# The Valuation of Artwork as an Exact Science

Combining conventions for pricing artworks with mathematical reason, a formula is devised and applied to individual artworks within an exhibition.

Blackboards, chalk, workings.
Performer: Dr Deborah Lockett, University of Leeds.

The Valuation of Artwork as an Exact Science

Though there is an argument that artworks should exist only for their own sake and be consumed intellectually rather than possessively, there is an extant and still relevant culture of ownership and indeed mass collection with which the contemporary practicing artist will inevitably engage, in some way, at some stage.

“Pricing works is a tricky business – essentially a work is only worth what someone is prepared to pay for it, it has no inherent value.” 

Many methods exist for divining the elusive ‘right’ amount to charge for the fruits of your endeavour, with myriad results. As such, it is easy to presume there is no reliable system, but as part of “Next to Nothing” my colleague and I will attempt to provide solace and solutions with the following table of algebraic variables and parameters.

To follow mathematical convention, let X represent the unknown value of the work, and so on:

 M = Cost of materials E = Cost of transport/travel/delivery V = Scrap value of materials F = Framing (if appropriate) L = Labour (artist’s own or delegated) R = Rate of commission (to gallery or institution) S = Skill/craftsmanship (artist’s own or delegated) A = Prestige by association or accumulative sales H = Height Δ = Hype/publicity/controversy W = Width Λ = Temporality/permanence D = Depth Ω = Eventual location/site T = Time (Duration) Φ = Perceived wealth of the buyer N = Size of edition Θ = Economic climate/fashion Γ = Format (if time-based) P = Parameter of multiplication

A methodology of formulae and proofs can and shall be applied to the work exhibited (and all other works), to prove that a value can be assigned to that which is defined by it’s intangible nature and subsequent inherent charm (Ψ).

 Wood, R. 2011. Degree Show Price Guidelines 2011, Chelsea College of Art and Design, UAL.

 Black Dogs Present: Next to Nothing. 15th Sept – 1st Oct 2011, The Light, Leeds.

 Dr Deborah C. Lockett, Research Assistant, Dept of Pure Mathematics, University of Leeds.

Conclusion:

1: Definitions of the notation for the
parameters: the unknown quantities (X,Y,Z) to be calculated from the known
quantities (others). Our first equation expresses X in terms of Y and Z (and R). Our aim is to produce equations expressing the unknowns Y,Z in terms of the knowns. Some of our parameters are not naturally numbers. We call these the 'secondary factors' and show a rudimentary way to attribute numerical values to these using suitably defined scales.

2: A straightforward algebraic equation for calculating the total production cost (Y), followed by some details of how parts of the production cost calculation can is put into formal mathematical language. Also: a linear equation attempting to model the differing cost of individual art pieces depending on the size of the edition (N).

3: An initial attempt at producing an equation to find our secondary subjective factor (Z). In this model, we have assumed that all factors are linear*, and the coefficients are weighting factors (to try to model the fact that some secondary factors are more influential than others). We assigned values to these weighting factors after discussions with other artists.

*However, note that it is highly unlikely that these factors really are all linear, so this sort of multivariable linear equation is probably not the best sort of model! To produce a more accurate model we'd need to research the influences much more, and probably adjust our scales for the factors.

Finally, an attempt to give a formal equation that allows for final adjustments to our calculated value X; based on the question "is the calculated cost X reasonable?"
[Summary: Dr.D.E.Lockett, 2011]

4: Actual calculations to solve our equations (for X) for a given artwork:

Have it your way’, Tom Railton, 2011.
Valued at £619.52 at the time of exhibition.