# Elasticity of Demand problem help

• MHB
• hallie
In summary, the conversation discusses finding the elasticity of demand using a price-demand equation and the formula E(p)=pf'(p)/f(p). The final answer is E(p)=11p-/400-11p, obtained by dividing the numerator and denominator by the greatest common divisor, -50, resulting in simpler terms with fewer negative signs.
hallie
Hi, I know this may seem like a dumb question, but I just can't seem to get by one part of each elasticity of demand problem I come across. For example:

Use the​ price-demand equation below to find​ E(p), the elasticity of demand.
x=f(p)=20,000-550p

I know that E(p)=pf'(p)/f(p), so in this problem that would get me E(p)=p(-550)/20,000-550p, but after that, I am unsure of how to divide the equation in order to simplify it.
I know the answer is E(p)=11p-/400-11p, but if anyone could tell me how to divide/simplify the equation in order to get to that answer, I would be extremely grateful.

Thank you!

Okay, it looks like you have derived:

$$\displaystyle E(p)=\frac{-550p}{20000-550p}$$

Now if we divide the numerator and denominator by -50, we obtain:

$$\displaystyle E(p)=\frac{11p}{11p-400}$$

Does this make sense?

Where do you get the -50 from?

hallie said:
Where do you get the -50 from?

Since there is a minus sign on one of the terms in the denominator and a minus sign on the numerator, if we divide by a negative number, then we will only have 1 minus sign in the denominator. I prefer the form:

$$\displaystyle \frac{a}{b-c}$$

over:

$$\displaystyle \frac{-a}{c-b}$$

Even though they are equivalent, I like fewer negatives. Then if we look at 550 and 20000, we see that 50 is the GCD, so dividing each term by -50 will result in the simplest terms in the form with fewer negative signs. :)

MarkFL said:
Since there is a minus sign on one of the terms in the denominator and a minus sign on the numerator, if we divide by a negative number, then we will only have 1 minus sign in the denominator. I prefer the form:

$$\displaystyle \frac{a}{b-c}$$

over:

$$\displaystyle \frac{-a}{c-b}$$

Even though they are equivalent, I like fewer negatives. Then if we look at 550 and 20000, we see that 50 is the GCD, so dividing each term by -50 will result in the simplest terms in the form with fewer negative signs. :)

Perfect! Thank you so much for this explanation! :)

## 1. What is the concept of elasticity of demand?

Elasticity of demand refers to the degree of responsiveness of the quantity demanded of a good or service to changes in its price. It measures the change in the quantity demanded relative to the change in price.

## 2. How is elasticity of demand calculated?

Elasticity of demand is calculated by dividing the percentage change in quantity demanded by the percentage change in price. This can also be expressed as the ratio of the change in quantity demanded to the change in price.

## 3. What factors influence elasticity of demand?

The main factors that influence elasticity of demand are the availability of substitutes, the necessity of the good or service, and the proportion of income spent on the good or service. Generally, goods and services that have close substitutes, are considered less necessary, and make up a small portion of a consumer's income tend to have a higher elasticity of demand.

## 4. How does elasticity of demand affect pricing strategies?

The elasticity of demand has a significant impact on pricing strategies. For goods or services with a high elasticity of demand, a small change in price can lead to a large change in quantity demanded, so businesses often need to carefully consider their pricing strategies to avoid losing customers. On the other hand, goods or services with a low elasticity of demand can have a higher price without significantly affecting demand.

## 5. Can elasticity of demand change over time?

Yes, elasticity of demand can change over time. It can be influenced by various factors such as changes in consumer preferences, the introduction of new substitutes or technology, and changes in income levels. It is important for businesses to regularly monitor and analyze the elasticity of demand for their products or services to adjust their strategies accordingly.

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