This document contains all the notes from the synchronous and asynchronous lectures throughout the year and is split up lecture by lecture. This document on its own, is sufficient to get a top mark in your end of year exam for the third year industrial economics module taught by Andrew Harkins.
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.
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