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Let's now consider the theory of natural monopoly
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and the difference between what is often called weak and strong natural monopoly
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Common examples of natural monopoly are,
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electricity distribution systems, and water piping systems,
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but often the concept of natural monopoly is used somewhat loosely or impressionistically.
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Does it mean that in a market setting there would just be a single producer?
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Or does it mean that there should just be a single producer.
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Well, we're going to look at this a little more rigorously and break down the concept of natural monopoly into two different cases.
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And as mentioned those cases will be strong natural monopoly and weak natural monopoly.
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As we will see this difference will relate to whether average cost AC is decreasing as the strong natural monopoly or in weak natural monopoly AC is increasing.
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We can define decreasing average costs by this equation here.
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What this means is that as more units of the goods are produced,
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the average cost of producing each unit falls
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So you could also put this on a graph,
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and here would be average cost, and as q is increasing, Ac is going down.
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And of course this could be true across some range of the output, but not all ranges of the output
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so this is defined across some particular range namely where the market will be.
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Now let's consider the concept of subadditivity.
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We can write subadditivity as follows, with a cost function here we have cost
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and in parentheses we have a sum of q super script i, close parentheses,
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being less than or equal to another sub here, c q super script i.
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What the left hand side portrays here is simply the cost of producing all those units in a single firm.
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What the right hand side portrays is the cost of taking those units and say producing them through using ten little different firms.
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And of subadditivity holds, well it's cheaper to produce that given quantity of ouput,
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in the single larger firm.
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In this setting, subadditivity is simply an assumption.
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With that which we don't have natural monopoly at all.
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Decreasing average cost is something which as we will see, may or may not hold.
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By definition we have strong natural monopoly
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when both assumptions hold, and thus we are considering the case of decreasing average cost.
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We can draw that case like this,
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so here we have a demand curve, we have the marginal revenue curve,
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we have an average cost curve
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and we have a marginal cost curve,
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and what's striking about this picture is that if we were too set price at marginal cost,
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right here, well that would be normally the efficient price,
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but at that price, you can see that average cost is above price
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so if average cost is greater than price,
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then the firm is earning profits which are less than zero,
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or the firm is suffering loses.
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In these cases, due to subadditvity in both strong and weak natural monopolies,
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it is cheapest for a single firm to supply all output
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but the general question, which arises,
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is a single firm sustainable?
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Well, in the case of strong natural monopoly,
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if we set prices equal to marginal cost,
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the tradition optimality condition, we can see that a subsidy is needed.
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Again you can see in this picture that where demand meets marginal cost,
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average cost is above that point,
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and its the subsidy that would be needed to make up that difference.
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And if you're wondering by the way, how is it that average costs are getting to be higher than marginal costs,
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well basically, it has to do with the presence of fixed costs in the production function.
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Namely costs that must be incurred no matter what,
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just to get the firm up and running.
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Those fixed costs will not contribute to marginal costs
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but they will make average costs higher.
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Sometimes, the regulators will allow a firm to set price equal to average costs,
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and then that means there will not be any subsidy needed for the firm,
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This is done for a few reasons ,
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one is simply that subsidies to firms are not politically popular,
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but another reason is that subsidies to firms are often distorting or cause corruption,
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or there's a problem, how do you know how much subsidy to send to the firm?
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What do you do, just call up the firm and ask, "Hey, what's your cost curve?"
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Well, they're probably going to lie to you, to get a higher subsidy.
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So in practice, with regulation, prices equals marginal costs under strong monopoly
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is not always attainable and often the regulators settle for something more in the neighborhood of price equals average costs.
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We'll now consider the case of weak natural monopoly
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where subadditivity agains holds
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but we do not have decreasing average cost.
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Rather, we have increasing average cost.
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The important mathematical point here is that for AC to be rising, marginal costs has to be greater than average cost
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that is, you only get an average to be rising by tacking on some larger numbers to that average.
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But if marginal costs is greater than average cost,
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and we're going to be trying to set prices equal to marginal cost,
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then indeed price itself will be greater than average cost
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and the firm will earn profits rather than suffering loses.
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We can see here in this diagram that, that price equal to marginal cost
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that is indeed above average cost, and thus profits will be greater than zero.
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The good news is, we don't need that subsidy anymore.
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The bad news, that we have a new problem, and that is entry is possible
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and that conceivably could raise total production costs.
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So the new firms, they engage in what is sometimes called cream skimming
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namely trying to serve the most profitable segments of the market,
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and leaving the initial enterent to cover all the others
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It's sometimes claimed for instance, if we opened the US Postal Service
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to full private competition you might get say, three or four suppliers
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mostly fighting over the lucrative urban segments of the market.
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What you would have is three or four different firms, varying those fixed costs
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we talked about.
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because of subadditivity this may not be socially efficient
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to be having three or four different firms paying the fixed costs of setting up a delivery network
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yet because of the struggle,
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over these profits based on monopoly or market power
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maybe, that's what you would get, at least according to this theory.
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So what does this look like?
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Well here you would imagine a bunch of firms,
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fighting over the top portion of this demand curve,
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the consumer surplus, for people who demand service the most,
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and the people who use this model to favor entry restrictions,
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well they focus on the fixed cost.
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They say you would have here, say three different firms varying those blocks of fixed costs
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to set up a delivery network,
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as opposed to the one, possibly state protected monopolist,
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and that is an argument for creating a state protected monopolist.
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Other economists will accept the logic of this view,
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but they come to a different policy conclusion, they place a lot of stress on innovation, and also the dynamic benefits of competition.
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So they understand that by having three competitors, as here you will pay more in terms of fixed costs,
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but over the longer run you'll have more innovation,
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saying how packages are delivered and tracked,
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and the benefits of that dynamic competition will out weigh the initial payment of fire to fixed costs.
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And these individuals would argue, then that we should allow a competitive market to operate,
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and how you will make this judgment call depends on,
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how important you think the fixed costs are,
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compared to these factors of innovation and dynamic competition.
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But in any case, sits the theory of weak natural monopoly, which helps you see this trade off.
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There are plenty of places where you can pursue these topics,
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one route to go is simply to study specific sectors and industries,
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but more generally, you can google strong weak natural monopoly.
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Also google natural monopoly regulation.
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And here's a very useful source, it's not online, it's not free,
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but it's a very good book, and it's called,
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"Natural Monopoly Regulation".