HOW SPACE MINING MISSIONS WILL DISRUPT MINERAL MARKETS AND CONTRACTS Ben Gilbert and Ian Lange This project received seed funding from the Dubai Future Foundation through Guaana.com open research platform. Executive Summary As the prospect for mining nearby asteroids for minerals that are valuable on Earth becomes more technically feasible, the business case is becoming more important to understand. Indeed the recent acquisitions of Deep Space Industries and Planetary Resources, the two companies most known for plans to mine asteroids, by firms who have announced plans to reduce those activities highlight the concerns with the business case. One main concern with the business case for space mining: high uncertainty about the price a space mining company can expect to receive for its asset. Current discussions around the potential revenues that come from mining a nearby asteroid generally take the current market price of the mineral in question as the price the mining company would receive. However, once it is clear that the space mining company is bringing a large amount of a mineral to Earth, the market price will fall. This research presents a model of mineral markets which is perturbed by a space mining entrant. We show how to calculate the changes in market equilibrium that arise when the buyers and other producers of the mineral respond to the entry of the space mining company. Our model begins by assuming that the space mining company would face a large up-front fixed cost in order to access an asteroid and set up mineral extraction and processing facilities. In this setting, in order to be profitable the company must be able to leverage the sheer abundance of minerals on the asteroid by achieving a relatively low marginal extraction cost. A market entrant with relatively low marginal extraction costs and abundant quantities will be able to exert market power, but may or may not be profitable due to the size of the up-front fixed costs. Even with market power, the space mining company’s entry into the market will drive down prices. As a result of the fixed cost and reduced prices, the space mining company looks for a buyer to sign a contract with in order to hedge their revenue against potential changes in the market price due to their entry into the market. Main results or outputs This project set out to derive the optimal contract for a space mining company and a mineral buyer to sign in order to facilitate space mining. This is an important topic as funding a large new project such as space mining will have many impacts on mineral markets, especially considering the strategic response of incumbent mining producers. Our model is based on the standard practices in the mining industry for procuring minerals and financial institutions demand for risk mitigation when providing financing for a project. In order to provide a rigorous analysis and discussion of the conditions for a space mining firm to enter a new market, we started with a standard firm entry model in the economics literature. These models are game theoretic in nature in that it starts with a market equilibrium and analyzes how the market would change if the space mining firm entered. However, the space mining firm must predict how the current market participants would respond to its entry in order to decide whether entry will provide it with a profit.

The model assumes that a space mining firm has higher fixed costs of extracting the resource but lower marginal costs than terrestrial firms. The smaller terrestrial firms have higher marginal costs but lower fixed costs in the model. Combined the terrestrial firms play their best strategy to the entering space mining firm who will have market power due to the low marginal costs and large amount of resources available to them. We first summarize the model, and then present the model in somewhat more detail. Model summary:

1) There are two parts to the model analyzing incentives for market entry of a space mining firm: the market conditions for entry, and the contracting conditions for entry.

2) Market conditions: a. If the mineral is abundant enough to make the business case for space mining, then

the supply from space will affect the market price on earth. In other words, the space miner will have “market power”. This market power can only drive the price down, not up, which makes the business case more difficult.

b. If the space mining firm makes the “business case” based on current market prices, without taking into account their post-entry impact on the market, profits will be lower than expected and the firm may go out of business. “Business case” analyses often only consider the firm’s cost structure and take price scenarios as given.

c. If the space mining firm rationally predicts its own post-entry impact on the price, the business case will depend on the shape of the terrestrial demand and supply functions in addition to the cost structure of the space mining. The scenarios in which the firm wants to enter the market are more limited.

d. We outline three scenarios: (1) the space mining firm will benefit from entering the market without a firm commitment from buyers (high demand, low terrestrial supply, low fixed costs of entry and operation), (2) the space mining firm will never enter the market without subsidized costs (low demand, high terrestrial supply, high fixed costs of entry and operation), and (3) the space mining firm will only enter the market with contractual guarantees from buyers (high fixed costs of entry, low fixed costs of operation).

3) Contracting conditions: a. Under “market conditions” scenario (3), we derive the optimal contracting

structure. We analyze the case in which the space miner might customize its supply chain specifically for its dedicated buyer, while the buyer might breach the contract after the space miner has initiated production.

b. Parties have one direct mechanism and two indirect mechanisms to prevent breach. The direct mechanism is a stipulated damage clause – a fee that the contract specifies the buyer must pay the seller upon breach. The indirect mechanisms are the space miner’s investments in supply chain customization, and their ability to stay in business or not if the buyer breaches contract.

c. If the space miner customizes the supply chain for a specific buyer, both parties will prefer renegotiation and continued trade over a complete contract breach.

d. If a buyer breach drives the space miner bankrupt, the buyer will be worse off because prices will rise.

e. Stipulated damage clauses should therefore either be zero or extremely large in order to prevent breach; no damage clause is needed if a breach will drive the space miner bankrupt, because the buyer needs the space miner’s supply.

f. If the space miner can stay in business after a breach, stipulated damage clauses should be extremely large in order to give the space miner assurances that their customization investments will not go to waste.

A Model of Market Entry Incentives and Optimal Contracting for Space Mineral Supply We present a model in two parts. The first part uses basic economic principles to articulate the incentives for a space mining firm to sell into a pre-existing terrestrial market and compete with incumbent firms for available buyers. The model establishes the conditions for a range of possible scenarios for market entry and competition. Under some conditions the space mining firm will not enter the market without long-term contractual guarantees from a large buyer or group of buyers. The second part of the model investigates the strategic properties of these contractual guarantees. Specifically we ask whether a contract can be written that (a) survives subsequent incentives to breach the contract, and (b) induces optimal investments by the space miner. We focus on relationship-specific investments between the space miner and the buyer, such as customization of the supply chain to meet a particular buyer’s needs. Our setting differs from the previous contracting economics literature in terms of the timing of entry and the outside options of the two parties. Part I: Market Entry Incentives Consider a thickly-traded terrestrial spot mineral market in which, initially, no space mining firms exist. We represent the potential market power that a space miner could exercise with a downward-sloping residual demand function for its product denoted by 𝑅(𝑃) where 𝑃 is the price paid by buyers. This assumption applies equally well regardless of whether the existing spot market is perfectly competitive or better approximated by a game-theoretic Cournot-Nash oligopoly; for our purposes it only matters that the entrant would face a downward-sloping residual demand function for its product. Take a perfectly competitive market as an example. We can derive 𝑅(𝑃) from the downward-sloping aggregate demand function 𝐷(𝑃) consisting of price-taking buyers, and the upward-sloping aggregate supply function 𝑆(𝑃) composed of pre-existing price-taking firms (not including the space miner). If the space miner enters, the space miner is large enough to determine the market price 𝑃 through its supply decisions. At that price the terrestrial suppliers offer quantity 𝑆(𝑃) to the market, price-taking buyers purchase 𝐷(𝑃), and the space miner sells the residual demand, 𝑅(𝑃) = 𝐷(𝑃) − 𝑆(𝑃).1 In what follows it will be convenient to work with the inverse of the residual demand function which we denote by 𝑃𝑅(𝑄𝑆𝑀) = 𝑅−1(𝑃). Without the space miner in the market, the competitive price is determined by the intersection of supply and demand of the incumbent firms and buyers, i.e., where 𝑆(𝑃𝐶) = 𝐷(𝑃𝐶) and 𝑃𝐶 denotes the competitive market price with no space mining firm. This is depicted in Figure 1. We assume that the space miner faces two kinds of fixed costs: a very large one-time entry cost denoted by 𝐹𝑒, and an (also potentially very large) annual operating or overhead cost whose present value we

1 In this case the space miner is acting as a monopolist competing against a competitive fringe. Note that if we were to model the existing market as a Cournot oligopoly, the space miner would still face a downward-sloping residual demand upon entry. This is true regardless of whether the firm enters as an imperfectly competitive Cournot player or a first-mover in a Stackelberg game, as long as the space miner is a large enough player relative to existing market size to exert market power.

denote by 𝐹𝑜. These fixed costs are in addition to the variable costs that depend on the quantity of the mineral that is mined, processed and delivered from space. The one-time entry cost 𝐹𝑒 includes all of the initial capital costs associated with constructing the mining facilities in space, constructing or modifying transportation infrastructure such as launch facilities and receiving terminals that will be used over the life of the venture to manage deliveries of equipment, workers, and mineral quantities, the costs of transporting the initial capital equipment to the space mining facilities, etc. The annual operating costs include the maintenance of the substantial capital equipment, the overhead of operating the business, etc. These fixed entry and operating costs are likely to be larger than those associated with opening and operating a terrestrial mine, at least for the first few space mining ventures, simply because of the physical challenges of operating in space. They will also be heavily influenced by the decision of which asteroid or celestial body to target for mining operations because these bodies differ in their distance from earth, velocity, and abundance of minerals. The space miner also faces variable costs 𝐶(𝑄𝑆𝑀) that depend on the quantity 𝑄𝑆𝑀 that the space miner extracts, processes, and delivers to the terrestrial market. We assume 𝐶(⋅) is an increasing, convex, continuously differentiable function such that 𝐶′ > 0, 𝐶′′ > 0. This reflects the fact that once the fixed cost capital investments are made, it may be inexpensive to bring a tiny quantity of the mineral back to earth, but these costs increase at an increasing rate as more fuel is required and larger, more powerful equipment is required to extract, process, and transport larger payloads. When making the entry decision, the space miner calculates the profit-maximizing quantity it would produce and the maximal profits it would earn at that quantity. In other words, they find the 𝑄𝑆𝑀

⋆ that maximizes

𝜋(𝑄𝑆𝑀) = 𝑃𝑅(𝑄𝑆𝑀) ⋅ 𝑄𝑆𝑀 − 𝐹𝑜 − 𝐹𝑒 − 𝐶(𝑄𝑆𝑀) and evaluate whether 𝜋(𝑄𝑆𝑀

⋆ ) > 0. The first order condition for a profit-maximizing quantity are the following:

𝑃𝑅′ (𝑄𝑆𝑀

⋆ ) ⋅ 𝑄𝑆𝑀⋆ + 𝑃𝑅(𝑄𝑆𝑀

⋆ ) − 𝐶′(𝑄𝑆𝑀⋆ ) = 𝑀𝑅 − 𝑀𝐶 = 0

where 𝑀𝑅 and 𝑀𝐶 denote marginal revenue and marginal cost, respectively. We can now evaluate whether 𝜋(𝑄𝑆𝑀

⋆ ) > 0, or equivalently

𝜋(𝑄𝑆𝑀⋆ )

𝑄𝑆𝑀⋆ = 𝑃𝑅(𝑄𝑆𝑀

⋆ ) −𝐹𝑜 + 𝐹𝑒 + 𝐶(𝑄𝑆𝑀

⋆ )

𝑄𝑆𝑀⋆ > 0

For notational ease we denote the term 𝑃𝑅(𝑄𝑆𝑀

⋆ ) = 𝑃𝑆𝑀⋆ which is the price that the space miner sets in

the market when selling its optimal quantity 𝑄𝑆𝑀⋆ . The second term is the Average Total Cost of

producing 𝑄𝑆𝑀⋆ , or Ex Ante ATC, that the space miner perceives before entering the market:

𝑃𝑆𝑀

⋆ − 𝐸𝑥 𝐴𝑛𝑡𝑒 𝐴𝑇𝐶 > 0 If the expected price per unit that the space miner can receive for the mineral exceeds the average total cost of producing each unit, the space miner will enter the market. There is no need for a complicated long-term contract with a buyer beyond standard contracts that are primarily used to coordinate the timing and location of deliveries and formalize the chosen price. Suppose the space miner enters the market but subsequently their residual demand shifts down, either because aggregate market demand declines or other suppliers have increased output. The key

distinction between 𝐹𝑒 and 𝐹𝑜 is that after entering the market, 𝐹𝑒 is sunk. If the space miner is already in the market and 𝑃𝑆𝑀

⋆ falls below the Ex Ante ATC, the space miner may continue to operate as long as

𝑃𝑆𝑀⋆ >

𝐹𝑜 + 𝐶(𝑄𝑆𝑀⋆ )

𝑄𝑆𝑀⋆ = 𝐸𝑥 𝑃𝑜𝑠𝑡 𝐴𝑇𝐶

This scenario is depicted in Figure 1. The space miner makes an operating profit but does not fully cover the sunk entry cost. Importantly, under the scenario in Figure 1, if the nascent space mining firm were to evaluate its business prospects taking the prevailing market price as given (𝑃𝐶), the firm may mistakenly conclude that entry is profitable because 𝑃𝐶 > 𝐸𝑥 𝐴𝑛𝑡𝑒 𝐴𝑇𝐶. This would ignore the fact that, despite the market power they exert upon entry, buyers have declining marginal demands such that the space miner cannot charge any price above the 𝑅(𝑃) curve for any possible level of output.

Figure 1: Competitive Mineral Market with Large Potential Space Mining Entrant

The analysis in this section shows that even with an abundant resource and the market power to determine the market price, there is a range of possible prices over which the space miner would not rationally enter the market (𝑃𝑆𝑀

⋆ < 𝐸𝑥 𝐴𝑛𝑡𝑒 𝐴𝑇𝐶). This range is determined by the pre-existing supply and demand conditions that dictate the position of the space miner’s residual demand function 𝑅(𝑃), and by the fixed and variable cost structure of the space mining enterprise. Within the range 𝑃𝑆𝑀

⋆ <𝐸𝑥 𝐴𝑛𝑡𝑒 𝐴𝑇𝐶, if the space miner had entered the market because of some mistaken beliefs, or if market conditions changed ex post, there is also a range of prices over which the space miner will stay in the market (𝐸𝑥 𝑃𝑜𝑠𝑡 𝐴𝑇𝐶 < 𝑃𝑆𝑀

⋆ < 𝐸𝑥 𝐴𝑛𝑡𝑒 𝐴𝑇𝐶), and a range over which they will exit and the venture will fail (𝑃𝑆𝑀

⋆ < 𝐸𝑥 𝑃𝑜𝑠𝑡 𝐴𝑇𝐶). These cutoff points are relevant for defining the boundaries of the contracting problem we explore in the next subsection. Although over these price ranges the space

miner will not rationally enter the market given existing demand, there may be a potential or nascent new buyer or buyers who are not willing to pay the current market price 𝑃𝐶 but may have an interest in contracting for supply directly from the space mining firm at some negotiated price 𝑃𝐵 where 𝑃𝑆𝑀

⋆ <𝑃𝐵 < 𝑃𝐶 . The challenge is to structure such a contract so that the buyer will not renege after the space miner enters, allowing the market to drive the price down to 𝑃𝑆𝑀

⋆ and potentially allowing this nascent buyer to purchase the mineral from a terrestrial supplier at the new, lower market price. We explore this contracting problem in the next section. Part II: Buyer and Space Miner Contracting Consider a large potential buyer who is contemplating a major business venture for which this mineral is a critical input. This buyer would like to purchase a quantity 𝑄𝐵 that is in the neighborhood of 𝑄𝑆𝑀

⋆ . The buyer’s venture has an expected value per unit of the mineral input 𝑣 that is below the ex ante competitive price, but larger than the space miner’s Ex Ante ATC, or 𝐸𝑥 𝐴𝑛𝑡𝑒 𝐴𝑇𝐶(𝑄𝐵) < 𝑣 < 𝑃𝐶 . However, there is some price 𝑃𝐵 where 𝐸𝑥 𝐴𝑛𝑡𝑒 𝐴𝑇𝐶(𝑄𝐵) < 𝑃𝐵 < 𝑣 < 𝑃𝐶 at which both the buyer’s venture and the space miner’s venture become profitable. There is therefore a potential gain from this buyer and the space miner entering a side contract outside the competitive market. The solution to this contracting problem will depend on the buyer’s and the seller’s outside options – what they can earn in their next best opportunity outside the contract. However, these outside options differ depending on whether the space miner has already sunk the fixed entry cost. For example, in the scenario depicted in Figure 1, the buyer may want to breach the contract after the space miner has sunk the fixed entry cost and pay the new market price 𝑃𝑆𝑀

⋆ rather than the higher contracted price 𝑃𝐵.2 The buyer anticipates that the space miner will stay in the market as long as 𝑃𝑆𝑀

⋆ > 𝐸𝑥 𝑃𝑜𝑠𝑡 𝐴𝑇𝐶. This may distort the pre-entry contracting incentives as the space miner will be wary of this potential breach. Either a contract must be written that anticipates and avoids such outcomes, or the parties will not enter the contract ex ante, and gains from trade will not be realized. In what follows, we extend the work of Spier and Whinston (1995)3 on contract breach with damage payments to the case in which threats to the contract come from within the contracting relationship rather than from external low-cost entrants. We will assume that there is uncertainty in the competitive spot market which translates an uncertain residual demand curve and optimal price 𝑃𝑆𝑀

⋆ . Effectively we treat this price as being

distributed 𝑃𝑆𝑀⋆ ~ [𝑃𝑆𝑀

⋆ , 𝑃𝑆𝑀⋆ ] according to some continuous cumulative distribution function 𝐺(𝑃𝑆𝑀

⋆ ) with

a probability density function 𝑔(𝑃𝑆𝑀⋆ ) and 𝑃𝑆𝑀

⋆ < 𝐸𝑥 𝐴𝑛𝑡𝑒 𝐴𝑇𝐶. The buyer and the space miner will therefore not know whether the buyer has an incentive to breach their contract until after the entry and startup investments have been made. In a bilateral contract of the scale considered here, we would expect the buyer and seller to engage in some degree of customization of their supply chain in order to meet each other’s particular specifications. For example, the location or size of receiving terminals or the specifications on the refinement of the mineral ore may be tailored to the specific relationship between the buyer and the seller rather than the standardized specifications that may hold in the larger spot market. In the

2 Under the scenario in which the buyer reneges and buys the mineral from the larger market, 𝐷(𝑃) will shift out by the amount of this large buyer’s demand, which also shifts 𝑅(𝑃) outward and raises the optimal 𝑄𝑆𝑀

⋆ and 𝑃𝑆𝑀⋆ .

We consider the relevant case in which the new 𝑃𝑆𝑀⋆ is still below the Average Total Cost curves of the space miner.

3 Spier, K. E., & Whinston, M. D. (1995). On the efficiency of privately stipulated damages for breach of contract:

entry barriers, reliance, and renegotiation. The RAND Journal of Economics, 180-202.

industrial organization literature, these are called relationship-specific investments; if the contracting relationship dissolves the parties may still be able to transact in the larger spot market, but any investments in supply-chain customization that were specific to the needs of this particular buyer and seller are worthless to a generic firm in the spot market. In some cases, these relationship-specific investments can make the contract more stable by reducing the value of exchange outside the relationship. In this case they are sometimes referred to as reliance expenditures. The important feature of these reliance expenditures are that they are observable to the buyer and seller but not verifiable in court; any explicit contract over the level of these investments is extremely costly or impossible to enforce and so while they add value to the relationship they are not part of the written contract. Part of the challenge between the parties is to manipulate the incentives to invest in 𝑟. For simplicity, we will assume the space miner makes reliance expenditures 𝑟 that reduce the Ex Post ATC to 𝑐𝑠(𝑟) < 𝑐𝑜 only for sales to this specific large-scale buyer, with 𝑐𝑠(0) = 𝑐𝑜, 𝑐𝑠

′(𝑟) < 0. In order to focus on the division of surplus rather than the marginal quantity decision, we express all terms on a per-unit output basis and denote 𝑓𝑒 = 𝐹𝑒 𝑄⁄ . For ease of notation, denote the Ex Post ATC as 𝑐𝑜. In order to deter a breach the parties may include a damage clause in the contract, or an amount of money Φ𝐵 that the buyer will be required to compensate the seller in the event of a breach. The timing of the game is as follows (Figure 2): the buyer and the seller meet before either has entered the market and agree on a price 𝑃𝐵 and damage clause Φ𝐵. The firms then enter, with the space miner incurring the fixed entry costs. The space miner then invests in reliance expenditures which reduces their cost of producing and selling for this specific large buyer. Once entry and investments are made, uncertainty about the terrestrial spot market, and hence the space miner’s residual demand curve, is realized. The buyer and seller can then calculate the price 𝑃𝑆𝑀

⋆ at which the space miner could sell to the spot market if the contract is breached, which, because of the space miner’s market power, is also the price that the large buyer would pay in the spot market if the contract is breached. The buyer then decides whether or not to breach and/or renegotiate with the space miner. Finally, production occurs, 𝐹𝑜 and 𝑐𝑜 or 𝑐𝑠(𝑟) are incurred, and payments are exchanged.

Figure 2: Timing of the Contracting Game Socially Optimal Entry and Investment Under the assumptions outlined above, the socially optimal outcome is for the buyer and space miner to enter and perform according to their contract. The total surplus from this outcome is equal to the buyer’s value net of the seller’s costs of reliance investments as well as entry, operating, and production costs:

𝑆(𝑟) = 𝑣 − 𝑐𝑠(𝑟) − 𝑓𝑒 − 𝑟

The socially optimal reliance investment level 𝑟⋆ maximizes the surplus from the relationship, as given by the first order conditions

𝑆′(𝑟) = −𝑐𝑠′(𝑟) − 1 = 0

If the buyer breaches, even if the space miner remains in the market they incur higher production and operating costs of 𝑐𝑜 ≥ 𝑐𝑠(𝑟) in order to sell on the spot market rather than within the customized relationship, whereas the change in the price to 𝑃𝑆𝑀

⋆ < 𝑃𝐵 is zero-sum for the buyer and seller. Breach and Renegotiation Once the buyer is in the market, they have an incentive to breach if the alternative spot market price they could pay is below the contract price 𝑃𝐵. If the buyer breaches, the space miners costs rise to 𝑐𝑜 ≥𝑐𝑠(𝑟). Therefore if the realized 𝑃𝑆𝑀

⋆ < 𝑐𝑜, they space miner will go bankrupt and exit the market. In this case, the buyer will be stuck paying the competitive market price 𝑃𝐶 > 𝑣, and their venture would also go bankrupt and exit the market. Therefore if 𝑃𝑆𝑀

⋆ < 𝑐𝑜, the buyer will not breach the contract. The ex post payoff to the buyer is 𝑣 − 𝑃𝐵 and the ex post payoff to the space miner after entry costs and reliance expenditures is 𝑃𝐵 − 𝑐𝑠(𝑟), creating an ex post surplus of 𝑣 − 𝑐𝑠(𝑟). Let’s consider the alternative case with 𝑃𝑆𝑀

⋆ > 𝑐𝑜. In this case, the buyer’s ex post payoff is 𝑣 − 𝑃𝐵 by performing to the contract versus 𝑣 − 𝑃𝑆𝑀

⋆ − Φ𝐵 by breaching (the space miner stays in the market but the buyer must pay the stipulated damage clause. Therefore as long as Φ𝐵 > 𝑃𝐵 − 𝑃𝑆𝑀

⋆ the buyer prefers not breach. However, 𝑃𝑆𝑀

⋆ is uncertain at the time the contract is signed, so at best Φ𝐵 could be based on some forecast of it – we cannot simply set Φ𝐵 = 𝑃𝐵 − 𝑃𝑆𝑀

⋆ at the contracting stage. The inability to do so allows for some outcomes in which breach and renegotiation occur. Suppose the damage clause is set at too low a level and the ex post outcome is Φ𝐵 < 𝑃𝐵 − 𝑃𝑆𝑀

⋆ . In this case, the buyer prefers to breach the contract because 𝑣 − 𝑃𝑆𝑀

⋆ − Φ𝐵 > 𝑣 − 𝑃𝐵. Upon breach, the buyer must still find sellers and the space miner must still find buyers. Given a choice between selling to the large pool of buyers in the spot market versus selling to the initial buyer for which they’ve customized their supply chain, the space miner may still prefer to sell to the initial buyer. The ex ante reliance expenditures have reduced the space miner’s costs for selling to the initial buyer, so the space miner will then have an incentive to offer some additional surplus to the original buyer in order to continue their relationship. The ex post surplus is 𝑣 − 𝑐𝑜 in the breached outcome versus 𝑣 − 𝑐𝑠(𝑟) if the relationship is renegotiated. Relative to the contract breach, there is a marginal “surplus” (or more properly, an avoided social loss) of 𝑐𝑜 − 𝑐𝑠(𝑟) available if the parties renegotiate. We suppose there is a Nash bargaining solution in which the buyer has bargaining weight 𝛼 ∈ [0,1] and receives a transfer from the space miner of 𝛼(𝑐𝑜 − 𝑐𝑠(𝑟)) in order to continue purchasing the mineral from the space miner. The buyer will purchase the mineral at the new 𝑃𝑆𝑀

⋆ and pay the damage clause for exiting the contract, but will allow the space miner to utilize the customized components of the supply chain and incur costs of 𝑐𝑠(𝑟) < 𝑐𝑜. The ex post payoff to the buyer in this case is 𝑣 − 𝑃𝑆𝑀

⋆ − Φ𝐵 + 𝛼(𝑐𝑜 − 𝑐𝑠(𝑟)) while the ex

post payoff to the space miner is 𝑃𝑆𝑀⋆ + 𝜙𝐵 − 𝑐𝑠(𝑟) − 𝛼(𝑐𝑜 − 𝑐𝑠(𝑟)) = 𝑃𝑆𝑀

⋆ + 𝜙𝐵 − (1 − 𝛼)𝑐𝑠(𝑟) −

𝛼𝑐0. In the presence of renegotiation, the buyer will only prefer to breach and renegotiate if

𝑣 − 𝑃𝐵 < 𝑣 − 𝑃𝑆𝑀⋆ − Φ𝐵 + 𝛼(𝑐𝑜 − 𝑐𝑠(𝑟))

𝑃𝑆𝑀⋆ < 𝑃𝐵 − Φ𝐵 + 𝛼(𝑐𝑜 − 𝑐𝑠(𝑟))

These incentives to breach on the part of the buyer, as a function of the random variable 𝑃𝑆𝑀

⋆ are illustrated in Figure 3.

Figure 3: Incentives to Breach Based on 𝑃𝑆𝑀

⋆

One key result of this analysis is that in order to prevent breach, the stipulated damage clause should either be zero (when breach is indirectly deterred by the space miner’s potentially bankruptcy, 𝑃𝑆𝑀

⋆ <𝑐𝑜) or very high (when breach is directly deterred by the damage clause). For example, because of the potential for renegotiation, this analysis implies that the damage clause required to prevent breach is larger than was discussed earlier without renegotiation: Φ𝐵 ≥ 𝑃𝐵 − 𝑃𝑆𝑀

⋆ +

𝛼(𝑐𝑜 − 𝑐𝑠(𝑟)) > 𝑃𝐵 − 𝑃𝑆𝑀⋆ . As before, however, the size of this cutoff damage clause is not known ex

ante when the contract is signed. An additional problem created by this uncertainty over the cutoff damage clause is that setting Φ𝐵 based on a forecast of 𝑃𝑆𝑀

⋆ fails to induce the optimal ex ante reliance expenditures. This occurs because ex post realizations of 𝑃𝑆𝑀

⋆ may be lower than expected, triggering breach and renegotiation. If this happens with non-zero probability, this reduces the space miner’s ex ante incentive to make reliance expenditures whose value may be given up in ex post renegotiation. To see this, consider the space miner’s ex ante expected payoff:

𝐸(𝜋𝑆𝑀) = 𝐺(𝑐𝑜)(𝑃𝐵 − 𝑐𝑠(𝑟)) + ∫ [𝑃𝑆𝑀⋆ + Φ𝐵 − (1 − 𝛼)𝑐𝑠(𝑟) − 𝛼𝑐𝑜]𝑔(𝑃𝑆𝑀

⋆ )𝑑𝑃𝑆𝑀⋆

𝑃𝐵−Φ𝐵+𝛼(𝑐𝑜−𝑐𝑠(𝑟))

𝑐𝑜

+ [1 − 𝐺(𝑃𝐵 − Φ𝐵 + 𝛼(𝑐𝑜 − 𝑐𝑠(𝑟)))](𝑃𝐵 − 𝑐𝑠(𝑟)) − 𝑟 − 𝑓𝑒

The first order condition for the privately optimal reliance expenditure is given by

𝜕𝐸(𝜋𝑆𝑀)

𝜕𝑟= −𝑐𝑠

′(𝑟) [1 − 𝛼 (𝐺 (𝑃𝐵 − Φ𝐵 + 𝛼(𝑐𝑜 − 𝑐𝑠(𝑟))) − 𝐺(𝑐𝑜))] − 1 = 0

This implies that 𝑟 < 𝑟⋆ long as 𝛼 > 0 and 𝐺 (𝑃𝐵 − Φ𝐵 + 𝛼(𝑐𝑜 − 𝑐𝑠(𝑟))) ≠ 𝐺(𝑐𝑜), or in other words

the space miner underinvests in the value of the relationship if the buyer has non-zero bargaining power or the damage clause payment is not large enough. This result suggests that a particularly large stipulated damage clause can induce the optimal relationship-specific investment - specifically one large enough to drive the probability of breach to zero:

𝑃𝐵 − Φ𝐵 + 𝛼(𝑐𝑜 − 𝑐𝑠(𝑟)) = 𝑐𝑜

⟹ Φ𝐵 = 𝑃𝐵 − (1 − 𝛼)𝑐𝑜 − 𝛼𝑐𝑠(𝑟) Notice that this is larger than the damage clause that merely prevents breach in expectation. We have shown that in this context damage payments for breach are either zero or very large. Large damage clauses can induce optimal reliance expenditures on things like supply chain customization, which improve the value of the relationship but create incentives for underinvestment if they are not perfectly enforceable by courts. This result differs from previous contracting models in the literature which conclude that damage payments can be “too large” if there is some probability that breach is economically efficient. In more common settings, it may be that the gain from breach by one party is greater than the loss from breach for the other party. This creates an opportunity for the breaching party to compensate the other party, leaving them both better off after a breach. If a new firm enters with very low costs, for example, breach is efficient and renegotiation should be allowed. Extremely high damage clauses preclude this. In our case, when the contract is designed to induce entry by a new firm, renegotiation can only maintain existing surplus. Because no new surplus is created, maintaining the contract is always efficient. In this setting the damage clause can be very large – larger than needed to prevent a breach in expectation, and in fact large enough to reduce the probability of breach to zero. With abnormally large damage clauses, the space mining firm must be able to verify, before the contract is signed, that the buyer can actually afford to pay the stipulated damage payment should breach occur. Various mechanisms exist in financial markets for firms to verify this. For example, they could post a bond in advance of the project, or have an independent auditor verify the value of the buyer’s assets. Obstacles or changes of direction during the project Modeling contracts using game theory depends crucially on assumptions about what types of information are available to the contracting parties, or verifiable by the courts for contract enforcement. One party can take actions that are hidden to the other party, creating what’s known as a “moral hazard” problem. One party may have higher costs or less effective technology than they claim, creating what’s known as an “adverse selection problem”. One party could take actions that violate the letter or spirit of the contract and are observable to both parties but not verifiable by the courts. This creates an opportunity for one party to “hold-up” or take advantage of the other party. In our study, we focused on this third case through our model of customization investments. In the space mining context, it’s not clear which of these contracting dimensions is most crucial to the success of a given venture because of the absence of experience with space mining. We chose to model the “hold-up” problem because initial space mining ventures will involve new challenges that require all parties to exert enormous efforts that may be costly but not verifiable to contract enforcement courts. There may therefore be incentives by one party or another to expend these efforts sub-optimally in order to reduce costs. However, there are multiple dimensions to this contracting problem that were left unexplored, including various combinations of moral hazard, adverse selection, and hold-up. The second major challenge is that numerical estimates for many of the parameters of the model do not exist, again because there is no experience on which to base any parameter estimates. Because of this, the model remains in a stylized form. The contribution of the model is that we show how to calculate these analyses and predict the qualitative outcome for a range of relevant cases. To make numerical predictions about specific minerals that may or may not suffer from the greatest risk of having a failed

space mining venture, we would need to heavily speculate on the shape of the space mining cost functions, for example. We have chosen to leave this exercise for future work. Potential impact and opportunities for implementation of the results In some way, the issues that we planned to investigate (difficulty of a space mining company to earn the current spot price for their product) with this project have become clear. The two companies with the most aggressive space mining business plans (Deep Space Industries and Planetary Resources) were bought by other companies and have had their space mining plans severely scaled back. We believe that the impact of our results will be in how consulting and investment firms consider the business case for space mining moving forward. The concept of strategic behavior by firms in an industry is not new or uncommon but there has been a good deal of discussion of the value of minerals on planetary bodies that does not consider this issue. The impact of this research is to give some bounds on what price a space miner can be expected to receive for its product given a current spot market price in the market. In general, most transactions in mineral markets are done through a spot market or very limited contracts. The London Metals Exchange will hold metals for mining companies as a way to ensure proper spot and futures market trading. While producing mines can rely on the spot market and the London Metals Exchange warehouses to fund their operations, developing new mines is rarely done with free cash flow and most certainly won’t be done in space mining. Developing new mines is often done through borrowing money from a bank or other investment company. These banks will often require some form of risk mitigation on the projects revenues, whether those be a forward contract with a buyer or financial hedging by purchasing futures or options on the mineral. In either case of risk mitigation, our results show that if the space mining company entered the market, they would be receiving less than the spot price for their production. In fact, our model shows that the drop in price caused by a space mining firm’s entry into the market can make the resulting operations unprofitable. In this case, the space mining firm decides not to enter the market. This result and others in the model are important for potential investors and firms to understand. The ability to bring a relatively large amount of a resource into market, even if that resource is extracted at relatively low marginal costs, may not ensure profitability due to the need to cover large fixed costs. Conclusion and next steps While this analysis is theoretical, it can provide predictions that can help us understand when space mining firms are more likely to find a receptive market. A clear next step would be to gather estimates of the fixed and marginal costs for terrestrial miners of a given resource, elasticity of demand for a given resource (how demand will change when price changes), and estimate of fixed and marginal cost for a space mining firm. This would allow us to parameterize the model in order to get some estimates of the change in market price when a space mining firm enters and calculate the potential profits to be made. We did not consider the impacts of supply chain risks or moral hazard on the entry incentives or optimal contract structure, which is an important area in which to extend our work. Another extension of the model is to derive conditions for a space mineral market and how it would be linked to the terrestrial market in order to determine whether any of the outcomes of our model would change. Our initial thoughts are that they would not change given that the two markets would be linked, by the ability to

bring the minerals from the lower priced market to the higher priced market. One could take parameters and scenarios from the terrestrial natural gas market, which until very recently had limited ability to move gas across the ocean, to formalize this model.