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EC 307: Economic Policy in the UK

Learn about the unique aspects of public sector procurement, optimal monopoly contracts, competition dynamics, and models for pricing and incentivizing cost control. Explore complexities and solutions in public procurement.

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EC 307: Economic Policy in the UK

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  1. EC 307: Economic Policy in the UK Week 12: Public Procurement Optimal monopoly contracts Competition 1

  2. 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

  3. 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

  4. 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

  5. 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 →0Y’(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

  6. 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

  7. 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

  8. 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

  9. A picture Efficient firm Efficient firm P P Inefficient firm Inefficient firm q+-e* q+-e* q--e* q--e* C q+-e+ C EPUK Lecture 2

  10. 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

  11. 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

  12. 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 Averch-Johnson 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. Auctions… EPUK Lecture 2

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