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Table 2 Equilibrium prices, demands, and profits in each scenario

From: Consumer heterogeneity and online vs. offline retail spatial competition

Scenario Retailer Equilibrium price Equilibrium demand Equilibrium profit
AH1 a \( \frac{t+2m}{6\theta } \) \( \frac{N\theta \left(t+2m\right)}{3\left(m+t\right)} \) \( \frac{N{\left(t+2m\right)}^2}{18\left(m+t\right)} \)
h \( \frac{2t+m}{6\lambda } \) \( \frac{N\left(2t+m\right)}{3\left(m+t\right)} \) \( \frac{N{\left(2t+m\right)}^2}{18\lambda \left(m+t\right)} \)
AH2 a \( \frac{t}{2\theta } \) \( \frac{N\theta}{2} \) \( \frac{Nt}{4} \)
h \( \frac{t}{2\theta } \) \( \frac{N\theta}{2} \) \( \frac{Nt}{4} \)
AH1H2 a \( \frac{{\lambda t}^2+m\left(2\gamma -\lambda t\right)}{2\theta \left(4\gamma -\lambda \left(t-m\right)\right)} \) \( \frac{N\theta \left(\lambda {t}^2+m\left(2\gamma - t\lambda \right)\right)}{\left(m+t\right)\left(4\gamma -\lambda \left(t-m\right)\right)} \) \( \frac{N{\left(\lambda {t}^2+m\left(2\gamma - t\lambda \right)\right)}^2}{2\left(m+t\right){\left(4\gamma -\lambda \left(t-m\right)\right)}^2} \)
h \( \frac{2{t}^2-{m}^2- mt}{2\left(4\gamma -\lambda \left(t-m\right)\right)} \) \( \frac{N\gamma \left(2{t}^2-{m}^2- mt\right)}{\left({t}^2-{m}^2\right)\left(4\gamma -\lambda \left(t-m\right)\right)} \) \( \frac{N\gamma {\left(2{t}^2-{m}^2- mt\right)}^2}{2\left({t}^2-{m}^2\right){\left(4\gamma -\lambda \left(t-m\right)\right)}^2} \)
AH1S1 a \( \frac{m}{3} \) \( \frac{2 N\theta}{3} \) \( \frac{2 Nm\theta}{9} \)
h \( \frac{m}{6} \) \( \frac{N}{3} \) \( \frac{Nm}{18} \)
AH1S2 a \( \frac{\theta t+2m-2t}{6\theta } \) \( \frac{N\theta \left(\theta t+2m-2t\right)}{3\left(m+\left(\theta -1\right)t\right)} \) \( \frac{N{\left(\theta t+2m-2t\right)}^2}{18\left(m+\left(\theta -1\right)t\right)} \)
h \( \frac{2\theta t+m-t}{6\lambda } \) \( \frac{N\left(2\theta t+m-t\right)}{3\left(m+\left(\theta -1\right)t\right)} \) \( \frac{N{\left(2\theta t+m-t\right)}^2}{18\lambda \left(m+\left(\theta -1\right)t\right)} \)
AH2S1 a \( \frac{m\left(3t+ t\theta -2\theta m\right)}{6\left(2t-\theta m\right)} \) \( \frac{N\theta \left(3t+ t\theta -2\theta m\right)}{3\left(2t-\theta m\right)} \) \( \frac{Nm\theta {\left(3t+ t\theta -2\theta m\right)}^2}{18{\left(2t-\theta m\right)}^2} \)
h \( \frac{m\theta \left(2t-m\right)}{6\left(2t-\theta m\right)} \) \( \frac{N\theta \left(2t-m\right)}{3\left(2t-\theta m\right)} \) \( \frac{Nm{\theta}^2{\left(2t-m\right)}^2}{18{\left(2t-\theta m\right)}^2} \)