EC 307: Economic Policy in the UK
Week 12:
Public Procurement
Optimal monopoly contracts
Competition 1
What’s different about the public sector?
• Monopsony position
• Non-transferable risk
• (for some items)
– Development cost >> unit cost
– Many parallel ‘offices’
• Buying and selling on ‘mixed’ markets
– Constraints on partnering
– Difficulties in self-supply
– Different opportunity cost of finance, legal position
•
•
•
•
Informational and cultural asymmetries
High costs of monitoring, negotiation, enforcement
Market imperfections (esp. with ‘thin’ supply side)
Some markets with special rules – e.g. defence
EPUK Lecture 2
2
A simple model – buying from a monopolist
• Procurement as analogous to regulation – just set the price!
• Price = cost + profit
• Cost is endogenous:
– Depends on (hidden) effort
– Depends on (hidden) information
– Determined by contractual incentives
• Contracts can only depend on verifiable things
• Two polar situations:
– Fixed price contracts – provide maximal (perhaps too great) incentives
for cost reduction, but large profits in exchange. All cost risk on firm.
– Cost-plus contracts – no incentive to control costs, but insures firm
against risk (e.g. innovation, inflation). Allows tight control of profits,
not of costs.
EPUK Lecture 2
3
Model, 2
• Two simple representations:
–
–
–
–
P = a + b*C(e, q) – e is effort, q is hidden information
P = a - b[C(e,q) – Cest] – target cost pricing
Fixed-price is b = 0 or b = 1; cost-plus is b = 1 or b = 0
b is the “power” of the contract
• Low-powered contracts tend to be used early in the project
life cycle and more for high technology items than for
nonstandard equipment
• The optimal contract (not derived here – can happily do this if
desired) involves:
– Offering a schedule a(b) and letting firm pick the b it wants
– Or schedules a(Cest) and b(Cest) and letting firm estimate C
• This fits realities: tenders involve variants and buyer and
seller (re) negotiate.
• Main result: firms with higher efficiency (q) will:
– Choose higher-powered contracts
– Reap larger profits (information rent)
EPUK Lecture 2
4
More carefully – optimal contracts with 2 ‘types’ of monopoly supplier
• Cost = q – e;
• Disutility Y(e)
[Y’(e) > 0; Y”(e) > 0; Y(0) = 0; lim as e →0 Y’(e)=].
• Assume first that cost can be observed; contractor gets
U = P - Y(e) > 0 (value of outside option – independent of q)
• Shadow cost of public funds is l > 0;
agency gets S - (1+l)(P+q-e)
• Social welfare is
W = S - (1+l)(P+q-e) + P - Y(e) = S - (1+l)(q-e+ Y(e)) - lU
• Social welfare criterion does not favour leaving contractor
with excess profit.
EPUK Lecture 2
5
Solution under complete information
• If the agency knows q and observes e, maximisation
of W s.t. U > 0 gives
– Y’(e) = 1 (in other words optimal effort e = e*)
– U = 0 (P = Y(e*))
– Marginal disutility of effort = marginal cost savings;
contractor keeps no rent.
• This can be achieved by many contracts:
– Stipulate e* and enforce it with a large penalty
– Use a fixed-price contract
P(C) = Y(e*) - (C – C*), where C* = q – e*
• This gives perfect incentive for cost-minimisation
• This also extracts all of contractor’s rent.
EPUK Lecture 2
6
Incomplete information
•
•
•
•
•
Agency knows that q is either high (q+) or low (q-) and observes cost.
Contract is based only on two observed variables (P and C)
In principle, both ‘depend’ on the contractor’s type: P(q), C(q)
Let U(q) = P(q) - Y(q – C(q)) be contactor’s ‘truthful’ utility
Incentive compatibility (IC): each type of firm prefers to be truthful:
–
–
–
–
P(q+) - Y(q+ – C(q+)) > P(q-) - Y(q+ – C(q-))
P(q-) - Y(q- – C(q-)) > P(q+) - Y(q- – C(q+))
Or Y(q- – C+) + Y(q+ – C-) - Y(q+ – C+) - Y(q- – C-) > 0
…which shows (by integration) that C+ > C- - the optimal cost is nondecreasing
in type.
• We also need individual rationality (IR) – each type gets at least 0
• In the event, individual rationality is only binding for the low type and
incentive compatibility is only binding for the high type
• The social welfare function when the contractor has type q is now:
W(q) = S – (1+l)[P(q) + Y(q-C(q))] – lU(q)
• Suppose the agency thinks that the contractor is inefficient (low q) with
probability p and tries to maximise W subject to IC and IR.
EPUK Lecture 2
7
Solving the problem
• Rewrite IC for high type as:
U- > U+ + F(e+), where F(e) = Y(e) - Y((e – q+ + q-)
• This is increasing and convex, so the objective is concave
• The function F determines the rent enjoyed by the efficient
type relative to the inefficient type via ‘slack’ – the reduced
disutility of effort. Because it is increasing, the efficient firm
gets more rent with higher- power schemes.
• The agency chooses cost and utility levels for both contractor
types to maximise welfare s.t. relevant constraints, giving:
– Y’(q- – C-) = 1 (e- = e*)
– Y’(q+ – C+) = 1 – (l/(1+l))(p/(1-p))F’(q+ - C+), so e+ < e*
• The efficient type exerts efficient effort and gets positive rent
• The inefficient type exerts less effort and gets no rent.
• Rent exists because the efficient type can (more cheaply)
imitate the inefficient type
EPUK Lecture 2
8
A picture
Efficient
firm
P
Efficient
P firm
Inefficient
firm
q--e*
q+-e*
C
Inefficient
firm
q--e*
EPUK Lecture 2
q+-e* q+-e+
C
9
Some methodology observations
• The equilibrium is separating – different types choose
different contracts and thus reveal their types.
• The agency would want to renegotiate – reducing the price
on offer – this is ruled out by assumption (legal or reputation
reasons)
• The direct mechanism is to offer a supply contract P(C) – an
alternative is to offer the contract based on q: {P(q), C(q)} –
the firm accepts by announcing qo, producing at cost C(qo)
and getting the agreed price. The parties could renegotiate
between the announcement and the production. If the firm
announces q- there is no scope for this, but if the firm has
revealed q+ both parties could benefit from renegotiation.
Because the agency and the firm would prefer to have the
firm exert more effort in exchange for more money – but this
would destroy incentive compatibility.
• This happens in real contracts where there is initial R&D.
EPUK Lecture 2
10
Interpretation
• This is a strength, not a weakness of fixed-price contracts: it
amounts to gain sharing between firm and customer – profit
and power are both correlated with (unobservable) efficiency
(q).
• This is only optimal if the firm’s profits do not damage the
customer’s objective function - a function of the ‘shadow price
of public funds’
– This should be internal rate of return on best unfunded public project
– Gain sharing if b < 1, but ‘no distortion at the top’ (b = 1 or q = qmax)
• If there is no shadow distortion, fixed price contracts are
always optimal
– Maximal incentive for production efficiency
– Firm’s rent is “just a transfer”
– … but there is always at least a political shadow price
EPUK Lecture 2
11
Other remarks and problems
• Contracting agencies do not maximise societal welfare
• There is a possibility of deadweight loss
• There are possible dynamic distortions as well – if we take
the regulatory analogy seriously, we could see an AverchJohnson effect
• The capture problem: the agency’s objective functions grows
to resemble the supplier’s:
–
–
–
–
Corruption, bribes, political power
Revolving door
Personal relationships
Mutual understanding (trade-off between contractual rigour and
partnership)
– Information distortion
EPUK Lecture 2
12
More generic problems
• Static problems
– Hold-up
– Foreclosure
– Lock in
• Dynamic problems
– Inappropriate (too weak or too strong) incentives to minimise cost
– Mismatch of marginal cost and marginal willingness to pay (monopoly
pricing, reversal of agency, allocational inefficiency)
– Loss of effort/innovation incentives near the end of the contract – or
too-strong incumbent advantage
– Amount, nature and ownership of intellectual property rights and other
rights to intangible property created during the contract
EPUK Lecture 2
13
Competing suppliers
• Original approach was single supplier,
–
–
–
–
Non-competitive contracts
Cost+ (esp. for R&D) or cost-based pricing
Poor incentive properties, heavy information requirements
Demand focus (jobs, technology, cheap (local) supply costs, long-term
relationships, ‘sales on wider markets’
• Competition began to come in mid-80’s
–
–
–
–
Trade-off benefits against demand focus
Narrow VFM criteria
Competition for contracts
Prime contractor model for risk transfer
• Competition for subcontracts
– Separate R&D, production
– Fixed price, firm price, target/incentive payment schemes
– Performance-driven (functional) specification
EPUK Lecture 2
14
The competitive sourcing problem
• Decision 1: how many (and which) suppliers to use?
• Decision 2: how to design contracting arrangements to
maintain competitive pressures
– Control (design and production) costs
– Control profits
• A theoretical wilderness – scads of oligopoly models; contract
models; allocation models
– Symmetric situations: auctions, markets
– Asymmetric situations due to incumbent, technological, IPR, political
(e.g. national champion) advantage
• Markets: separate decisions about how many suppliers, type
of contract: analogous to regulatory models
• How many firms?
– More = competition, product diversity, reduced information asymmetry
– Fewer = less duplication of fixed cost
EPUK Lecture 2
15
More on competition problem
• Information asymmetry in markets:
– Correlation: make i’s payment depend on j’s price offers, reports, etc. > benchmarks and yardsticks
– Scale: more suppliers -> better chance of finding a low-cost one, less
stable collusion
– When duplication costs are low (e.g. when all suppliers sell on private
or other markets), this effect may dominate
– Otherwise, the government may wish to create markets
• Tendering
– By far the most common method
– Sensitive control of mechanism design
– Complex legal and regulatory structure – the ground rules (both de
facto and de jure) are clear and common knowledge
– An excellent excuse to use auction analysis :-)
– Some useful history: (e.g. Szymanski, S. (1996) ‘The Impact of
Compulsory Competitive Tendering on Refuse Collection Services’,
Fiscal Studies, 17(3), 1–19)
EPUK Lecture 2
16
Auctions…
EPUK Lecture 2
17