User:AndreaMameri

BIOGRAPHY

HELLOOOOOOO

Pythagorean theorem

To refresh the memory and for me to complete the assignment, I will talk to you a little about the Pythagorean Theorem. I will try to make this fun. (Math is never fun, sry)

The Pythagorean Theorem can only be completed when working with right angle triangle. This means that one of the angles which make up a triangle is 90 degrees. The triangle is then composed of different lines. The longest line in the triangle is called the HYPOTENUSE; it is usually located right across the 90 degree angle. In the Pythagorean Theorem the HYPOTENUSE is represented by the letter C.

The Pythagorean Theorem is: $a^{2}+b^{2}=c^{2}$

The remaining two sides are represented by the letter A and the letter B. The order does not matter.

If a problem is given, the variables need to be plugged into the formula. If the HYPOTENUSE is given, this is plugged into the C, if one of the sides is given then this is plugged into A or B. Whichever side you are solving for, you make the equation equal that.

Example: One side of a right angle triangle is 5 cm. The other side is 12 cm. Solve for the HYPOTENUSE.

$a^{2}+b^{2}=c^{2}$

$5^{2}+12^{2}=c^{2}$

$25+144=c^{2}$

$169=c^{2}$

$c^{2}=169$

Failed to parse (syntax error): {\displaystyle c = √169}

$c=13$

Calculus in economy

As I mentioned earlier on, the faculty that I am currently in is Commerce in the Sauder School of Business. Surprisingly enough, for me anyway, math is a big part of Commerce. Here I will be discussing how calculus plays a very important part in finding the elasticity of the economic curve.

First of all, I would like to explain what elasticity actually is. In economics, elasticity is the ratio of the percent change in one variable to the percent change in another variable. Elasticity is used to measure how responsive one variable is to the other. It is said that if a variable has high elasticity then if that one variable is changed then this would impact the other greatly. On the other hand, if the variable is said to have a low elasticity then this means that if that same variable is changed then nothing or little with happen to the other variable. So, when is elasticity used? Mainly when looking at price elasticity of demand, price elasticity of supply, income elasticity of demand. Elasticity is essential in economics (according to professor Gateman). It is useful in understanding the marginal theory. For example, what happens to consumption if one more product increases its prices.

The formula for elasticity is:

Elasticity = (percentage change in Z) / (percentage change in Y)

From the get go, we see 2 variables that might have a relationship to each other. This already plays a big part in calculus.

Using some fairly basic calcululus, we can show that (percentage change in Z) / (percentage change in Y) = (dZ / dY)*(Y/Z)

where dZ/dY is the partial derivative of Z with respect to Y. Thus we can calculate any elasticity through the formula:

Elasticity of Z with respect to Y = (dZ / dY)*(Y/Z)

"A good or service is considered to be highly elastic if a slight change in price leads to a sharp change in the quantity demanded or supplied. Usually these kinds of products are readily available in the market and a person may not necessarily need them in his or her daily life. On the other hand, an inelastic good or service is one in which changes in price witness only modest changes in the quantity demanded or supplied, if any at all. These goods tend to be things that are more of a necessity to the consumer in his or her daily life."

Now… lets look at an example:

Demand is Q = 110 - 4P. What is price (point) elasticity at $5?

We saw that we can calculate any elasticity by the formula: Y = (dQ / dp)*(P/Q)

That is the case in our demand equation of Q = 110 - 4P. Thus we differentiate with respect to P and get: dQ/dP = -4

So we substitute dQ/dP = -4 and Q = 110 - 4P into our price elasticity of demand equation

Price elasticity of demand: = (dQ / dP)*(P/Q)

Price elasticity of demand: = (-4)*(P/(110-4P)

Price elasticity of demand: = -4P/(110-4P)

We want price elasticity at P = 5, so we substitute this into our price elasticity of demand equation:

= -4P/(110-4P) = -20/90 = -2/9

Our price elasticity of demand is -2/9.

Since it is less than 1 > Demand is Price Inelastic

Bibliography: http://www.investopedia.com/university/economics/economics4.asp

http://en.wikipedia.org/wiki/Elasticity_(economics)

http://economics.about.com/cs/micfrohelp/a/calculus_d.htm