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EC 307: Economic Policy in the UK

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’

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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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