A learning curve model with knowledge depreciation

Empirical studies in several industries have verified that unit costs decline as organizations gain experience or knowledge in production, which is referred to as the learning curve effect. In the past two decades, there has also been analytical work on the relationship between a firm's learning curve effects and its pricing and output decisions. Learning rates differ significantly across firms in the same industry and recent empirical evidence has shown that knowledge depreciation may be an important reason for these differences. We propose and analyze a learning curve model with knowledge depreciation and provide several new insights. First, we show that there exists a steady state where knowledge level and unit cost remain constant over time and there exists an optimal path to this steady state. Many empirical researchers have observed this ‘plateau’ phenomenon, whereby unit costs decline but reach saturation after some time. While this has been traditionally modeled exogenously in the learning curve literature by assuming that cost reduction stops at some level of knowledge through a convex, decreasing unit cost function, we provide an alternative endogenous explanation. We are also able to show that, unlike in the model without knowledge depreciation, the production rate along the optimal path to the steady state may decrease over time. Also, the knowledge level along the optimal path may actually decline over time. Finally, we show that the optimal production rate decreases at higher interest rates and increases at higher knowledge depreciation rates. In turn, this implies that a high interest rate environment discourages firms from achieving high knowledge levels and results in higher prices. On the other hand, higher knowledge depreciation rates result in higher production rates and lower prices.