Using what we developed in the preceding chapters, we now show how to estimate market power using a dynamic model in which firms incur costs that are quadratic in the change of output and face linear demand functions. Because demand is linear in output, revenue is quadratic in output. The equation of motion – a definition stating that output in this period equals output in the previous period plus the change in output – is linear. Thus, the single-period payoff is a linear-quadratic function of the endogenous state variable (lagged output) and the control variable (the change in output). In addition, the constraint is linear in these variables.
This model is a special case of the model of quasi-fixed inputs discussed in Chapter 6. We know that there is a linear equilibrium to this model, defined for all values of the state variable (lagged outputs). If we restrict attention to this linear equilibrium, we can obtain a measure of market power under either the open-loop or Markov Perfect assumption. This model illustrates the methods discussed in Chapters 6 and 7. The ability to write the equilibrium conditions in closed form, as a function of the index of market power, makes this model easy to estimate.