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Consider now the following demand function:
D = α − p + γe
where α is the market potential, e is the advertisement “effort”, and γ is its marginal impact on sales. The cost function for the effort is represented by (1/2)ke2 where k is a constant. Find the Stackelberg equilibria for the following two scenarios and compare them. In which scenario are the manufacturer and the retailer better off? How is the comparison for the integrated system? Who puts more effort?
(a) The manufacturer moves first and determines both the wholesale price, w and the effort, e. As such she incurs the effort cost. In response the retailer decides on the selling price, p.
(b) Now the effort burden is on the retailer with the same cost structure and sales impact. The manufacturer sets the wholesale price and the retailer responds with the selling price and the effort level.
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