## Technology-Neutral Procurement – An Assessment

In the absence of full cost information or of externalities, should policies to support production of a good always be technology-neutral?   Scenarios can be constructed which suggest not, but the gains from departing from technology neutrality may be too small to be worthwhile.

Suppose a government wishes to secure the production of a good which can be produced by more than one technology.  It might be a good required by the government sector, or one required by firms or households which the government wishes to subsidise because it supports its social or environmental policy.  Should the government proceed in a technology-neutral manner, or could it be appropriate to favour one technology over another?  There are some circumstances in which the latter approach is clearly better.  One is where the government has full information on the production costs of the different technologies, so can choose the technology or combination of technologies offering the lowest cost.  Another is where the apparently similar goods obtained from the different technologies are not actually identical, an example being intermittent electricity obtained from sources such as wind and solar on the one hand, and continuous electricity (subject only to maintenance requirements and faults) obtained from nuclear on the other.  A third is where the technologies differ in respect of production externalities: again electricity provides an example via the contrast between generation from fossil fuels and from low-carbon sources.

Suppose however that none of these circumstances apply: in other words the government has less than full information on costs, the alternative technologies produce goods which are genuinely identical, and there are no production externalities.  I want to consider a line of reasoning suggesting that a technology-neutral approach may still not be best.  This post is largely prompted by a paper by Fabra & Montero (1), although I shall present the material in my own way and draw my own conclusions.

In the interests of simplicity, I shall assume that the quantity $Q,$ of the good to be secured has been pre-determined, that just two production techniques are available, and that the full cost of securing production is met by the government.  However I shall consider two interpretations of ‘best’. There is the view a government may well take that what is best is to minimise the cost to itself, and so minimise the additional tax revenue required.  Then there is the standard economists’ view that the aim should be to maximise welfare, defined as economic benefits less economic costs.  The economic benefits are the benefits to consumers of the good, but these are fixed by the quantity $Q,$.  To maximise the effect on welfare, therefore, we can focus on minimising the economic costs.  The cost to the government is not itself an economic cost, since it simply reflects a transfer from taxpayers to the government and then to producers.  The true economic cost has two components.  One is the cost of producing the good.  The other is the distortionary effect on the economy of the additional taxation, sometimes referred to as the excess burden of taxation (2).  In the literature this is sometimes quantified as the ratio $\lambda,$ of the excess burden to the direct tax burden, and sometimes as the ratio of the sum of the excess and direct burdens to the direct burden, known as the marginal cost of public funds (MCF); thus MCF = $1 + \lambda,$

To illustrate these two interpretations of ‘best’ and how they can be achieved, let us flesh out our scenario with sufficient detail to permit the use of mathematical optimisation techniques.  Let us assume that the government must pay the same unit price for all amounts of the good produced using a technique, but can discriminate in respect of price between the two techniques.  Let the quantities produced using the two techniques be $q_1,$ and $q_2,$.  Suppose that each technique is available to many small firms with a range of production costs such that the aggregate production costs as progressively higher-cost firms come into production are (3):

$C_1=(c_1+x_1)q_1+\dfrac{q_1^2}{2}\qquad(E1)$

$C_2=(c_2+x_2)q_2+\dfrac{q_2^2}{2}\qquad(E2)$

Costs here are taken to include normal profit, so we can assume that a firm will produce if and only if the unit price offered by the government equals or exceeds its unit cost.  At aggregate level, therefore, the quantity of the good produced by a technique will be such that the aggregate marginal cost (4) equals the price offered:

$c_1 + x_1 + q_1 = p_1\qquad(E3)$

$c_2+x_2+q_2=p_2\qquad(E4)$

Suppose further that the government knows the above formulae and knows the values of $c_1,$ and $c_2,$, but not of $x_1,$ and $x_2,$.  The latter, from the government’s point of view, are independent random variables, each with uniform distribution over the range $[-k, k],$ where $k,$ is a known constant.  In the central case which we will consider the known values are: $c_1=100,\:c_2=20,\:k=10$.  We also assume that $Q=100,$ and $\lambda=0.2,$

To determine the unit price(s) the government should offer, it clearly needs to undertake some sort of auction process.  I shall consider five possible types of auction, setting out the relevant maths in some detail for the first and in outline for the others (5).

An immediate question is whether the government should hold separate auctions for the two techniques or a single auction embracing both.  I will consider the separate auctions (technology-specific) case first.  This requires the government, using only the information it has, to determine the optimal quantities to be obtained by use of each technique.  Because some of its information is stochastic, it needs to consider the expectation, denoted $E,$, of the range of possible outcomes of any choice of quantities, and choose the quantities that minimise that expectation.

If the aim is to minimise cost to the government, the problem can be formulated as:

$\min E[p_1q_1+p_2q_2]\qquad(E5)$

Since we require $q_1 + q_2 = Q,$, and using E3 and E4, we can eliminate $p_1, p_2$ and $q_2,$ and express the problem as:

$\min E[c_1+x_1+q_1)q_1+(c_2+x_2+Q-q_1)(Q-q_1)]\qquad(E6)$

Given that the distributions of the variables $x_1,$ and $x_2,$ have been defined as symmetrical about zero, we have $E[x_1] = E[x_2] = 0,$, so that on evaluating the expectation in E6 we can ignore the terms containing $x_1,$ or $x_2,$.  For future reference, we also note that, since $x_1,$ and $x_2,$ are independent, $E[x_1x_2] = E[x_1]E[x_2] = 0,$ but $E[x_1^2],$ and $E[x_2^2],$ importantly are not zero but equal $k^2/3,$ (6).  Rearranging the terms not containing $x_1,$ or $x_2,$, the problem becomes:

$\min [2q_1^2+(c_1-c_2-2Q)q_1 + c_2Q + Q^2]\qquad(E7)$

Differentiating with respect to $q_1,$, the first order condition is:

$4q_1 + c_1 -c_2 -2Q = 0\qquad(E8)$

implying (7):

$q_1 = \dfrac{c_2 -c_1 + 2Q}{4}\qquad(E9)$

Substituting our known values we have $q_1,$ = (20 – 100 + (2 x 100))/4 = 30, from which we can infer $q_2,$ = 70, $p_1,$ = 130 + $x_1,$, $p_2,$ = 90 + $x_2,$.  The implied expectation of the cost to the government is:

$E[p_1q_1+p_2q_2]=E[(130+x_1)30+(90+x_2)70]=$ 10,200 $(E10)$

where, again, we can ignore terms containing $x_1,$ or $x_2,$.  Although the aim in this case was not to maximise welfare, we may note that the economic cost is:

$E\Big[(c_1 + x_1)q_1 + \dfrac{q_1^2}{2} + (c_2 + x_2)q_2 + \dfrac{q_2^2}{2} + 10,200 \lambda \Big]$

$= E\Big[(100 + x_1)30 + \dfrac{30^2}{2} + (20 + x_2)70 + \dfrac{70^2}{2} + 10,200(0.2)\Big]$ = 9,340    $(E11)$

To obtain this outcome, the government must proceed by what I shall call Auction Type 1:

Invite bids from technique 1, and set the strike price at the level just sufficient to bring forth production at the level ($q_1,$ = 30) determined by the minimum cost to government problem E5 AND Invite bids from technique 2, and set the strike price at the level just sufficient to bring forth production at the level ($q_2,$ = 70) determined by the problem E5.

It is important to note that this procedure (and all the others to be considered) only works because of our assumption that there are many small firms with a range of production costs.  Because of this, we can take it that each firm’s bid reflects its actual costs.  A firm can gain nothing from a higher bid since, with many small firms, such a bid cannot significantly raise the strike price, but can (if the bid exceeds the strike price) result in the firm losing the business it could have gained.

If the aim is to maximise welfare, which as we have seen requires minimising economic cost, the problem is formulated as:

$\min E\Big[(c_1 + x_1)q_1 + \dfrac{q_1^2}{2} + (c_2 + x_2)q_2 + \dfrac{q_2^2}{2} + \lambda (p_1q_1 + p_2q_2)\Big]\qquad(E12)$

Substituting as before for $p_1,\:p_2$ and $q_2,$, eliminating terms in $x_1,$ and $x_2,$, and setting the derivative with respect to $q_1,$ equal to zero, we can obtain:

$q_1 = \dfrac{Q}{2} + \dfrac{(1 + \lambda )(c_2 - c_1)}{2(1 + 2\lambda )}\qquad(E13)$

Substituting known values we have $q_1,$ = 100/2 + 1.2(20 – 100) / 2.8 = 15.714.  From this we can obtain the cost to the government (10,608) and the economic cost (9,054).  As we might expect, the former is considerably more than when we aimed to minimise the cost to the government, while the latter is considerably less.

To obtain this outcome, we require Auction Type 2:

Invite bids from technique 1, and set the strike price at the level just sufficient to bring forth production at the level ($q_1,$ = 15.714) determined by the minimum economic cost problem E12 AND Invite bids from technique 2, and set the strike price at the level just sufficient to bring forth production at the level ($q_2,$ = 84.286) determined by the problem E12.

A feature of both the approaches we have considered is that, given our known values, they result in different prices for electricity according to the technique by which it is produced.  Suppose instead that the government holds what we will call Auction Type 3:

Invite bids from techniques 1 and 2, and set a single strike price at the level just sufficient to bring forth total production at the required level $(Q ,$ = 100).

In this case, from E3 and E4 we can infer:

$c_1 + x_1 + q_1 = c_2 + x_2 + q_2 = c_2 + x_2 + Q - q_1\qquad(E14)$

implying:

$q_1 = \dfrac{Q}{2} - \dfrac{(c1 + x1) - (c2 + x2)}{2}\qquad(E15)$

Although we can infer formulae for $p_1 = p_2,$ and $q_2,$, these all contain the variables $x_1,$ and $x_2,$.  On calculating the expected cost to the government $x_1,$ and $x_2,$ drop out as before since we are simply multiplying the common price by the fixed quantity $Q,$; given our known values the expected cost to the government is 11,000.  In calculating the expected economic cost, however, the production cost formulae include the squares of $q_1,$ and $q_2,$ resulting in squares of $x_1,$ and $x_2,$ which as we have seen take the expected value $k^2/3,$.  The expected economic cost is 9,083, of which these expected values of squared variables contribute -102/6 = -17.

This type of auction does not achieve the best outcome on either of our interpretations of ‘best’.  It results in an expected cost to the government higher than either Type 1 or Type 2, and an expected economic cost higher than Type 2.  What it does minimise, by equalizing the prices and therefore the marginal costs of production using the two techniques, is the total production cost.  But that is not what we want to minimize under either of our interpretations of ‘best’.

It may come as a surprise that the government can do better than any of the approaches considered so far.  The key here is that the government can hold a single auction without committing itself to set a common strike price.  This is sometimes termed a product mix auction (8), the principle being applicable to differentiated goods or to a common good that can be produced in more than one way. Given that, based on our assumptions, each firm’s bid reflects its actual costs, the set of bids received in an auction provides the government with a lot of cost information.  It can use that information to choose strike prices for each technique according to its aim.

If the aim is to minimise the cost to the government, the problem to be solved after holding the auction is:

$\min p_1q_1 + p_2q_2\qquad(E16)$

Proceeding as above, albeit without needing at this stage to consider the expectation, we obtain:

$q_1 = \dfrac{Q}{2} - \dfrac{c_1 - c_2 + x_1 - x_2}{4}\qquad(E17)$

Note that we  do not ignore the terms in $x_1,$ and $x_2,$; their values have effectively been revealed by the auction, so at this stage we are dealing with actual values, not with the expectation of a formula containing variables.  Using E17 we can infer formulae for $p_1,\:p_2$ and $q_2,$, all of which contain $x_1,$ and $x_2,$, and for the cost to the government for the particular values of $x_1,$ and $x_2,$ which is:

$p_1q_1+p_2q_2=\dfrac{Q^2}{2}+\dfrac{Q(c_1+c_2}{2}-\dfrac{(c_1-c_2)^2}{8}-\dfrac{x_1^2+x_2^2}{8}\qquad(E18)$

For purpose of comparison with our earlier results, especially from Auction Type 1, we want the expectation of E18 over the range of possible values of $x_1,$ and $x_2,$, which is:

$\dfrac{Q^2}{2} + \dfrac{Q(c_1 + c_2)}{2} - \dfrac{(c_1 - c_2)^2}{8} - \dfrac{2k^2}{24} =$ 10,192    $(E19)$

We can also calculate the expectation of the economic cost which is 9,326.

For this expected outcome we require Auction Type 4:

Invite bids from techniques 1 and 2, and using the results of the auction, set the strike prices for each technique at levels which a) are just sufficient to bring forth total production $Q,$ = 100 and b) among the combinations of strike prices which satisfy (a), minimise cost to the government.

If the aim is to minimise economic cost, the problem to be solved, again after holding the auction, is:

$\min \Big[(c_1 + x_1)q_1 + \dfrac{q_1^2}{2} + (c_2 + x_2)q_2 + \dfrac{q_2^2}{2} + \lambda (p_1q_1 + p_2q_2)\Big]\qquad(E20)$

Proceeding as above, this can be solved to obtain:

$q_1 = \dfrac{Q}{2} - \dfrac{(1 + \lambda )(c_1 - c_2 + x_1 - x_2)}{2(1 + 2\lambda )}\qquad(E21)$

The expected cost to the government is 10,604 and the expected economic cost is 9,037.  These expected outcomes are achieved by Auction Type 5:

Invite bids from techniques 1 and 2, and using the results of the auction, set the strike prices for each technique at levels which a) are just sufficient to bring forth total production $Q,$ = 100 and b) among the combinations of strike prices which satisfy (a), minimise total economic costs.

Table 1 below summarises the above results.

What can be inferred from these results?

Firstly, the classification of auction types reveals an ambiguity in the term ‘technology-neutral’.  Should we reserve that term for type 3 with a single auction and a single strike price?  Or should we also include types 4 and 5, the product-mix auctions, on the grounds that they have a single auction embracing both technologies?  The assertion is often made that climate change policies should be technology-neutral, often I suspect without awareness of the possibility of a product-mix auction.

Secondly, the choice of aim is important.  Comparing auction types 1 and 4 on the one hand with types 2 and 5 on the other, the former result in the cost to government being c 400 (3.8%) lower, while the latter result in the economic cost being c 300 (3.2%) lower.

Thirdly, although the product-mix auctions 4 and 5 give the best results, the gains they offer relative to the best alternatives are very small, at least given the parameter values in our central case.   Focusing on expected economic cost, type 5 yields an advantage of only 17 (0.2%) over type 2.  Table 2 below shows the effects on expected economic cost of various changes in parameters, variation 0 being our central case.  Variations 1-3 show that changes in $\lambda,$ have little effect on the advantage of type 5 over type 2, and variation 5 shows that a change in $c_2,$ also has little effect.  However, variations 4 and especially 6 show that larger values of $k,$, the half-width of the random variability in production cost, result in larger advantages of type 5 over type 2.

It can be seen that type 5 is superior to types 2 and 3 in all cases except variation 2, when with $\lambda,$ = 0 the expected economic costs with types 3 and 5 are equal.  However, the advantage of type 5 over the better of types 2 and 3 is never more than 0.5% (variation 4).

Given that a product-mix auction may be perceived as introducing additional complexity for limited benefit, it is of interest to compare the outcomes of type 2, the technology-specific approach, and type 3, the technology-neutral common price approach.  Looking at variations 0 and 4, and then at 5 and 6, it can be seen that, other things being equal, changes in $k,$ do not affect the outcome of type 2, but do affect that of type 3 (because as we have seen of the squared terms in $x_1,$ and $x_2,$).  As a consequence, increased variability in production cost (higher $k,$) tends to favour type 3 over type 2, the difference in the case of variation 6 being 2.1%.

Comparing variations 0, 1, 2 and 3, it can be seen that the relative outcomes of types 2 and 3 are also affected by $\lambda,$ with higher values tending to favour type 2.  However, only with $\lambda,$ = 0.4  in the case of variation 3 does the difference exceed 1%, and many empirical estimates of $\lambda,$ are considerably lower than that.  Browning (1976) estimated its value for US taxes on labour income as in the range 0.09 to 0.16 (9).  Harrison, Rutherford & Tarr (2002), in a study of Chile, found a value of 0.076 for VAT and 0.185 for a tariff (10).  Auriol & Warlters (2009) found an average value across 38 African countries in the range 0.19 to 0.21 (11).

Conclusion

We have considered a limited range of scenarios.  Alternative scenarios might include any or all of the following features: more than two available techniques; different production functions; larger firms with scope for gamesmanship; government providing subsidies rather than meeting full costs.  The sorts of results we have obtained might not carry over to all scenarios.

However, it has been shown that, if a technology-neutral auction is taken to mean an auction with a common strike price for different techniques for producing the same good, it will not necessarily yield more economic welfare than a technology-specific auction.  For the scenarios considered, however, the advantage of the technology-specific auction is very small given likely ratios of the excess burden of tax to the direct burden.

It has also been shown that a suitably designed product-mix auction, which can be considered technology-neutral in the sense that a single auction embraces alternative techniques, can achieve more economic welfare than any other auction type.  However, the advantage over the best alternative auction type, in all the cases we have considered, is rather small.

Although the single auction common price approach is generally sub-optimal, from a welfare perspective it is no more than very slightly sub-optimal in any of the cases we have considered, except that in which the excess burden of tax ratio is very high.  This suggests that a government aiming to maximise welfare may be unlikely to go far wrong with a technology-neutral approach.

Our most significant finding is a rather obvious one.  Whether the auction type is technology-neutral or technology-specific, the choice of aim matters.  An auction designed to minimise cost to the government will result in a sub-optimal outcome from a welfare perspective.  Equally, an auction designed to maximise welfare will mean a higher cost than necessary to the government.  The difference in both cases may be of the order of 3-4%.

Notes and References

1. Fabra N & Montero J-P (2022) Technology Neutral vs. Technology Specific Procurement  MIT Centre for Energy and Environmental Policy Research   https://ceepr.mit.edu/wp-content/uploads/2022/03/2022-005.pdf  See especially pp 6-15
2. Wikipedia – Excess burden of taxation https://en.wikipedia.org/wiki/Excess_burden_of_taxation
3. For a more formal specification of the relation between firm-level and aggregate production costs see Fabra & Montero, as 2 above, p 6
4. Obtained by differentiating E1 and E2 with respect to q1 and q2 respectively.
5. Readers familiar with elementary algebra and calculus should be able, from the information given, to confirm all my results, although the algebra is in some cases rather tedious.
6. Wikipedia – Continuous uniform distribution – Moments https://en.wikipedia.org/wiki/Continuous_uniform_distribution#Moments  See formula for second moments and put a = -k, b = k.
7. To confirm that this value of q1 corresponds to a minimum, note that the second derivative is 4 > 0.
8. The idea appears to be due to Paul Klemperer: see the first version (2008) of his paper on the topic at https://www.nuffield.ox.ac.uk/economics/papers/2009/w6/BoeTarp28_7_09.pdf
9. Browning E K (1976)  The Marginal Cost of Public Funds  Journal of Political Economy Vol 84(2) p 283  https://www.jstor.org/stable/1831901
10. Harrison G W, Rutherford T F & Tarr D G (2002)  Trade Policy Options for Chile: The Importance of Market Access  The World Bank Economic Review Vol 16 No. 1 p 57  https://documents1.worldbank.org/curated/en/760701468001806330/pdf/35057.pdf
11. Auriol E & Warlters M (2009)  The Marginal Cost of Public Funds and Tax Reform in Africa  Toulouse School of Economics Working Paper Series 09-110   https://www.tse-fr.eu/sites/default/files/medias/doc/wp/dev/wp_dev_110_2009.pdf