this duopoly, substitute Q2 into the
reaction function Q1 = r2(Q2) and solve for Q*1. Then substitute Q*1 into Q2 = r2(Q1) and
solve for Q*2. The Cournot equilibrium is (Q1*, Q2*).
SEE THE SOLVER TEMPLATE FOR THE SOLUTION OF LINEAR Cournot case on
the website.
Demonstration 9-4. (Remember in this example c2 = 0 and c1 =0)
Suppose:
The inverse market demand function is:
P = 10 – Q1 – Q2 where a =10 and b =1.
The firms’ cost functions are:
C1(Q1) = 0 where C1(Q1) is total cost and MC1 is assumed to be c1 =0
C2(Q2) = 0 where c2 = 0. Same as above
The long way for both firms:
Then derive the two marginal revenues
MR1 = 10 – Q2 - 2Q1 (twice the slope of inverse demand for Q1)
MR2 = 10 – Q1 - 2Q2 ((twice the slope of inverse demand for Q2)
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Long way for Firm 1
Next for firm 1, set
MR1 = MC1
10 – Q2 - 2Q1 = c1
10 – Q2 - 2Q1 = 0
(MC1 or c1 is assumed to be zero in this example. Please keep in mind that c1 = 0 is a
special case) and then solve for Q1 = r1(Q2) which implies that Q1 = (10-0)/)– 0.5Q2
(Remember: Firm 1’s reaction function which is Q1 = [(a - c1) / 2b – 1/2Q2 ].
The Formula way for Firm 1: use the above formula and P = 10 – Q1 – Q2 where
a =10 and b =1. Here c1 is assumed to be zero.
Q1 = (a - c1)/2b – 0.5Q2 = (10 - 0)/2 – 0.5Q2 = (10/2) – 1/2Q2 , where a=10, b = 1 and c1 =
0.
Long way for Firm 2.
Similarly, for firm 2 set MR2 = MC2 (the long way)
10 – Q1 - 2Q2 = c2
10 – Q1 - 2Q2 = 0 where c2 = 0
and divide both side by 2 and then solve for Q2 = r2(Q1):
Since $20 < $100 the firm has no incentive to cheat (that is the solution is collusion).
The incentives for firm B are the same. Thus, firms can collude by using this type of
trigger strategy which involves punishing the cheating firm by charging a lower
price until the game ends.
Repeated Games with a Known Final Period: The End-of-Period Problem
Suppose a game is repeated some known number of times with strategies and payoffs as
supposed in Table 10-12.
Table 10-12: A pricing Game
Firm
A
Firm B
Price Low High
Low 0,0 50,-40
High -40,50 10,10
Let us assume for simplicity the game is repeated twice (two one-shot games) and the
players know the game will end in period two. This means after the game is played twice
there is no tomorrow (at the end of the second period). At that time there are no trigger
strategies and no punishments even if player A cheats. The two-shot game is really played
as a one-shot game twice. Player A kept charging the high price. In this case since there is
no tomorrow. Player A can charge a low price in the second period and player B cannot
punish him/her. In fact player A would be happy if player B continues charging the high
price in the second. In this case player A if charges the low price it will earn 50. But
player B knows that player A will charge the low price and thus B will do likewise. This
means this two-shot game will end in the first period and will not go to the second or end
period in this example. Nash equilibrium in this two-shot game is to charge low price in
each period. The game is played as two one-shot games and each player will earn zero
profit in each of the two periods.
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In that collusion will not work even if the game is played three, four, 1000 times. This
type of “backward unraveling” continues until the players realize no effective punishment
can be used during any period. The key reason is that each player knows that promises of
cooperation will be broken any time because the period has an end and then there is no
tomorrow. So the solution is low prices with zero profits.
Demonstration 10-8
Suppose firms A and B will play the game in Table 10-12 twice. Assume that firm A’s
strategy is to charge high price each period provided that firm B (the opponent never
charged a low price in any previous period. Assume interest rate = 0.
1. How much will firm B earn?
2. How much firm A earn.
Answer: Since firm A will also charge a high price each period, the opponent firm B will
be able to trick firm A in the second period because in this period the game will end.
Firm A will stick to its strategy for the first and second periods because it will not
discover B’s cheating until the second period, and at that time it will be too late to punish
firm B. Then firm B will charge a high price in the first period and earn 10 and charge a
low price and earn 50 in the second period for a total of 60 (this is better than cooperating
and charging higher price in each period for a total profit of 10 + 10 in the two periods).
Correspondingly, Firm A will earn 10 in the first period and make a loss of 40 in the
second period, for a total loss of 30 in the two periods. Since each player knows when the
game will end and trigger strategies will not enhance profits.
Applications of the End-of-Period Problem
End of period problem arises when workers know precisely when a repeated game will
end. In the final period, there is no tomorrow and there is no way to punish a player for
doing something wrong in the last period. Here is an implication of the end-of-period
problem for managerial decisions.
Resignations and Quits
Workers weigh the benefits from shirking with the cost of being fired. If the benefits are
less than the costs, workers will find it in their interest to work hard. If the worker
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announces today that he/she will quit tomorrow than there is no reason for the worker to
work hard because the threat of being (the trigger strategy) fired has no bite.
What can the manager do to overcome the end-of-period problem? He can fire the
worker today but legally this may not be feasible. Moreover, there is a more fundamental
reason why the manger should not adopt this policy. To avoid being fired on
announcement, workers will not announce their plans of quitting until the end of the day
and in this case they get to work longer than if they announce their plans. Consequently,
the manager will not solve the end-of-period problem but instead he/she will be
continuously be surprised by worker resignations.
A good strategy is to give the workers some rewards for good work that extend
beyond the termination of employment with the firm. In this case the worker will not take
advantage of the end-of-period problem. But if the worker takes advantage of the end-of-
the period problem the manager, being well connected, can punish the worker by
informing potential employers about it.
Multistage Games
These games differ from the class of simultaneous games one-shot infinitely
repeated games in the sense that timing is very important for multistage games. In
particular, multistage games permit players to make sequential rather than simultaneous
decisions.
Theory
In order to understand how multistage games differ from one shot and infinitely
repeated games. We need to introduce the extensive form of a game. An extensive- form
game summarizes who these players are, the information sets available to those players at
each stage, the strategies available to the players, the order of moves and the payoffd
from the alternative strategies.
Fig. 10-1 depicts the extensive form of a game assume that there are two players:
A and B; and that player A is the first mover and player B is the second mover. Each
player has two strategies: Up and Down. The numbers at the end of branches in this
figure are the players payoffs since player A is the first mover the first number is that
players payoff and the second number is player B’s payoff.
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(Fig. 10)
(0, 0)
(6, 20)
(5, 5)
(10, 15)
A
B
B
Down
Down
Down
Up
Up
Up
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In Fig. 10-1, player A moves first, and once this player moves, it’s player B’s
turn. If player A chooses Up and player B makes the same Up move, then the payoff for
A and B, respectively, are (10,15). But if player B moves in the other direction and
chooses the Down strategy then their respective payoffs are (5, 5). As in simultaneous-
move games, each player’s payoff depends on both player’s actions. This is the similarity
between these types of games. For example, if the first move of player A is Down and
player B chooses Up then player A’s payoff is (0), but if B chooses Down player A’s
payoff is (6). There is important difference between the sequential and simultaneous
types of games. Since player A is the first mover in this case, this player cannot make
decisions based on player B’s moves, but player B gets to make decision after player A.
Thus, there is no conditional “if” in player A’s strategy.
Let’s see how strategies work in this game. Suppose the strategies are: player B
chooses Down if player A chooses Down. What is the best strategy for A? The best
strategy for A is Down because in this case A will make 6, which is better than 5. Given
that player A chooses Down, does player B have an incentive to change his strategy? The
answer is NO. Choosing Down instead of Up, B earns 20 instead of 0. Since neither
player has an incentive to change his/her strategies then there is a Nash equilibrium
associated with those strategies.
Player A: Down;
Player B: Down if player A chooses Up, and Down if player A chooses Down. (player B
threatens to play Down all the time).
The payoff: (6, 20)
Is this a reasonable game? Why doesn’t A choose Up and make 10 instead of choosing Down and making 6? The answer is in the way B’s strategy is formulated. If A chooses Up, B threatens to choose Down all the time. In this case A will make 5 instead of 6. Should A believe B’s threats? If B chooses Down it will make 5. What to make out of all this? There are two Nash equilibria in this game.
Nash Equilibrium: As explained above when B threatens to play Down all the time.Nash Equilibrium: When A finds that B’s threats are not credible.
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Player A: UpPlayer B: Up if player A chooses Up and Down if player A chooses Down.
Player B will have to chooses Up if A chooses Up. In this case, the neither player has an incentive to change his/her mind. The second Nash equilibrium is more reasonable because B’s threats are not credible in the sense that A can choose Up and this will force B to choose Up and NOT Down because it will have a lower payoff (5 instead of 15) if it follows upon its threat to choose Down.
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Chapter 11
Pricing Strategies for Firms with Market Power
In this chapter we deal with pricing strategies of firms that have some market
power: firms in monopoly, oligopoly and monopolistic competition. As we learned in
chapter 8, firms in perfect competition are price takers and they don’t have a pricing
strategy of their own. This chapter goes as far as providing practical advice on
implementing pricing strategies for those firms with market power, typically using
information that is readily available to managers, including publicly available
information such as the price elasticity of demand.
The optimal pricing strategies for firms with market power vary depending on the
underlying market structure and the instruments (e.g., advertising) available. To account
for that, this chapter presents more sophisticated pricing strategies that enable a manger
to extract greater profits from the consumers.
BASIC PRICING STRATEGIES
We will first look at the very basic pricing strategy which relies on single or
uniform pricing. This strategy uses the profit-maximizing rule: MR=MC to derive the
optimal price. This rule is then mathematically manipulated to provide a rule of thumb
that makes use of the markup to arrive at the price.
Review of the Basic Rule of Profit Maximization
Firms with market power can restrict output to charge a higher price; thus they
have a downward-sloping demand curve. In this case the price is different from marginal
revenue. The profit-maximizing rule for firms with market power is given by
MR = MC.
This rule is first solved for the equilibrium output which in turn is substituted in the
inverse demand equation to solve for the optimal or equilibrium price as was illustrated in
chapter 8. Managers of large firms may have research department that have economists
who can estimate demand and cost functions and apply this rule and to solve for optimal
price and output
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Demonstration 11-1
Suppose the inverse demand equation is given by
P = 10 -2Q (downward sloping demand = market power)
and the cost function is
C(Q) = 2Q.
Determine the profit-maximizing output and price.
Answer: Recall MR has twice the slope of the price in this case.
Then
MR =10 – 4Q.
Set MR = MC
10-4Q* = 2
Solve for Q*. Then Q* = 2 units. Plug Q* into the inverse demand equation
P* = 10 -2Q* = $6.
A Simple Pricing Rule for Monopoly and Monopolistic Competition
Some small firms such as retail clothing stores do not hire economists to estimate
their demand and cost functions. They can, however, rely on publicly available
information such as information on price elasticity of demand (see chapter 7 for estimates
of price elasticity for different industries). We can derive a rule of thumb from the profit-
maximization rule and estimate the price with minimal or crude information and still be
consistent with profit-maximization.
Formula: Marginal Revenue for a firm with Market Power (Monopoly and Monopolistic
Competition):
MR = P[(1+Ef)/Ef] where Ef = %∆Q/%∆p = (∆Q/∆P)*P/Q
where Ef is the firm’s own direct price elasticity of demand. Substitute this in the profit-
maximization rule
P[(1+Ef)/Ef] = MC
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Solve for the price:
P = [Ef /(1+Ef)]MC
or
P = (K)MC
where K = Ef /(1+Ef) can be viewed as the profit maximization (optimal factor)
markup factor.
Example: The clothing store’s best estimate of elasticity is -4.1 and this is known. Thus,
the optimal markup is
K = -4.1/(1- 4.1) = 1.32.
Then the optimal price
P = (K)MC = 1.32*MC
(That is, 1.32 times marginal cost).
The manger should note two things about this price elasticity: First, the more
elastic the price is, the lower the markup factor and the price (if Ef = -infinity, then K= 1
and P = MC as is the case in perfect competition); the lower MC is, lower the price.
Demonstration 11-2
Suppose the manger of a convenience store competes in a monopolistically
competitive market and buys Soda at a price of $1.25 per liter. Chapter 7 reports
that the price elasticity of demand for the typical grocery is -3.8. The manger of this
convenience store believes that demand is slightly more elastic than -3.8. Let the
price elasticity of the convenience store is -4. What is the profit maximizing price for
this store?
P = [-4/(1-4)]MC = 1.3 MC
A Simple Pricing Rule for Cournot Oligopoly
Strategic interaction is an important issue in Cournot oligopoly. Each firm
maximizes profit taking into account of the output of the rival firms in the industry. It
believes that the output of the rivals will stay constant. The maximization rule is the same
as in the monopoly case,
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MR = MC.
But under Cournot monopoly, MR depends on the firm’s output and on the rivals’ output
as well. Each oligopolistic firm uses this rule to derive its interaction functions in which
its own output depends on the rivals’ outputs. Then the interaction functions are used to
determine the profit-maximizing outputs (Q1*, Q2*)
Fortunately and similar to monopoly, a simple markup pricing rule can be used in
Cournot oligopoly when the oligopolistic firms have identical cost structures and
producing similar products. Suppose the industry consists of N firms with each firm
having identical cost structures and produces similar products. In this case we can use
the markup pricing rule for monopoly and monopolistic competition to derive a pricing
formula for a firm in a Cournot Oligopoly. First, it can be shown that if products are
similar then
Ef = N*EM
where Ef is the price elasticity of demand for the typical firm, EM is the industry’s price
elasticity of demand and N is the number of firms in the industry. Recall that the markup
pricing rule under monopoly and monopolistic competition is given by
P = [Ef /(1+Ef)]MC
where MC is the individual firm’s marginal cost. Upon substitution for Ef from above, the
profit maximizing price for a firm under Cournot is given by:
P = [NEM /(1+NEM)]*MC (rule of thumb pricing under Cournot)
Demonstration 11-3
Suppose a Cournot industry has three firms, with market elasticity Em equal -2 and the
individual firm’s MC is $50. What is the firm’s profit maximizing price under Cournot
oligopoly
P = {(3)(-2)/[1+(3)(-2)] }*$50 = $60
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STRATGIES THAT YIELD EVEN GREATER PROFITS
These are strategies that can be implemented under monopoly, monopolistic competition
and oligopoly by which the manager can earn a profit greater that it can get using the
single pricing rule (MR = MC) whether directly or through a pricing formula. These
strategies which include: price discrimination, two–part pricing, block pricing and
commodity bundling, are appropriate for firms with various cost structures and degrees of
market interdependence.
Extracting Surplus from Consumers
All the above four strategies aim at extracting consumer surplus and turn it into profit for
the producers.
I. Price Discrimination
Price discrimination is the practice of charging different prices to different consumers for
the same good or service sold. There are three types of discrimination; each requires that
the manager have different types of information about consumers.