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We study a simple model for the evolution of the cost (or more generally theperformance) of a technology or production process. The technology can bedecomposed into $n$ components, each of which interacts with a cluster of $d-1$other, dependent components. Innovation occurs through a series oftrial-and-error events, each of which consists of randomly changing the cost ofeach component in a cluster, and accepting the changes only if the total costof the entire cluster is lowered. We show that the relationship between thecost of the whole technology and the number of innovation attempts isasymptotically a power law, matching the functional form often observed forempirical data. The exponent $\alpha$ of the power law depends on the intrinsicdifficulty of finding better components, and on what we term the {\it designcomplexity}: The more complex the design, the slower the rate of improvement.Letting $d$ as defined above be the connectivity, in the special case in whichthe connectivity is constant, the design complexity is simply the connectivity.When the connectivity varies, bottlenecks can arise in which a few componentslimit progress. In this case the design complexity is more complicated,depending on the details of the design. The number of bottlenecks alsodetermines whether progress is steady, or whether there are periods of stasispunctuated by occasional large changes. Our model connects the engineeringproperties of a design to historical studies of technology improvement.

The Role of Design Complexity in Technology Improvement