With a market share demand curve of Q_M = 150-.5P, Becky's Bookshelves can sell more than her current 50 bookshelves at $160.00 each. Once Becky found the amount she could sell given her market share, she revised her firms demand curve to be Q = 200 - P. With her new output, she has a marginal cost of $100 and assuming AVC is covered, she is currently maximizing profit.

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Given the market share demand curve Q_M = 150-.5P, we know that at a price of $160, Becky can sell Q=150-0.5(160) = 70 bookshelves. This means that her new demand curve Q = 200 - P only applies to prices above $160, since at prices below $160 her quantity demanded is determined by the market share demand curve. At a price of $160, Becky's marginal revenue is -0.5*70 + 150 = $115, and since her marginal cost is $100, she is currently earning positive profit. To check if she is maximizing her profit, we need to compare her marginal revenue and marginal cost at her current output level, which is Q = 200 - P = 200 - 160 = 40. Her marginal revenue at this output level is -1, which means that she can increase her profit by selling one more unit, since the additional revenue (the price she gets for the extra unit) is higher than the additional cost (her marginal cost of $100). Therefore, Becky is not currently maximizing her profit.

With a Market Share Demand Curve of QM = 150-

With a Market Share Demand Curve of Q_M = 150-