# MathRocks' question at Yahoo Answers regarding price elasticity of demand

• MHB
• MarkFL
In summary, the question is about calculating price elasticity using a regression model for the number of people taking city buses at a given price per ticket. The point-price elasticity of demand is used to evaluate the elasticity at a specific price, and to find the price at which elasticity is unitary. The answer to part (a) shows that at a price of $5, demand is relatively elastic, while the answer to part (b) states that elasticity is unitary at a price of$4.
MarkFL
Gold Member
MHB
Here is the question:

Calc price elasticity problem and demand?

Suppose that 50000 people take city buses each day and pay for a ticket. A regression model suggests that the number of people taking city buses at price p dollars per ticket is given by

x=50000*sqrt(6−p)(a) Evaluate the price elasticity of demand at \$5 per ticket. E(5)= (b) For what value of p is the demand unitary? p= Here is a link to the question: Calc price elasticity problem and demand? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response. Re: MathRocks' quation at Yahoo! Answers regarding price elasticity of demand Hello MathRocks, In our problem, the point-price elasticity of demand is: $$\displaystyle E_d=\frac{p}{x}\cdot\frac{dx}{dp}$$ Using the given $$\displaystyle x=50000\sqrt{6-p}$$ we find: $$\displaystyle E_d=\frac{p}{50000\sqrt{6-p}}\cdot\frac{-25000}{\sqrt{6-p}}=\frac{p}{2(p-6)}$$ (a) Evaluate the price elasticity of demand at \$5 per ticket.

Letting $p=5$, we find:

$$\displaystyle E_d(5)=\frac{5}{2(5-6)}=-\frac{5}{2}$$

At this price, we may say demand is relatively elastic.

(b) For what value of p is the demand unitary?

For this, we want to set:

$$\displaystyle E_d=-1$$

$$\displaystyle \frac{p}{2(p-6)}=-1$$

Now we solve for $p$:

$$\displaystyle p=2(6-p)$$

$$\displaystyle p=12-2p$$

$$\displaystyle 3p=12$$

$$\displaystyle p=4$$

Thus, we find that elasticity is unitary at a price of \\$4.

To MathRocks and any other guests viewing this topic, I invite and encourage you to register and post other price elasticity of demand problems in our http://www.mathhelpboards.com/f18/ forum.

Best Regards,

Mark.

## 1. What is price elasticity of demand?

Price elasticity of demand is a measure of how much the quantity demanded of a product changes in response to a change in the product's price. It is calculated by dividing the percentage change in quantity demanded by the percentage change in price.

## 2. How is price elasticity of demand calculated?

Price elasticity of demand is calculated by dividing the percentage change in quantity demanded by the percentage change in price. The formula for price elasticity of demand is (Q2 - Q1) / ((Q1 + Q2) / 2) / (P2 - P1) / ((P1 + P2) / 2), where Q1 and Q2 are the initial and final quantity demanded, and P1 and P2 are the initial and final price.

## 3. What does a high price elasticity of demand indicate?

A high price elasticity of demand indicates that the quantity demanded of a product is highly sensitive to changes in price. This means that a small change in price can lead to a significant change in the quantity demanded.

## 4. What factors determine the price elasticity of demand?

The price elasticity of demand is determined by factors such as the availability of substitutes, the necessity of the product, and the proportion of the product's price to the consumer's income. Products with close substitutes, considered non-essential, and with a high price relative to income tend to have a higher price elasticity of demand.

## 5. How can price elasticity of demand be used in business?

Price elasticity of demand is an important concept for businesses as it helps them understand how changes in price will affect the demand for their products. By knowing the price elasticity of demand, businesses can make informed decisions on pricing strategies, product differentiation, and marketing efforts to maximize profits.

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