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Monopolist profit maximizing calculations

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Monopolist Profit Maximizing Calculations:

Still having some problems understanding how to calculate these economics equations. I haven't taken calculus yet, so some of the concepts seem foreign to me here. But I'm not just looking for an answer, but the steps on how the answer was arrived. I know at least for the first part, I'll need to find the TR (total revenue) by multiplying price times quantity and then find the MC (marginal cost) and MR (marginal revenue) and solve for Q. But the thing that's throwing me is finding the derivatives with respect to price (dTC/dQ) - I never arrive at the right answer. Please help!

  1. A retailer has an exclusive license to sell a line of handbags. The bags are so distinctive that consumers do not consider any competing offerings to be close substitutes. The retailer thus can be treated as a monopoly. The demand for the handbags is given by P=360-0.1Q. The marginal cost is constant and equal to 40, so variable cost is 40Q. The fixed cost is 90,000. Find the monopolist's profit-maximizing quantity.
  2. As before, a retailer has a monopoly on a type of handbag. The demand for the handbags is given by P=360-0.1Q. The marginal cost is constant and equal to 40, so variable cost is 40Q. The fixed cost is 90,000. Find the monopolist's profit-maximizing price.
  3. As before, a retailer has a monopoly on a type of handbag. The demand for the handbags is given by P=360-0.1Q. The marginal cost is constant and equal to 40, so variable cost is 40Q. The fixed cost is 90,000. Find the monopolist's total revenue if it uses the profit-maximizing price and quantity.
  4. As before, a retailer has a monopoly on a type of handbag. The demand for the handbags is given by P=360-0.1Q. The marginal cost is constant and equal to 40, so variable cost is 40Q. The fixed cost is 90,000. Find the monopolist's total cost if it produces the profit-maximizing quantity.
  5. As before, a retailer has a monopoly on a type of handbag. The demand for the handbags is given by P=360-0.1Q. The marginal cost is constant and equal to 40, so variable cost is 40Q. The fixed cost is 90,000. Find the monopolist's maximum profit.

Reference no: EM131489519

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