4. The inverse market demand for Hummers in NYC is p = 120 - 2Q. The cost of producing one Hummer is c = $40. The manufacturer licenses a single dealer to sell Hummers in NYC. Therefore, the dealer acts as a monopoly in NYC in this market. The manufacturer sells each Hummer to the dealer for w(wholesale price). In addition, the manufacturer levies a fixed fee off on the dealership. Consider a two-stage game in which in Stage 1 the Hummer manufacturer sets the per-unit price charged to the dealer w, and the fixed fee f. In Stage 2, the dealer determines the amount of Hummers to sell to maximize the dealership's profit. For parts (a) through (d), assume that f = 0. (a) Suppose the unit price the manufacturer charges the dealer wis given (determined in the first stage of the game). Compute the dealer's profit-maximizing sales of Hummers as a function of w. (b) Compute the manufacturer's profit-maximizing price wit charges the dealer for each Hummer sold. (c) Compute quantity of Hummers sold by the dealer, and the price p charged to buyers. (d) Compute the profit made by the dealer and the manufacturer. (e) Can you find a price w and a fixed fee f which the manufacturer charges the dealer so that, both, the dealer and the manufacturer earn higher profit compared with the profits you computed in the previous