Econ: Solving Elasticity Problem & Analyzing Revenue Function

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In summary, the demand for a product is inelastic when the price is raised by 4x, but elastic when the price is raised by 1x. The revenue function is unit elastic when the price is raised by 1x.
  • #1
mathkid3
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The demand function for a product is given by p = 800 -4x, 0 <= X <= 200, where p is the price (in dollars) and x is the number of units.

(a) Determine when the demand is elastic, inelastic and of unit elasticity.

(b) Use the result of part (a) to describe the behavior of the revenue function.(Angry)
 
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  • #2
The elasticity $E$ of a demand function $p(x) = 800-4x $ is given as $\displaystyle E = \frac{x\times p'(x)}{p(x)}$
 
  • #3
hi,

Thanks for your help here. I am only in an Elementary Calculus 1 class and where I am sure your answer is correct...they have not introduced us to the formula you use.

What they have done is give us the following formula and I wanted to ask if you could respond again, taking this basic elementary formula and stating it again in a way I could proceed?

N = (p/x)/(dp/dx) They state this is
Formula for price
elasticity of demand

Thank you sir!
 
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  • #4
mathkid3 said:
hi,

Thanks for your help here. I am only in an Elementary Calculus 1 class and where I am sure your answer is correct...they have not introduced us to the formula you use.

What they have done is give us the following formula and I wanted to ask if you could respond again, taking this basic elementary formula and stating it again in a way I could proceed?

N = (p/x)/(dp/dx) They state this is
Formula for price
elasticity of demand

Thank you sir!

If you consult the relevant Wikipedia page you will see that pickslides' definition of the elasticity is the standard definition, yours is the reciprical of this (see the note below about notation if you are not familiar with the dash notation for a derivative).

The same page gives you all the information you need to interpret the Elasticity, or if you are required to use the reciprical definition is easilly reinterpretable in terms of that since N=1/E the way you have defined it.

For your information:
\[ p'(x)=\frac{dp}{dx}\]
is what picksides notation denotes.

CB
 
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  • #5
I'm sorry, I'm a scientist, not an economist. I am not qualified to provide a response to this content. Please consult an expert in economics for assistance.
 

Related to Econ: Solving Elasticity Problem & Analyzing Revenue Function

1. What is elasticity in economics?

Elasticity in economics refers to the measure of how responsive the demand or supply of a product is to changes in its price. It is a crucial concept in understanding how consumers and producers behave in the market and how prices affect the quantity of goods bought and sold.

2. How is elasticity calculated?

Elasticity is calculated by dividing the percentage change in the quantity demanded or supplied by the percentage change in the price. The formula for price elasticity of demand is (ΔQ/ΔP) x (P/Q), where ΔQ is the change in quantity, ΔP is the change in price, P is the original price, and Q is the original quantity. A higher value indicates a more elastic demand or supply, while a lower value indicates a more inelastic demand or supply.

3. What are the different types of elasticity?

The different types of elasticity include price elasticity of demand, price elasticity of supply, income elasticity of demand, and cross-price elasticity of demand. Price elasticity of demand measures the responsiveness of quantity demanded to changes in price, while price elasticity of supply measures the responsiveness of quantity supplied to changes in price. Income elasticity of demand measures the sensitivity of demand to changes in income, and cross-price elasticity of demand measures the responsiveness of demand for one product to changes in the price of another related product.

4. How do you interpret the value of elasticity?

The value of elasticity can be interpreted as the degree of sensitivity of quantity to price changes. A value greater than 1 indicates a relatively elastic demand or supply, meaning that a small change in price leads to a significant change in the quantity demanded or supplied. A value less than 1 indicates a relatively inelastic demand or supply, meaning that a change in price has a small effect on the quantity demanded or supplied. A value of 1 indicates unit elasticity, where the percentage change in quantity equals the percentage change in price.

5. How can elasticity be used to analyze revenue function?

Elasticity can be used to analyze revenue function by determining the optimal price and quantity combination that maximizes revenue. A firm can calculate the price elasticity of demand for its product and use this information to adjust prices accordingly. If the demand is relatively elastic, a decrease in price could lead to an increase in revenue, while an increase in price could lead to a decrease in revenue. On the other hand, if the demand is relatively inelastic, a decrease in price could lead to a decrease in revenue, while an increase in price could lead to an increase in revenue. By considering elasticity, a firm can make informed decisions to optimize its revenue function.

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