## Double Marginalization Problem

Instructor: Alex Tabarrok, George Mason University

This short video covers the double marginalization problem. The problem is what happens to social welfare, prices, and profits when one monopoly sells to another

This short video covers the double marginalization problem. The problem is what happens to social welfare, prices, and profits when one monopoly sells to another monopoly. It is a classic problem with applications in industrial organization, innovation policy, and development.

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Corrected. Please bear in mind that MRU Development Economics is basically just Tyler and myself. We do have some great student and technical help but sometimes errors sneak through, especially on our first run. Our motto of Learn, Teach, Share reminds everyone that this is a joint enterprise like Wikipedia so we are grateful when people spot errors.

Can you double check? I just took the test and the system is telling me less is more.

So, what should be the correct answer to #6? I think "less" should be right, but it is marked as wrong.

It's not terribly important but it is easy to prove with a bit of calculus. Write an inverse linear demand curve as P=A-bQ. Note that A is the vertical intercept and b is the slope. Revenue is P*Q or PQ=AQ-bQ^2 now take the derivative to get MR=A-2bQ, i.e. a curve which begins at the same vertical intercept, A and has a slope of 2b.

Thank you.

Good question. Here is what you are missing. Dead weight loss is NOT about profits. DWL is a measure of social loss, to be precise DWL measures potential gains from trade that do not occur. The height of the demand curve at the Xth unit tells us the value that consumers place on the Xth unit of the good, the height of the MC curve at the Xth unit tells us the cost of producing that unit. Thus, whenever the demand curve is above the MC curve there is a potential gain from trade. The trouble is that a monopoly can increase profit by reducing output (for the reasons you explain in your question) even though less output means fewer gains from trade and more DWL. In other words, producing more would lower the monopolist's profit but it would increase social surplus--that is it would increase consumer surplus more than the loss in monopoly profits so society as whole would be better off.

OK. I think I can understand, and therefore I think I can answer my own question, but I'll ask it anyway. Suppose I'm a competitive business. My MC is \$1. To make a profit I have to charge \$1.20. But this profit incurs a DWL--despite the fact that I'm not a monopoly. So therefore DWL is not unique to monopolies, but applies to competitive businesses as well. Answering my own question, I suppose that profit is included in the MC, i.e., it represents the return on capital which is an expense. Then by definition no competitive business can incur a DWL, and hence DWL is only a probem for monopolies.

Daniel: When you are in a perfectly competitive market you just can't decide what you are going to charge. The market decides the price for you, you either sell or not sell, your marginal cost is going to tell you whether you're going to sell or not. If the going rate is above your MC then you'll go into business and pocket the difference, if your MC is above the going rate you go home instead and tweet about how "foreign" competition is selling below cost (dumping) and the government should protect your industry by giving you subsidies and imposing tariffs on foreign goods. :-)