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Consider a Cournot firm with profit function given by L(x, y)=xP(x+y)-cx, where x is own output and y is rival’s total output. Assume P(.) is continuous and log-convex. Show that L is log-supermodular if and only if c=0. What can you conclude about the reaction “curve”? Hint: You may want to use the fact that P(x+y) is log-supermodular in (x, y) if and only if P(.) is log-convex.
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