Problem 3 Monopoly Power, Continuously A monopoly producer of How To Get Into Stanford tutorial videos has marginal costs that are given by MC 20 1 4 Q, and the market demand from high school students for such videos is given by Q D 120 2P (which can also be written as P 60 1 2 Q D ) Using the same intercept, twice the slope rule, this monopolist knows that her marginal revenues are MR 60 Q Assume that fractional or decimal quantities of videos are possible, i e use smooth curves in your analysis How many videos will this monopolist produce What will be the (single) price per video Illustrate your answer with a diagram showing demand, MR, and MC curves Compute the consumer surplus and producer surplus associated with your answer to part a), and indicate them on your diagram How large is the deadweight loss associated with monopoly power Show your work Confirm that the inverse elasticity pricing rule holds for this monopolist that is, that (P MC) P 1 DQ D DP x P Q where DQ D DP is measured in absolute value (so it's a positive, not a negative, number) Show your work Show how after selling videos at the price and quantity you computed in part a) the monopolist can increase producer surplus by selling a few additional units to high school students who did not already buy Plug in numbers (note that there are multiple correct answers) to propose a specific price and quantity of additional videos, and compute the effect on producer surplus and consumer surplus In words, briefly explain why some monopolists may prefer to maintain a single price strategy rather than selling additional units such as you described part d)

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Problem 3: Monopoly Power, Continuously A monopoly producer of How To Get Into Stanford tutorial videos has marginal costs that are given by MC =

Problem 3: Monopoly Power, Continuously

A monopoly producer of "How To Get Into Stanford" tutorial videos has marginal costs that are given by MC= 20 + 1/4 Q, and the market demand from high school students for such videos is given by Q^D=120-2P (which can also be written as P=60 - 1/2 Q^D). Using the "same intercept, twice the slope" rule, this monopolist knows that her marginal revenues are MR=60-Q. Assume that fractional or decimal quantities of videos are possible, i.e. use smooth curves in your analysis.

How many videos will this monopolist produce? What will be the (single) price per video? Illustrate your answer with a diagram showing demand, MR, and MC curves.

Compute the consumer surplus and producer surplus associated with your answer to part a), and indicate them on your diagram. How large is the deadweight loss associated with monopoly power? Show your work.

Confirm that the "inverse elasticity pricing rule" holds for this monopolist: that is, that (P-MC) / P = 1 / [DQ^D/DP x P/Q] where DQ^D/DP is measured in absolute value (so it's a positive, not a negative, number). Show your work.

Show how after selling videos at the price and quantity you computed in part a) the monopolist can increase producer surplus by selling a few additional units to high school students who did not already buy. Plug in numbers (note that there are multiple correct answers) to propose a specific price and quantity of additional videos, and compute the effect on producer surplus and consumer surplus.

In words, briefly explain why some monopolists may prefer to maintain a "single-price" strategy rather than selling additional units such as you described part d).