distinguish between linear and non linear demands funcions
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"Shorting a call" is better known as writing a naked call. Basically, a naked call is a call on a position you don't hold, and it has unlimited risk--if you get exercised and the strike price plus the premium is lower than the stock price, you must make up the difference out of your margin account--or you'll receive a margin call from your brokerage. Many brokerages won't allow you to write a naked call, and the ones that will demand a very large margin account and a lot of experience in trading options.
There was a demand for a huge number of manual calculations to create tables - many of them for navigational purposes - where similar calculations needed to be repeated many times.
Options are priced using a theoretical model known as a "Black Scholes Model". The black scholes model price options based on a set of mathematical parameters known as the "greeks" which covers the variables that influence options prices. However, this is only a theoretical model because it cannot take into consideration the actual demand and supply condition of specific options in the market. Actual demand and supply most often move the price of an option away from its theoretical value.
Some of the business applications are: (1) Finding the number of ouputs produced to maximize the profit. (2) Calculation of marginal revenue , marginal cost (3) Calculation of marginal average cost (4) Calculating elasticity of demand