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!!!