Transcript cost research and development

Research and Development
Chapter 22: Research and
Development
1
Introduction
• Technical progress is the source of rising living
standards over time
• Introduces new concept of efficiency
– Static efficiency—traditional allocation of resources to
produce existing goods and services so as to maximize
surplus and minimize deadweight loss
– Dynamic efficiency—creation of new goods and services to
raise potential surplus over time
• Schumpeterian hypotheses (conflict between static and
dynamic efficiency)
– Concentrated industries do more research and development of
new goods and services, i.e., are more dynamically efficient,
than competitively structured industries
– Large firms do more research & development than small firms
Chapter 22: Research and
Development
2
A Taxonomy of Innovations
Product versus Process Innovations
• Product Innovations refer to the creation of new goods and new
services, e.g., DVD’s, PDA’s, and cell phones
• Process Innovations refer to the development of new technologies
for producing goods or new ways of delivering services, e.g.,
robotics and CAD/CAM technology
• We mainly focus on process or cost-savings innovations but the
lines of distinction are blurred—a new product can be the means
of implementing a new process
Drastic versus Non-Drastic Innovations
• Process innovations have two further categories
• Drastic innovations have such great cost savings that they permit
the innovator to price as an unconstrained monopolist
• Non-drastic innovations give the innovator a cost adavantage but
not unconstrained monopoly power
Chapter 22: Research and
Development
3
Drastic versus Non-Drastic Innovations
• Suppose that demand is given by: P = 120 – Q and all firms have
constant marginal cost of c = $80
• Let one firm have innovation that lowers cost to cM = $20
• This is a Drastic innovation. Why?
– Marginal Revenue curve for monopolist is: MR = 120 – 2Q
– If cM = $20, optimal monopoly output is: QM = 70 and PM = $70
– Innovator can charge optimal monopoly price ($70) and still
undercut rivals whose unit cost is $80
• If cost fell only to $60, innovation is Non-drastic
– Marginal Revenue curve again is: MR = 120 = 2Q
– Optimal Monopoly output and price: QM = 30; PM = $90
– However, innovator cannot charge $90 because rivals have unit
cost of $80 and could under price it
– Innovator cannot act as an unconstrained monopolist
– Best innovator can do is to set price of $80 (or just under) and
supply all 40 units demanded.
Chapter 22: Research and
Development
4
NonDrastic Innovation: QM < QC
Drastic Innovation: QM > QC
Non-Drastic Innovations
(cont.)
so innovator cannot
charge
soDrastic
innovator vs.
can charge
M because rivals
M without
monopoly
price
P
M
monopoly
price
P
Innovation is drastic if monopoly output Q at MR = new marginal
c’ exceeds
the competitive output QC atcan
oldundercut
marginalthat
costprice
c
constraint
$/unit = p
$/unit = p
PM
c
c
PM
c’
Demand
c’
Demand
MR
QC QM
MR
Quantity
QM QC
Chapter 22: Research and
Development
Quantity
5
Innovation and Market Structure
• Arrow’s (1962) analysis—
– Innovative activity likely to be too little because innovators
consider only monopoly profit that the innovation brings and not
the additional consumer surplus
– Monopoly provides less incentive to innovate that competitive
industry because of the Replacement Effect
• Assume demand is: P = 120 – Q; MC= $80. Q is initially 40.
Innovator lowers cost to $60 and can sell all 40 units at P = $80.
• Profit Gain is $800–Less than Social Gain
$/unit
120
80
60
A
B
40
60
Initial Surplus is Yellow
Triangle--Social Gains from
Innovation are Areas A ($800)
and B ($200)
But Innovator Only Considers
Profit Area A ($800)
Quantity
120
Chapter 22: Research and
Development
6
Innovation and Market Structure (cont.)
• Now consider innovation when market structure is monopoly
– Initially, the monopolist produces where MC = MR = $80 at Q =
20 and P = $100, and earns profit (Area C) of $400
– Innovation allows monopolist to produce where MC = MR = $60
at Q = 30 and P = $90 and earn profit of $900
– But this is a gain of only $500 over initial profit due to
Replacement Effect—new profits destroy old profits
$/unit
120
100
90
80
60
C
A
20 30
MR
60
Monopolist Initially Earns
Profit C—With Innovation it
Earns Profit A—Net Profit
Gain is Area A – Area C
Which is Less than the Gain
Demand
to a Competitive Firm
120
Chapter 22: Research and
Development
Quantity
7
Innovation and Market Structure (cont.)
• Preserving Monopoly Profit--the Efficiency Effect
• Previous Result would be different if monopolist had to worry
about entrant using innovation
– Assume Cournot competition and that entrant can only enter if it
has lower cost, i.e., if it uses the innovation
– If Monopolist uses innovation, entrant cannot enter and monopolist
earns $900 in profit
– If Monopolist does not use innovation, entrant can enter as lowcost firm in a duopoly
• Entrant earns profit of $711
• Incumbent earns profit of $44
– Gain from innovation now is no longer $900 - $400 = $500 but
$900 - $44 = $856
– Monopolist always has more to gain from innovation than does
entrant—this is the Efficiency Effect
Chapter 22: Research and
Development
8
Competition and Innovation
• The incumbent/entrant model just discussed seems closer in
spirit to Schumpeter’s ideas than Arrow’s analysis.
• Dasgupta and Stiglitz (1980) come even closer by directly
embedding innovation in a model of Cournot competition
–
–
–
–
–
Profit for each firm: i = P(Q) – c(xi)qi – xi
Here, firm’s unit cost falls as the firm engages in R&D activity
What is the equilibrium?
Define x* as the optimal R&D level of each firm
From Chapter 9, we know that
s
P  c ( x*)
 i
P

–But with n symmetric firms si = 1/n, So we have
1 

P 1 
  c x *
n 

Output Condition
Chapter 22: Research and
Development
9
Competition and Innovation (cont.)
• How much should x* be?
– The usual marginal calculations apply. Every increase in
x costs $1. The benefit is the cost reduction this brings,
c(x)/x, times the number of units q* to which this cost
reduction will apply
dc xi 

qi  1
dxi
R&D Condition
– Both the Output Condition and the R&D Condition must
hold simultaneously in any equilibrium
– One obvious implication of the R&D Condition is that the
R& D effort of any one firm will fall as the number of n
firms increases because this will decrease the output of
each firm
Chapter 22: Research and
Development
10
Competition and Innovation (cont.)
• Making n endogenous means allowing firms to enter until
they no longer have an incentive to do so
• This will occur when firms earn zero profit after allowing
for R&D costs. Defining n* as the equilibrium number of
firms, the Output Condition then implies:
P
P  c x * 
n *
• Substitution into the R&D Condition then yields:
n* x*
1

 Industry R&D as Share of Sales
PQ *Q * n *
• Industry R&D effort declines as n* rise, i.e., as industry
becomes less concentrated—fairly strong theoretical support
for Schumpeterian Hypothesis
Chapter 22: Research and
Development
11
Competition and Innovation (cont.)
• But empirical support for Schumpeterian view is mixed
– Need to control for science-based sectors (e.g., chemicals,
pharmaceuticals, and electronics) and non-technology based
sectors (e.g., restaurants and hair stylists)—R&D much more
likely in science-based sectors regardless of firm size
– Need also to distinguish between R&D expenditures and true
innovations. Common finding [e.g., Cohen and Klepper
(1996)], is that large firms do somewhat more R&D but
achieve less real innovative breakthroughs—e.g., Apple
produced the first PC
– Market structure is endogenous. Innovations might create
industry giants (e.g., Alcoa) not the other way around.
• Bottom Line: Validity of Schumpeterian hypotheses is
still undetermined
Chapter 22: Research and
Development
12
R&D Spillovers and Cooperative R&D
• Technological break-throughs by one firm often “spill over’
to other firms
– Spillover is unlikely to be complete but likely to arise to some extent
– We can model this in the Dasgupta Stiglitz world by now writing a
firm’s unit cost as a function of both its own and its rival’s R&D
• c1 = c – x1 - x2
• c2 = c – x2 - x1
• To obtain solution, need also to assume that R&D is now subject
to diminishing returns, i.e., R&D cost is r(x) = x2/2.
• In this setting, response of firm 1’s R&D to firm 2’s R&D
depends on size of spillover term .
– When  is small, R&D expenditures are strategic substitutes—the
more firm 1 does the less firm 2 will do
– When  is large, R&D expenditures are strategic complements—the
more firm 1 does the more firm 2 will do
Chapter 22: Research and
Development
13
R&D Spillovers and Cooperative R&D (cont.)
• However, determination of whether R&D efforts are strategic
substitutes or strategic complements is not sufficient to
determine what happens when there are spillovers
– Let Demand be given by: P = A – BQ
– Let ci = c – xi – xj;
– Each firm now chooses both production qi and research
intensity xi
– To make things simple, suppose that A = 100, B = 2; and that
firms have to choose between setting x at either 7.5 or 10
• Now consider two cases
– First case: Low Spillovers;  = 0.25
– Second case: High Spillovers;  = 0.75
Chapter 22: Research and
Development
14
sh Equilibrium is for both firms to
oose the high level of research
ensity (xR&D
= 10). Spillovers
Why? When degree
and Cooperative R&D (cont.)
spillovers  is small, firm know that
The Pay-Off Matrix for  = 0.25
ts rival can do R&D knowing that it
l get most of the benefits. Since this
Firm 1
uld advantage the rival, each firm
es to avoid being left behind by doing
s of R&D
Low Research
High Research
Intensity
Intensity
Low Research
$107.31, $107.31 $100.54, $110.50
Intensity
Firm 2
High Research $110.50, $100.54 $103.13, $103.13
Intensity
Chapter 22: Research and
Development
15
sh Equilibrium is for both firms to
oose the low level of research intensity
= 7.5). R&D
Why? When
degree of and Cooperative R&D (cont.)
Spillovers
llovers  is large, firm knows that it
The Pay-Off Matrix for  = 0.75
l benefit from technical advance of its
al even if it doesn’t do any R&D itself.
Firm 1
each firm tries to free-ride off its rival
d each does little R&D
Low Research
High Research
Intensity
Intensity
Low Research
$128.67, $128.671, $136.13, $125.78
Intensity
Firm 2
High Research $125.78, $136.13
Intensity
Chapter 22: Research and
Development
$133.68, $133.68
16
R&D Spillovers and Cooperative R&D (cont.)
• MORAL of the foregoing analysis is that the Outcome of
non-cooperative R&D spending depends critically on the
extent of spillovers.
• What if R&D spending is cooperative?
• R&D cooperation can take two forms:
– 1. Do R&D independently but choose x1 and x2 jointly to maximize
combined profits, given competition in product market is maintained.
– 2. Do R&D together as one firm, e.g, form a Research Joint Venture.
That is, effectively operate as though the degree of spillovers is  =
1, again though, continue to maintain product market competition.
• The two types have very different implications.
Chapter 22: Research and
Development
17
R&D Spillovers and Cooperative R&D (cont.)
• Consider first the case of coordinated but not centralized
R&D using our generalized demand and cost equations
– Total R&D spending now rises unambiguously as  increases.
– To see this note that given our earlier demand and cost assumptions,
and given the fact that x1 and x2 are chosen to maximize joint profits,
the optimal values for x1 and x2 are:
2 A  c 1   
2
9  21   
– This is unambiguously increasing in  but this is a good
news/bad news story.
– The good news is that for the high spillover case ( >1), the freeriding problem is no longer an issue and firms now do more R&D
x1  x2 
– The bad news is that for the low spillover case ( < 1), there is no
longer a fear of being left behind by one’s rival. So in this case firms
do less R&D which means costs (and consumer prices) are higher.
Chapter 22: Research and
Development
18
R&D Spillovers and Cooperative R&D (cont.)
• What about a Research Joint Venture?
– As noted, this effectively changes  to 1.
– For our general demand and cost equations, it can be shown that:
x1  x2 
4 A  c 
9B  8
– This is clearly more R&D than occurred with simple coordination
for any given value of 
– As a result, it leads to lower costs and more output to the benefit
of consumers
q1  q2 
3 A  c 
9B  8
– Profits are also higher. Thus, in the presence of spillovers, Research
Joint Ventures are unambiguously beneficial.
– The only trick is to make sure that cooperation is limited to research
and does not spill over to other dimensions of competition
Chapter 22: Research and
Development
19