Price Elasticity, Partial Derivative

In summary, the conversation revolves around a question regarding a price elasticity problem and a partial derivative. The initial given information is used to calculate the demand, and then the conversation shifts to the specific problem of obtaining the partial derivative. The individual asks for a step by step explanation and expresses gratitude for any help.
  • #1
levijohnson
1
0
Hi all,

I've got a question regarding a price elasticity problem and a partial derivative.
That's what's given for the exercise:
Screen Shot 2013-10-20 at 14.40.12.png


So, first of all we calculate all the demand with the given information. Which is:
Screen Shot 2013-10-20 at 14.38.24.png



And then we come to the actual problem. (4. b) )

Screen Shot 2013-10-20 at 14.38.11.jpg

How do they get the partial derivative here? I assume that they are using the quotient rule, right? I would be really glad for a step by step explanation.

Thank you so much!
 
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  • #2
Hello there,

You should write your questions (Using the template btw, which you did not use!) instead of showing us images. This is because PF can't be sure that those images will stay up, and if they don't, then this thread will be of no use.

I believe somewhere in the PF guidelines, you can read what I just said.
 

FAQ: Price Elasticity, Partial Derivative

What is price elasticity?

Price elasticity is a measure of how sensitive the demand for a product is to changes in its price. It is calculated by dividing the percentage change in quantity demanded by the percentage change in price.

Why is price elasticity important?

Price elasticity is important because it helps businesses determine how much they can increase or decrease the price of a product without significantly affecting its demand. This information can also be used to make pricing decisions and develop marketing strategies.

What factors affect price elasticity?

There are several factors that can affect price elasticity, including the availability of substitutes, the necessity of the product, and the proportion of the product's cost to the consumer's income. Other factors include brand loyalty, time frame, and the type of market.

What is a partial derivative?

A partial derivative is a mathematical concept used to calculate the rate of change of a function with respect to one of its variables, while holding all other variables constant. In the context of price elasticity, a partial derivative is used to measure the sensitivity of demand to changes in price, while considering other factors that may also affect demand.

How is price elasticity related to partial derivatives?

Price elasticity is related to partial derivatives because it is calculated by taking the partial derivative of the demand function with respect to price. This allows us to measure the impact of a change in price on demand, while holding all other factors constant.

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