Delay dynamics in nonlinear monopoly with gradient adjustment. (English) Zbl 1480.91106
Summary: Two types of boundedly rational monopolists are considered, when they are unable to determine the profit maximizing output levels. In the first case, the monopolist knows the price function and in the second case it can access only past output and price values. In applying gradient dynamics, the marginal profit is either known or approximated by finite differences based on two past profit data. Stability conditions are derived first with discrete time scales, which are also applied in a special case. Two models of continuous-time dynamics are then introduced. The first is a natural modification of the discrete model, and the other includes an inertia coefficient with the derivative. In each case, a delay differential equation is obtained with two delays. Stability conditions are derived and the stability-switching curves are constructed and illustrated.
MSC:
| 91B24 | Microeconomic theory (price theory and economic markets) |
Keywords:
gradient adjustment; delay differential equation; boundedly rational monopoly; discrete-time and continuous-time dynamics; stability switching curvesReferences:
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