microeconomics, homeworkLet’s say we are given two markets, with demand functions $Q_1 = 50 - p_1$ and $Q_2 = 30 - P_2,$ a constant marginal cost of $10, and following different scenarios:
a. We can charge different prices in different markets. b. We can’t charge different prices, so have to offer the same in both.
What are the quantities and prices at which we will decide to operate?
For part a I get that I will horizontally add MR curves for both markets, intersect the resulting curve with the MC, and in each market, produce where MC = MR in that market (since for optimization, I would have to have equal MRs in both). Prices would be different, with the one in less elastic market higher than the one in the more elastic one.
For part b, I am not sure. I want to say it’s as simple as summing the MR curves again, picking the intersection with MC, and producing at that price in both. But I don’t know how to show that that would maximize my profits.
If you can charge different prices in the two markets, which is called “price discrimination,” you follow the monopolist’s profit maximization function of MR= MC in EACH market, setting the respective (different) prices in each market obtained from the equality.
If you can charge only ONE price in the two markets, then treat the two markets as one by adding the demand functions, and letting P1=p2. Then set the price where MR= MC for the COMBINED market.
Some embellishments of Tom's answer and potential pitfalls...
For the separated markets: Yes, both equations MC = MR_1 and MC = MR_2 must hold. Note that the MC is the same in both equations. (This doesn't matter for the cost function given, but would for, e.g., C = q^2.)
For the combined market: be careful about how you add the demand curves! At a price of 40, how much would be demanded? I hope your answer is not 0. Here's one set of notes on how you should add the curves.
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