The Case of the Fair Ticket Price, or

    What the Ticket-Scalper did before the show

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	This is an example to illustrate a relationship between price and demand.  I am assuming a constant supply, with no other factors being changed but the price.  All other things being equal, I expect that the lower the price, the more people who will be willing to pay that price, and the higher the price, the fewer the number of people who are willing to pay the price.  It is this that the chart shows.   Let's plug in some numbers and create a scenario to make the chart clear.  Suppose a local band is going to play in a hole-in-the-wall club that only holds 50 people, and they plan to sell tickets for their show.  The band members are discussing what price to charge for the tickets, with one saying they should charge $1, another saying $5, and a third suggesting $10.  So the band is trying to sell 50 tickets.  Which price should they charge?   Price A is $1, price B is $5, and price C is $10.  Suppose that 100 people would be willing to pay $1 for a ticket, 50 people would pay $5 for a ticket, and only 10 people would pay $10 for a ticket.   According to our chart, the price is too high at $10 per ticket.  The gross sales on 10 tickets comes to $100, but 40 tickets remain unsold--the bar's going to be pretty empty.   At $1 per ticket, all the tickets would be sold, and then some.  50 people will get tickets, but 50 more people who would be willing to pay $1 won't get to see the show.  Gross sales will only be $50, as well.  $1 is too low a price.   At $5 a ticket, exactly 50 people are willing to buy all 50 tickets, leaving nobody who is willing but unable to see the show.  Gross sales come to $250, much more than gross sales at the other two prices.  In this case, $5 per ticket is the optimum price, the price where the supply of tickets matches the demand for them.   Again, we're assuming that nothing is changing but the price to be charged for the tickets.  If the bar held 100 people instead of 50, then, in this particular case, $1 per ticket would be the optimum price, because 100 people, and only 100 people, are willing to pay $1 per ticket.    The mystery is that we don't know beforehand what price 50, and only 50, people are willing to pay to see the show.  We don't know how many people are willing to pay $1, or $5, or $10 for a ticket.  We might try different methods to get a better idea as to what price we should charge.  We could look at how other, similar-sized shows did, or the band's own past shows, for example.  But we can't charge just any price that we want to charge without the risk of having too many or too few buyers.  Our task is to discover the optimum price--whatever it happens to be--we cannot force a price of our choosing to be the optimum price.   What do scalpers do?  They try and find the optimum price, too.  If, in our example, we were to only charge $1 per ticket, scalpers would find more buyers at $4, 5, and $6 per ticket, but fewer buyers willing to pay more than that.  If we were to charge $5, the optimum price, scalpers will only find fewer buyers willing to pay a higher price, and thus will make little or no profit from reselling the tickets.  If we charged $10 per ticket, scalpers would have a hard time finding anybody willing to pay more, and they would lose money trying to resell tickets.   Thus, a price too high reduces demand below the available supply, and leaves us with unsold tickets.  A price too low creates a demand greater than the supply and causes a shortage of tickets, ensuring that some people who are willing to pay will not get to see the band.   A low price also encourages scalpers.  The optimum price, however, is the economically efficient price, and gives the best all-around results for the seller and the buyers, and discourages scalpers.  If it is to have any real meaning, a "fair" ticket price can only be the optimum price.  A price too high or too low cannot be considered "fair".   The optimum price doesn't happen automatically, though.  The seller has to work to find out what the optimum price is.  It is through a negotiation process, the give-and-take between buyers and sellers, that optimum prices are discovered.  If a seller doesn't want to do this necessary work, ticket-scalpers, price-gougers, and other types of resellers are usually happy to do the work and profit from the difference between the seller's price and the optimum price, if they can.  Commodities markets, for example, are all about letting speculators (who become the resellers) discover the optimum price, while the commodities producers  avoid the risk and uncertainty of fluctuating prices.  The commodities market is a form of insurance for the producers, and the price they pay is the additional profits that could be made if they themselves had tried to find the optimum price instead of letting the speculators do it.   It must be pointed out that the supply, price, and demand for any product and service, while important, are not the only factors involved in decisions of buying and selling.  This example simply assumes that no other factors change except for the chosen price by the seller in order to illustrate the specific relationship between price and demand.  In any real world situation, other factors can change, too, and would have to be considered in the process.  Other factors may have their own effect on  price, supply, or demand, but do not change the relationship between price and demand.
	Variations on a theme   The numbers I used are just examples to illustrate the relationship between price and demand.  In the text above, I already pointed out that if we had 100 tickets to sell, the optimum price would be $1, not $5.  But again, I must stress, we don't know beforehand what the optimum price is.   Suppose we had 50 tickets to sell, as in the original example, and decided to charge $10 per ticket.  If we discover that 30 people, not 10, are willing to pay $10 per ticket, we would have 20 unsold tickets and gross sales of $300.  This would tell us that $5 per ticket is not the optimum price, since 50 people at $5 only results in gross sales of $250.  Since 50 x $6 is $300, then we would know that the optimum price is something over $6 per ticket, even though we still don't know exactly what that optimum price is.  It could be $6.50, $7, or even $8 per ticket, but at least we've narrowed the range down a little.   Would it be possible that 30 people would be willing to pay $10, but we could only get 50 people if we charged $5?  That's a good question, and beyond my economic expertise at this point to prove or disprove.  But I would tend to think that it's not possible, unless some other factor also changed, or was having an impact on prices and demand.  In that case, though, we have a more complicated scenario involving more than just a price change.    We might imagine that there are two bands playing shows at the same time.  The 30 who were willing to pay $10 have little or no interest in seeing the other band, but the other 20 people who are willing to pay only $5 to see the first band would prefer to see the other band rather than pay some price more than $5.   This would not disprove the general relationship between price and demand, because more people are still willing to pay the lower price of $5 instead of the higher price of $10.  However, our optimum price has changed because we have to consider the additional factors of the demand and prices charged to see the other band.  We might find that gross sales will be greater if we charge $8 per ticket, have 40 people buy, and leave 10 tickets unsold, than if we have 50 people buy at $5 per ticket.  In such a case, scalpers would find that more people are willing to buy at less than $8 per ticket, and fewer at more than that, and therefore they can't make any profit by scalping the $8 tickets.  This might be telling us information about the relative demand between the two bands.   But again, we've created a more complicated scenario that involves more variables, and thus is more difficult to solve.