Suppose that the supplier sells each unit to the retailer for pw = c, but, in addition, requires the retailer to pay a fixed fraction of the retailer's profits, . Formulate the retailer's profit-maximization problem under this contract and show that this contract maximizes the total industry profit. That is, show that for any given , the sum of the supplier's profit and the retailer's profit is equal to the profit made by a vertically integrated monopolist. (Hint: The retailer gets (1 ) r rather than r . No need to re-do the vertically integrated monopolist's profit.)