How does Rackspace, a hosting services provider, structure supplier contracts?

Suppliers might have a fixed cost per unit but this information is not public knowledge. Rackspace must assume the probability supplier is low cost is ‘p’ and ‘1-p’ is the probability of dealing with a high cost supplier. It might also assume that this ratio stays constant going forward. Without knowing the true costs of manufacturing server hardware, Rackspace is limited to making such a guess about costs.

If Rackspace had full knowledge of the costs, it could structure a cost-plus contract that allows for 10-15% profit margins for the suppliers. But cost-plus contracts create an incentive for suppliers to overstate costs and grab excess share of profits. And of course, without knowledge of the costs (suppliers won’t reveal), i.e., in the presence of asymmetric information, the hosting provider must optimize the difference between the value created by the suppliers for Rackspace and the fixed fees paid to the suppliers. It could structure two contracts: contract-low and contract-high.

Contract-L: supply us X_L number of servers and we will pay you F_L in fees.

Contract-H: supply us X_H number of servers and we will pay you F_H in fees.

The idea is to set X_L, F_L, X_H and F_H such that a low-cost supplier will find contract-L more profitable, and a high-cost supplier will find contract-H more profitable. The next step is to write expressions for the incentive-compatibility constraints to induce a low-cost supplier to select contract-L and a high-cost supplier to select contract-H. Define one participation constraint for each type of supplier and finally, assuming that each supplier chooses the contract designed for it, write the expression for Rackspace’s expected net benefit.

Now the problem is to maximize the expected net benefit which can be done using quadratic manipulation if your net benefit equation is of that type of course, or otherwise, use calculus: take a derivative over number-of-servers and set the derivative equal to zero to determine your optimal number of servers for contract-L, and contract-H.

I shall post a full calculation showing the incentive compatibility and participation constrains in a subsequent post.

Note on utility function

Accurate mechanism design requires the formulation of a mathematical model that shows the value created by the system of suppliers for Rackspace- its utility function. Correlation is a distant second choice. We could use linear regression over the total revenues generated year over year as a dependent variable and the number of servers, customers served as independent variables using the last forty-eight quarters of data. This approach reveals the correlation between number of customers and servers deployed and total sales for Rackspace. Of course, the net of sales and fees paid to hardware suppliers is the benefit that Rackspace will want to maximize.

A simpler way to estimate the utility function for Rackspace is to recognize the fact that indefinitely increasing capacity will not lead to indefinitely increasing sales. This is indeed the familiar “decreasing marginal utility” function wherein each unit of capacity added beyond sustainable market share will lead to lower and lower sales.

It is extremely difficult to establish exactly what the Rackspace utility function actually is. The most common utility functions are exponential, power, log and iso-elastic. Exponential utility is a good choice for a function that helps in the calculations based on its acceptance by academics “since calculating expected utility with an exponential utility function reduces to calculating the moment generating function of the random wealth distribution” as noted here: http://bit.ly/17r3Xi4.

Another choice for a utility function might be one derived directly from the cloud computing industry demand function. It is possible to simulate the demand function for the industry as a whole assuming Rackspace is a price-taking firm. Prices have stabilized in the cloud computing industry with no clear price leader so it might be a reasonable assumption.