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 Originally Posted by rong
A short version, ignoring math and graphs, the monopoly version of a road prices itself to max profit which typically is at a higher price and lower supply than perfect competition. This economic profit (profit beyond that received at free market price) is what you're saying is the incentive for a new supplier.
I agree with this, I just wanted to establish that the price is still limited by a min-maxing algorithm that attempts to sell the most tolls for a moderately high (albeit likely too-high) amount. I would only caution against the use of the term "free market price." It is extremely difficult (impossible) to know what that would be, so it is merely a theoretical construct that is of limited use in these discussions. One which we hope is less than the monopolist's price.
 Originally Posted by rong
But 2 things effect this. Firstly the entry barrier of massive costs to enter the market ie build a new Road. Secondly the road has a maximum supply which the incumbent can take advantage of whenever it sees fit. This excess is pretty much the same as a factory increasing production capacity and not using it as a message to competition that it is willing to compete on price if required, thereby instantly removing the economic profit that exists in the status quo that is the incentive for a new entrant. And it's a very credible threat because the incumbent wants to maximise profits, hence it's current monopolistic pricing strategy. So a natural move for the incumbent upon realisation of a new entrant is one of 2 things. Either reduce price to competitive market points which will be standard profit maximisation or alternatively use the excess supply it has and reduce price below the competitive price at the cost of short term profit with the intention of crippling new entrant and then once new entrant fails increasing price back to monopoly profit maximisation point.
So with roads this is built in to the basic set up which is why it creates a quite natural monopoly.
So if I'm understanding you, your point is the following:
1. Monopolist owns the only reasonable route between A and B. His costs are $10,000 per day. He charges an extravagant toll that allows him to gross $40,000 per day in revenue. The price is set at a rate that will min-max his price*volume.
2. Would-Be Competitor considers building up an alternate route which might cost him $15,000 per day, at least initially.
3. Would-Be Competitor decides not to risk it for fear that Monopolist will simply lower his revenues to $14,000 per day (or $10,000 or $2,000), which will make it impossible for him to recoup his investment in a reasonable amount of time.
This is challenging, but I don't think its necessarily a market failure yet. For one thing, if Would-Be Competitor assesses the market value of the route at $20,000 per day (which is greater than $15,000), he may still choose to take the hit and weather the storm of price manipulation by the Monopolist, with the expectation that eventually the price will stabilize at around $20,000, and he will begin earning a $5,000/day profit. Monopolist cannot manipulate the market forever, he pays dearly every day. Would-Be Competitor can be capable of playing the long game if the profit potential is there.
The other thing is that while there may be no similar alternate, there are very likely to be inferior routes unless it's a single bridge to an island or something. The monopolist can only gouge his price to a height that will get people to grudgingly choose his route over inferior alternatives. Basically, that's one of a lot of fail-safes that prevent such blatant gouging from being practical.
Finally, lets be real. The state is going to stick its nose in and bust up suspected monopolies. It has a hair trigger for that sort of thing, often when there's actually no monopoly at all, so I wouldn't be that worried about it.
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