~I wanted to be sure that everyone understands the controversy around expressing the supply & demand functions two different ways. Keep in mind that an increase in demand will usually increase the price or an increase in supply will usually decrease the price. Historically, This is how most economists originally viewed these situations. So, using this point of view, supply & demand became the independent variable (horizontal axis) and price became the dependent variable (vertical axis).

 

~Later, when the point of view changed (mathematicians viewpoint), the axes didn't. Therefore, the conflict was born.  Most mathematicians agree that it makes more sense & is more logical with price as the independent variable (on the horizontal axis). So, as a student in a calculus based business course, you will see the equations for these quantities both ways. In the early stages of the course, it makes little difference.

~Most authors will express them as x=f(p) for both supply & demand functions. Keep in mind that x=D(p) & x=S(p) for these functions (different equations) where x represents the # of units of the item & p the price/unit. The demand equation estimates the # of units consumers are willing to purchase & the supply equation represents the number of units to be available. Another popular symbol used for x is q.

 

~At the beginning stages, we are usually involved in finding the market equilibrium point. We do this by solving these equations simultaneously using simple algebra.  At this point, the consumers & producers usually settle, but not always (as we shall see).

 

~However, common sense tells us that the reverse labeling of the axes makes more sense. Graphically, this means that the vertical axis (dependent variable) is x, q, D(p), or S(p) and the horizontal axis (independent variable) is price (p). When a consumer shops, he or she usually looks at the price of an item and decides (mostly on this, but not always) whether to purchase it or not. There are many times we purchase items out of necessity. In those cases, price does not play a dominate roll. Also, if the demand for that item is so great relative to the supply, the price we are willing to pay increases quite significantly (as we see involving popular toys for children at Christmas time). However, for normal situations, if the price of the item is too high, we usually hold back on a purchase with the hope of a reduction in price (sales). So, price is the factor which dictates the demand. It also would dictate the supply of the item (from a producers' standpoint). Producers' want to sell items at higher prices to increase their profit margins.  So, they would supply more, if this is the case.

  

~In a free market society, prices usually settle near "market equilibrium". This point is where buyers & sellers agree on the transaction. Be aware that this is not always advantageous to the buyer or seller. For example, the stock market uses a "bid & ask" system of trading. For most stocks, the "spread" between these prices are usually quite small, say within a few cents. For most individual traders, this difference is not very significant, but for large institutional traders, it is very significant (very large quantities change hands).

 

~However, for those of us that deal in option trading, this spread could be significant. The "bid" is the price a buyer is willing to pay, while the "ask" is the price the seller is willing to sell. The "bid price" is lower than the "ask price". Usually market equilibrium occurs somewhere in between, but not always. It depends on the type of order submitted. "limit orders" indicate specific prices for execution, while  "market orders" do not. Placing a "market order" for an option contract will usually result in a disadvantage for the buyer since it results in the higher "asked" price in most cases. On the other hand, this type of order by the seller usually results in the lower "bid" price. Like I mentioned earlier, for stocks the spread is usually very small & insignificant, but for options, it is usually much greater (on a percentage basis). This could result in a very significant amount of money, if a large order is placed. Notorious situations usually occur in pre-market and post-market trading where the volume of trading is greatly reduced (creates higher volatility).  So, be very careful here.

~Note:  Jim Cramer, a popular TV business commentator, is adamant about placing market orders.  He states "never, never, place a market order". Well, I disagree.  As a trader of stocks & options, there are situations where you must "dump" a stock or option contract immediately or purchase one immediately, without delay.  Certain market conditions could dictate this. So, the only way you can do this without delay, is with a market order.  Yes, I agree, you probably will lose out somewhat on your trade, but you could avoid a disaster in many cases or paying a much higher price for the stock or option later.

I still remember the day when AOL was flying high in the market & I wanted to buy 100 shares to ride the upswing. The price was moving up so fast that I had to place a limit order to protect myself from paying too much initially on the opening. The previous day had a range of 143-150.  

I place my limit order to buy 100 shares at 148. Well, it open slightly above that price the next day & never looked backed. I didn't change my order since I felt it would hit that price sometime during the day of trading. Well, it didn't & I never got it. If I had placed a market order at opening, I would have had it at 148.50. It continued rising in price & I was out. Looking back, I'm glad this happened since the stock price eventually came crashing down.

 

~There are situations where it would be advantageous to take the economists view for solving certain types of problems. One of which is computing the "producers or consumers" surplus. By placing the price on the vertical axis (considering price the dependent variable), it makes the calculation much more convenient & easy to visualize. By using basic integration and area relationships, these quantities are found easily. 

 

~So, in conclusion, both views are considered in such courses. For some students, this poses confusion (#1 culprit in the learning process).  So, students of calculus based business courses should know both ways of expressing these functions & the motivations behind each point of view.