There are various patterns that the required evaluation might follow. In order to capture the attention of the receiver perhaps the simplest method is the most effective – answer the four points made point by point.
It may be agreed that transactions costs will rise as the number of bids to be examined increases, but marginal cost seems likely to fall with the number of bids – the specification of the contract, once drawn up, is a fixed cost. The extra costs incurred have to be weighed against the extra benefits of obtaining as full information as possible about potential bidders.
There will certainly be search costs and it could well be that the marginal cost of search might rise. On the other hand, there must be an element of arbitrariness in identifying only those of ‘known reliability’. This could militate against considering new entrants who may have a greater incentive to be price conscious than ‘nominated’ suppliers and who might justifiably feel aggrieved if they cannot be allowed to bid.
This sounds like a piece of special pleading. There is no presumption that, as the number of bidders increases, the Department need incur greater risks by awarding contracts to a firm with a greater likelihood than others of going bankrupt.
Why not leave to the firms themselves the assessment of whether or not, in the light of the probability of success, they should incur the costs of making a bid? They are in a better position to judge than a government official.
It might be added, that, even if the case for selective tendering were to be conceded, what evidence can the officials in the Department produce that the optimal number of bidders should be ‘five to eight’?
Have Figure 5.1 before you. You should be able to identify the point at which the equipment is produced as minimum cost. This is the point C on the iso-cost line DE where the firm uses OL, of labour and OK, of capital. If we know the amount of capital employed (OK1) and the rate of return on capital employed represented by the profit constraint, then we can identify a point in the right-hand side of the diagram which specifies the maximum allowable amount of profit – call it π1. The firm identifies a minimum total level of profit – call it π4. As this minimum must be reached, whatever the amount of capital employed, a line drawn parallel to the vertical axis from π4 denotes the firm's condition for supplying the equipment. This is clearly indicated by redrawing the relevant parts of Figure 5.1 (see Figure A1.2).
The firm will only be induced to supply the equipment if the vertical line representing minimum total profit π4 lies at or to the left of π1.
Figure A1.2 Constraints on government–firm agreements
There is a given upper limit on the amount the purchasing authority is prepared to pay for a piece of equipment given by the iso-cost line E’D’. The isoquant in our diagram represents alternative factor combinations capable of producing the equipment. The total profit opportunities available to the firm when operating at different points on the isoquant are shown by curve π’π’. The rate of return constraint is indicated as before by line 0P. Finally the total profit constraint faced by managers is shown by the vertical line at π4. To keep shareholders happy, the managers must operate to the right of π4. To satisfy the rate of return constraint, they must operate to the left of 0P. The technical constraint of the production function combined with the government's limit on the amount it is willing to pay means that managers must operate to the left of π’π’. The combination of these constraints gives a feasible area smn. Which point managers prefer depends on their objectives. Profit maximisers would operate at ‘m’. Technology freaks obsessed with smart new capital equipment would go to ‘s’. Managers wishing to maximise employees would go to ‘n’. Managers who value profits in excess of the minimum required to keep shareholders quiescent but also value increase in employment might operate at a point between ‘n’ and ‘m’ depending upon the precise ‘trade-offs’ implied by their preferences. Note that although technology freaks and profit maximisers are cost inefficient, they are never actually technically inefficient (they will maximise output for any given inputs and hence be on the π’π’ frontier). Staff maximisers at ‘n’ however will find that, if they satisfy the rate of return constraint, they will be inside the π’π’ frontier which will therefore not be binding. In other words, they must be operating ‘wastefully’. In a sense, they are forced to squander resources by operating ‘off the production function’ in a technically inefficient manner not merely in a cost efficient manner.
The average rate of return on capital employed for manufacturing industry is frequently used as a starting point for negotiation about a ‘reasonable’ rate of return in circumstances where the government has an interest in markets where competition is difficult, if not impossible, to establish. However, as argued in Section 5.2, in defence contracting producers face considerable uncertainties about costs of developing new weapons and about their ability to meet delivery dates. If the defence authorities insist on rigorous ‘post-costing’ and are rigid about delivery dates, a case could be made for negotiating a rate of return which allows for a ‘risk premium’ over and above the average rate of return.
Stage 1
Call total profit P, estimated profit Pe, and the percentage of costs allowable as profit as α (where α<1). If estimated and actual costs are the same, then actual and estimated profit will be the same. Put in symbolic form:
P=Pe= αCewhereCeequals estimated costs.
What has to be done is to add a term to this equation which expresses the taxation of excess profit in the first case, and of excess costs in the second.
Stage 2: Excess profit
In this case, we have to tax the difference between estimated costs (Ce) and actual costs (Ca) where Ca<Ce. Calling the percentage tax βP(β < 1), then the excess profits are reduced according to the expression β(Ce−Ca). So our excess profit formula becomes:
Checking this against Table 5.1, we find:
Stage 3: Excess costs
In this case, the addition of a percentage rate of profit raises the total outlays by the purchasing authority above the estimated amount C(1 + α). An expression must be added representing the reduction of total costs used in calculating the percentage profit. The appropriate expression is:
or
P=Ca(α−β)+βCe
Testing the formula against Table 5.1, we find:
Stage 4
The only remaining element in the formula is the placing of a maximum on the amount of profit which the firm is permitted to make. This is done very simply by adding to the formula the condition: ‘Always provided that P ≤ P Max where P Max = maximum allowable profit’.
