4.2 Learning curves

The motivation

Unit costs decrease as cumulative output increases.

Strategic implications for pricing and marketing strategy

Formulation

$$c_t = c_1n_t^{\alpha_c}e^{u_t},$$

where

• c_t is unit cost in time period t (adjusted for inflation)
• c₁ is unit cost in initial time period
• n_t cumulative production up to but not including time t
• $\alpha_c$ is unit cost elasticity with respect to unit volume
• u_t stochastic disturbance term (our $\epsilon_t$)

Note. Response is unit cost. A multiplicative model.

Make linear by taking logs.

$$\ln(c_t) = \ln(c_1) + \alpha_c \ln(n_t) + u_t.$$

Estimate $\alpha_t$ from a simple regression.