Imagine that your are selling spring water from your own spring (or any product whose cost of production is negligible). Suppose now that two of your neighbors open competing spring water businesses. Now all of you must share the market. Use the price function p = 32 - 0.01x (for 0 s xs 3200) and analyze, comparing a monopoly with competition among three suppliers (a "triopoly"). (a) For a monopoly, calculate the quantity x that maximizes your revenue. Also calculate the price p and the revenue R. P = R = (b) For a triopoly, find the quantities x, y, and z for the three suppliers that maximize revenue for each. Also calculate the price p and the three revenues. [Hint: Find the three revenue functions, one for each supplier, and maximize each with respect to that supplier's variable.] x = y = revenue revenue revenue

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