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Woefully Imperfect Market Puzzle
Asif Shakur and Shekar ShettySalisbury University
Salisbury, Maryland, USA
Motivation and Objectives
We have uncovered abundant evidence of woefully imperfect markets
Semiconductor Integrated Circuit (IC) market is one example
Used Textbook Market is another example
Conventional economic models were found inadequate in these markets
Our objectives are to bridge the gap between conventional models and our model
A Familiar Conventional Model
Hotelling’s Model is one of the earliest known models
It can be invoked to explain away trivial instances of market imperfection
Price of a soda can is known to be exorbitant at airports compared to supermarkets
Customers are willing to pay for convenience and a cold can of soda!
Empirical Data Semiconductor MarketOperational Amplifier (741) Price /100 chipsVendor A Vendor B Vendor C Vendor D $18 $22 $49 $95 Semiconductor MarketTransistor (TIP 31C) Price /100 Vendor A Vendor B Vendor C Vendor D $29.30 $159 $69 $30
Empirical Data … continued!
Semiconductor MarketMemory (2114 RAM) Price / chipVendor A Vendor B Vendor C Vendor D $13.75 $1.69 $1.29 $2.58 Textbook Market (used)Electric Circuit Theory (Johnson) Price /single copyVendor A Vendor B Vendor C Vendor D $10 $30 $55 $100
Empirical Data … characteristics
These are undifferentiated products
Same transportation costs
Synopsis of Market Models
Monopoly Oligopoly Monopolistic Competition Competition
Maximize Profit MR = MC MR = MC MR = MC p = MR = MC
Price price setter price setter price setter price taker
Market Power p > MC p > MC p > MC p = MC
Entry No Entry Limited Entry Free Entry Free Entry
Conventional Model Characteristics
A monopoly does not care what the rival firm does … there are NO RIVALS!
A competitive firm does not care what the rivals do because it does not matter!
An oligopolistic firm seriously considers how its actions affect its rivals and how the actions of its rivals will affect it.
A monopolistically competitive firm seriously considers how its actions affect its rivals and how the actions of its rivals will
affect it.
These strategies (GAMES) lead to NASH EQUILIBRIA
Paradoxes of Imperfectly Competitive Markets
Under smooth dynamics, outputs may follow chaotic trajectories
Entry of a new firm in the market may actually decrease the total output and increase the equilibrium price
Entry of a new firm in the market may actually increase the equilibrium price
Entry of a new firm in the market may actually increase the profit of the incumbent firm
A merger of two or more firms can decrease the profits of all merged firms
The entry of a new firm in the market might decrease social welfare
Even if the entry of a firm would raise social welfare, this entry might not be profitable
Justification for a New Model Hotelling’s model is not viable because there is no product differentiation in our semiconductor and textbook markets
Similarly, Chamberlin/Robinson monopolistic competition is not viable because there is no product differentiation in our semiconductor and textbook markets
Is Cournot’s model a viable candidate?
Cournot Model
In the Cournot Model of non-cooperative oligopoly, the firms choose their output levels without colluding (no cartels!) but they make conjectures about the reactions of their rivals
in response to their actions
Monopoly, Duopoly, and Oligopoly!
In order to set the stage for Cournot’s oligopoly, let us review the structure of a monopoly
We posit a linear inverse demand function p(q) = a – bq
The revenue isR = pq
R = aq – bq2
Monopoly … continued!
The marginal revenue can be obtained as a partial derivative of R with respect to the output q.
MR = R/qMR = a – 2bq
In terms of elasticity ɛ
MR = p (1-1/ɛ)
Monopoly … pricing!
The cost curve C(q) = kq where k is a constant
The marginal cost MC = C/q = k
A monopoly sells where p = MC = MR so we have k = a – 2bq
Hence the output and price for a monopoly are
qm = (a-k)/2bpm = (a+k)/2
Cournot Oligopoly … pricing!
Without loss of generality, we posit a tractable linear demand curve
q = a- p
Total demand = q1 + q2 for two firms
In the Cournot model, each firm conjectures that the other firm will act in a way to keep the quantity that it sells fixed. We will calculate the reaction function of each firm to the quantity supplied by the other.
Cournot Oligopoly … profit maximization!
/q1 [(a - q1 - q2 )( q1 ) - k q1] = 0a - 2q1 - q2 - k = 0
So firm 1’s reaction function will be given as
q1* = (a - q2 - k) / 2
Following a symmetric procedure, firm 2’s
reaction function will be given asq2
* = (a – q1 - k) / 2
Cournot Equilibrium
A Cournot Equilibrium (C.E.), as in a Nash game (e.g. prisoner’s dilemma) occurs when neither firm wants to change and is content
with its output and profit. Imposing this criterion on q1
* and q2* yields
C.E. = (a – k) / 3
q1
q2
2
ka
ka
Isoprofit curves
COURNOT REACTION FUNCTION
Straight line is REACTION FUNCTION for firm 1 reacting to firm 2
ka
2
ka
3
ka
3
ka q1
q2
2
ka
ka
C.E.
R12
R21
R12 Reaction function of firm 1 reacting to firm 2
R21 Reaction function of firm 2 reacting to firm 1
COURNOT EQUILIBRIUM
Cournot Equilibrium … conclusion
At the Cournot equilibrium we have the following price / output equations:
q1 = q2 = (a – k) / 3
Q = 2 (a – k) / 3p = (a + 2k) / 3
Conclusion: Cournot equilibrium price is only
marginally higher than the perfectly competitive price and only marginally lower
than the monopoly price
In general, for n firms in a Cournot oligopoly
qn = (a – k) / (n + 1)
Woefully Imperfect!
The plethora of market models cannot explain the existence of glaring and woefully
widespread price differences that we have found in the semiconductor and other markets.
This puzzling observation clearly challenges the notions of efficient markets and rational and informed buyers and sellers populating
these markets.
Habit Persistence
We will attempt to explain this puzzle by invoking behavioral and habit persistence
hypotheses that appear to override the efficient markets and the rational and informed
participant hypotheses
The equity premium puzzle, a term coined by Mehra and Prescott (1985) is an analogous
puzzle, and has been reported previously for the stock market
Deep Habits
Ravn (2006) explores the concept of “Deep Habits” which are the offshoots of Behavioral
Science
Habit persistence is a preference specification that yields a utility function that
depends on the quasi-difference of consumption
Utility Function for Habit Persistence
Ravn (2006) explores the concept of “Deep Habits” which are the offshoots of Behavioral
Science
Let us specify the utility function without habit persistence as ∫[t]U(c[t]) where is the
subjective discount factor, c is the consumption in a very small time period t, U is the utility
function and the integration is performed from 0 to . Then the utility function with habit
persistence is hypothesized to be ∫[t]U(c[t] - c[t-1]) where the parameter denotes the
intensity of habit persistence.
“Bounded Rationality” & Habit Persistence
It seems to us that that the resolution of our woefully imperfect market puzzle lies in the
domain of behavioral science and habit persistence
At the heart of the rational and efficient market hypothesis is a fallacious assumption
that market participants will seek out the lowest price
Four Ways to Spend Money!
Milton Friedman made an astute observation about the four ways people spend money
1. You can spend your own money on yourself
2. You can spend your own money on somebody else. Then you are more concerned about the cost and less concerned about the content of the Birthday present!
3. You can spend somebody else’s money on yourself (Government = 10%)
4. You can spend somebody else’s money on somebody else(Government … not concerned about how much it is
and what I get = 40% of national income!!!)
Woefully Irresponsible Spending Habits
The popularly held Weltanschauung that markets are generally efficient and populated by rational individuals
making informed choices was found to be woefully inadequate
Individuals employed by state and federal institutions do not exhibit a proclivity for seeking out the most
competitive bids even under the unlikely assumption of the non-existence of venal and other ulterior motives
The size of this market is approximately 50% of the national income!!!