INDUSTIAL ECON STRATEGY
WEEK 1 – DYNAMIC MONOPOLY
-Monopoly models are most appropriate in industries that have one dominant firm with
considerable market power, eg – Google (Search Engine).
-Can also think of it as a benchmark in industries with competing firms or in cases where
firms are not acting strategically.
-Recall that in static monopolies, firm will profit maximise such that they produce the output such
that MC = MR. We recall that this is socially inefficient as it generates deadweight loss.
-To achieve socially efficient level, we could regulate the price such that they create a price
ceiling, although this can be costly and difficult.
-Another possibility is if the monopolist is price discriminating – if perfect, the total surplus
increases, but the whole surplus goes to the producer and none to the consumer. This is
very difficult to achieve though.
-Dynamic monopoly models shed new light on the monopoly problem and its possible solutions. The
most interesting case of this is where a monopolist sells a durable good – a good that can be used
more than once and provide a stream of benefits over time ,eg – cars, electronics, books.
Dynamic Monopoly Model:
-We have discrete time periods, 1,2,…,T.
-The monopolist makes a sequence of pricing decisions, p 1, p2,…,pT.
-The new issue is to consider the context of a dynamic monopoly – intertemporal price
discrimination – perhaps setting different prices in different periods could yield higher profits; eg –
set a high price early on in product life-cycle and lower price as product becomes older.
-This is something we see in practice, eg – new cameras, TVs etc.
The Coase Conjecture:
-Coase (1972) uses land as an example –
suppose a monopolist has a large number of
identical plots of land (q bar).
-The monopolist maximises revenue at price
p*.
-Having sold q*, the monopolist faces a
problem. They have a number of plots leftover
( ), but they could sell more at p’<p*.
-BUT then early buyers may anticipate this
and could delay their purchase, knowing
prices will later be reduced.
,-The Coase Conjecture is that as t -> infinity, a durable goods monopolist will price at the competitive
equilibrium price, pc, as buyers know that future prices will fall.
A Model of Durable Monopoly (Section 10.1.2 of B+P book):
-We suppose that time evolves in two discrete periods, t=1,2. The good is durable such that it can be
consumed in period 1 and 2 if bought in period 1. We suppose consumption brings a payoff of per
period and discount future payoffs at a rate .
-The consumers have their own valuations, - these are private to the consumer.
-The monopolist knows that each buyer has linear utility and valuations are distributed uniformly.
-Any uniform distribution has the
following properties.
-b is the maximum value the
distribution can take, while a is the
minimum. Thus probability of each
value is equal.
-CDF is very useful – x is the specific
valuation/price we are looking at.
-Look logically – if a = 0, b = 1 (very
often the case), then f(x)=x.
-Demand function given by the
fraction of consumers who want to buy – anyone with valuation above price would buy. We find
relevant values of CDF and plot for each x (price).
Prices in the Static Case:
-This means that the firm picks a price in period t=1 and consumer consumes in period 1 and 2 but
they cannot buy the good in period 2.
-Buyer pays a price equal to their
total utility from both periods.
-We find demand by figuring out
the probability that an individual
will buy at the given price
(valuation greater/equal to price).
-This is the CDF and then we plug
this into demand from previous
slide and multiply by price to find
expected revenue.
-We then profit maximise by differentiating w.r.t p, setting equal to 0. We find profit maximising
price and multiplying by demand at this price, we find expected profit. (N=1 in this case).
Prices in Dynamic Case (Coase’s Argument):
,-In this case, we have discrete time periods whereby the durable good can be bought in either
period 1 or period 2.
-If we pick the optimal
price from the static case,
we find that those who buy
in the first period have a
valuation > price, providing
theta > 0.5.
-All the above people have
left the market, so those
left must have that
.
-Thus, rearranging, the new
demand function in period 2 can be satisfied by . We can differentiate this as above to find
the optimal second period price, . We are assuming however that period 1 buyers do not
anticipate a price fall in the second period.
-Period 1 buyers would prefer to delay however if their payoff from buying in period t = 1 (left side)
is less than their payoff if they wait (right side). Rearranging, we get that . These people
would rather wait also.
-This means that if people anticipate a price drop, a greater number of people would rather wait till
tomorrow to buy. Thus, the monopolist should pick a higher price in period 1 such that more buyers
delay. Thus, it cannot be optimal for the monopolist to pick the static price in the first period – the
monopolist is competing against its future self.
Solving the 2 Period Model:
-We solve the 2 period model using backward induction – the monopolist picks a price and some
fraction of buyers will buy and some will wait at each period in time.
-In first period, people will
buy if utility (payoff – price)
from buying in period 1 is
greater than that of period 2
(alongside).
-Therefore, in second period,
there are a fraction of buyers
left ( ). Plug into the CDF
and demand function and
simplify (note lower limit is
0).
, -Differentiate and maximise to get optimal price in second period. Note this is lower than price in
period 1. We find optimal profit in second period.
-We then have p(1) in terms of p(2) and then we maximise as before:
-Computing FOC w.r.t p(1) we find the
optimal p(1) and expected maximum
profit.
-Comparing the 2, we find selling in 1
period (static) is greater than selling in
2 period (dynamic) case. It is lower for
every value of delta.
-This means in dynamic case,
consumer surplus is greater.
-Graphically:
Commitment:
-Thus, the monopolist would prefer to be static; is there a way of preventing buyers delaying their
purchase?
-If the monopolist could commit credibly to maintaining/increasing the price in period 2, the firm
would be able to restore its previous level of profit.
-This could be feasible if they have a reputation to maintain in other parallel markets, eg –
known for never discounting in other markets.
-Limited time special offers means commitment to higher future prices.
-Limited edition products, where you commit to low capacity can also prevent delays.
-Similar with numbered units to encourage people to buy.
WEEK 1 – DYNAMIC MONOPOLY
-Monopoly models are most appropriate in industries that have one dominant firm with
considerable market power, eg – Google (Search Engine).
-Can also think of it as a benchmark in industries with competing firms or in cases where
firms are not acting strategically.
-Recall that in static monopolies, firm will profit maximise such that they produce the output such
that MC = MR. We recall that this is socially inefficient as it generates deadweight loss.
-To achieve socially efficient level, we could regulate the price such that they create a price
ceiling, although this can be costly and difficult.
-Another possibility is if the monopolist is price discriminating – if perfect, the total surplus
increases, but the whole surplus goes to the producer and none to the consumer. This is
very difficult to achieve though.
-Dynamic monopoly models shed new light on the monopoly problem and its possible solutions. The
most interesting case of this is where a monopolist sells a durable good – a good that can be used
more than once and provide a stream of benefits over time ,eg – cars, electronics, books.
Dynamic Monopoly Model:
-We have discrete time periods, 1,2,…,T.
-The monopolist makes a sequence of pricing decisions, p 1, p2,…,pT.
-The new issue is to consider the context of a dynamic monopoly – intertemporal price
discrimination – perhaps setting different prices in different periods could yield higher profits; eg –
set a high price early on in product life-cycle and lower price as product becomes older.
-This is something we see in practice, eg – new cameras, TVs etc.
The Coase Conjecture:
-Coase (1972) uses land as an example –
suppose a monopolist has a large number of
identical plots of land (q bar).
-The monopolist maximises revenue at price
p*.
-Having sold q*, the monopolist faces a
problem. They have a number of plots leftover
( ), but they could sell more at p’<p*.
-BUT then early buyers may anticipate this
and could delay their purchase, knowing
prices will later be reduced.
,-The Coase Conjecture is that as t -> infinity, a durable goods monopolist will price at the competitive
equilibrium price, pc, as buyers know that future prices will fall.
A Model of Durable Monopoly (Section 10.1.2 of B+P book):
-We suppose that time evolves in two discrete periods, t=1,2. The good is durable such that it can be
consumed in period 1 and 2 if bought in period 1. We suppose consumption brings a payoff of per
period and discount future payoffs at a rate .
-The consumers have their own valuations, - these are private to the consumer.
-The monopolist knows that each buyer has linear utility and valuations are distributed uniformly.
-Any uniform distribution has the
following properties.
-b is the maximum value the
distribution can take, while a is the
minimum. Thus probability of each
value is equal.
-CDF is very useful – x is the specific
valuation/price we are looking at.
-Look logically – if a = 0, b = 1 (very
often the case), then f(x)=x.
-Demand function given by the
fraction of consumers who want to buy – anyone with valuation above price would buy. We find
relevant values of CDF and plot for each x (price).
Prices in the Static Case:
-This means that the firm picks a price in period t=1 and consumer consumes in period 1 and 2 but
they cannot buy the good in period 2.
-Buyer pays a price equal to their
total utility from both periods.
-We find demand by figuring out
the probability that an individual
will buy at the given price
(valuation greater/equal to price).
-This is the CDF and then we plug
this into demand from previous
slide and multiply by price to find
expected revenue.
-We then profit maximise by differentiating w.r.t p, setting equal to 0. We find profit maximising
price and multiplying by demand at this price, we find expected profit. (N=1 in this case).
Prices in Dynamic Case (Coase’s Argument):
,-In this case, we have discrete time periods whereby the durable good can be bought in either
period 1 or period 2.
-If we pick the optimal
price from the static case,
we find that those who buy
in the first period have a
valuation > price, providing
theta > 0.5.
-All the above people have
left the market, so those
left must have that
.
-Thus, rearranging, the new
demand function in period 2 can be satisfied by . We can differentiate this as above to find
the optimal second period price, . We are assuming however that period 1 buyers do not
anticipate a price fall in the second period.
-Period 1 buyers would prefer to delay however if their payoff from buying in period t = 1 (left side)
is less than their payoff if they wait (right side). Rearranging, we get that . These people
would rather wait also.
-This means that if people anticipate a price drop, a greater number of people would rather wait till
tomorrow to buy. Thus, the monopolist should pick a higher price in period 1 such that more buyers
delay. Thus, it cannot be optimal for the monopolist to pick the static price in the first period – the
monopolist is competing against its future self.
Solving the 2 Period Model:
-We solve the 2 period model using backward induction – the monopolist picks a price and some
fraction of buyers will buy and some will wait at each period in time.
-In first period, people will
buy if utility (payoff – price)
from buying in period 1 is
greater than that of period 2
(alongside).
-Therefore, in second period,
there are a fraction of buyers
left ( ). Plug into the CDF
and demand function and
simplify (note lower limit is
0).
, -Differentiate and maximise to get optimal price in second period. Note this is lower than price in
period 1. We find optimal profit in second period.
-We then have p(1) in terms of p(2) and then we maximise as before:
-Computing FOC w.r.t p(1) we find the
optimal p(1) and expected maximum
profit.
-Comparing the 2, we find selling in 1
period (static) is greater than selling in
2 period (dynamic) case. It is lower for
every value of delta.
-This means in dynamic case,
consumer surplus is greater.
-Graphically:
Commitment:
-Thus, the monopolist would prefer to be static; is there a way of preventing buyers delaying their
purchase?
-If the monopolist could commit credibly to maintaining/increasing the price in period 2, the firm
would be able to restore its previous level of profit.
-This could be feasible if they have a reputation to maintain in other parallel markets, eg –
known for never discounting in other markets.
-Limited time special offers means commitment to higher future prices.
-Limited edition products, where you commit to low capacity can also prevent delays.
-Similar with numbered units to encourage people to buy.
