Parametrization and Equilibrium Profits Sample Clauses

Parametrization and Equilibrium Profits. To get intuition into the way the game unfolds, we need to specify equilibrium profits under alternative market structures (monopoly, duopoly, triopoly, N-opoly) and where the order of entry establishes a first mover advantage. In Appendix (B.2) we derive profit functions from the canonical differentiated products demand model by Xxxxx and Xxxxx (1984) but tweak it to account for first mover advantage. Specifically, in their model, utility for a representative consumer is given by U (q) = αq − 1 qrΣq, where the matrix Σ captures substitutability between products, and the vector α specifies maximum willingness-to-pay (WTP) for each product. The derived demand curves from the utility maximization problem are linear and functions of α and Σ.13‌ Further, to model first mover advantage, we allow αj(κ) to be different for each product i and to depend on a parameter κ, which adds a degree of vertical differentiation between brand and the first and second generic entrants. Thus let κ ∈ [0, 1] be such that in a triopoly, κ = 0 implies WTP for first and second generic is the same i.e. αT (0) > αT (0) = αT (0), and κ = 1 means that the first generic entrant has the maximum advantage relative to the second generic entrant, where we set it to be the same as that for the branded drug, i.e., αT (1) = αT (1) > αT (1). Similarly, in a duopoly αD(0) > αD(0) and αD(1) = αD(1) capture the WTP differences for between the branded and