Download Project: Elasticity Of Demand

Project: Elasticity Of Demand
If you change the price of an Item you sell, you should expect the number of sells to change. In
general, a higher price means less demand for your product. We are going to investigate how
much a price change really affects the sales of a given item. The change in demand as related to
change in price varies with different products. For example, a change in the price of a candy bar
by one dollar will affect the demand for that candy bar in a substantial way, but if the price of a
computer system is changed by one dollar, the demand is not affected at all. Instead of
considering the absolute change in price, it is easier to consider and compare the percent change
in price. We investigate how a 1% change in price affect the demand. We look at the percent
change in demand rather than the absolute change.
The percent change in demand is given by ∆q/q, and the percent change in price is given by
∆p/p. The ratio of percent change in demand to the percent change in price is (∆q/q)/( ∆p/p). If
the absolute value of the ratio is large then a change in price caused a larger change in demand.
We can also rewrite the ratio as follows:
( q/q)/( p/p) = ( q/q) *(p/ p) =( p/q) *( q/ p) = (p/q)/( p/ q) = ( p/q)/(dp/dq) for very
small changes in the independent variable.
Therefore the Elasticity of Demand for a product is defined to be the ratio of percent change in
demand to percent change in price which is given by the equation, E = (p/q)/(dp/dq). If the
Absolute value of E > 1 the elasticity is called elastic , which means that 1% change in price
causes a relatively larger change in demand . If the absolute value of E = 1 (this is called unit
elastic) then a 1% change in price produces approximately a 1% change in demand. If the
absolute value of E < 1 (this is called inelastic) then a 1% change in price little or no change in
demand.
Elasticity and revenue are related as follows:
Maximum revenue occurs when demand is unit elastic. If demand is inelastic, then revenue is
increased by raising the price. If demand is elastic then revenue is increased by lowering the
price.
Elastic Demands : silver, furniture, cars, musical instruments, T.Vs, sporting goods, etc.
Inelastic Demands: electricity, beverages, food, clothing, Medicines, insurance, water, etc
Example I : A white water rafting company wishes to raise their rates from $75 to $80 per
person. He is afraid that in doing this, the number of customers will decrease from 100 to 90 per
week.
a) What is the elasticity of demand?
b) Should the company raise the price?
First find the percent change in price, the percent change in demand and then the elasticity.
Ans: E = -1.5 Show your work and give your conclusion in complete sentences.
Example 2:
10.
If the demand for a product is given by q = 1000 - 2p^2 , find the elasticity at p =
Solution: Since E = (p/q)*(dq/dp), fill in this formula as follows:
E = ( p/q)*(-4p) = (10/800)*(-40) = -0.5 therefore at a price of $10, a 1% increase in price will
result in approximately .5% decrease in demand. The demand is inelastic.
Now try the same problem again for the price p = $15. Show your work and give your answers in
complete sentences.
Example 3: If the demand for a product is given by p = 6 - 0.5q , Find the elasticity at q = 80.
Solution: Since E =( p/q)/(dp/dq), fill in this formula as follows:
E = (p/q)/ (-0.5) = (-34/80)/(-0.5) = ??
Find the answer and determine if this demand is elastic, unit elastic or inelastic. Interpret the
results as in example 2.
Problems to turn in;
1) The demand for Hand-Held Radios made by a certain company is given by q = 300 - p. Use
Excel to determine the Elasticity of demand. In the first column put in values for p starting with
0. You may have to expand your original values entered as needed. In the second column type in
the elasticity formula for the given demand equation. Run your values to determine where unit
elasticity occurs. Verify this answer by algebra. Set your Elasticity equation = -1 and solve.
Verify that revenue is maximum at that value by showing that MR = 0.
2) Assume the demand equation for bananas is q = 5000 - 100p^2, where q is in pounds of
bananas and p is the price per pound.
a) If the current price of bananas is $2 /lb, how many pound will be sold?
b) Is the demand elastic or inelastic at $2? What would be correct to say? 1) "People must have
their bananas." or 2) " Bananas are a luxury item."
c) At a price of $2/lb what is the total revenue for the banana farmer?
d) Use the equation for revenue and find maximum revenue. Find the price for Maximum
revenue.
e) What quantity is sold at the price found in d).
f) show that E = -1 for the price you found in d).
3) According the elasticity value given would the following be a luxury item or a necessity?
Item
Milk
jewelry
Poultry
furniture
lightbulbs
elasticity
-0.31
-2.60
-0.27
-3.04
-0.33
Luxury or Necessity
_______________
_______________
________________
________________
________________
4) Girl Scouts raise money by selling cookies door to door. For a certain new cookie, the
following data has been collected, where p is the price of the box of cookies and q is the quantity
sold at that price:
p $1.00 $1.25
$1.50 $1.75 $2.00 $2.25 $2.50 $3.00
q
2765 2440
1980
1660 1175
950
480
200
Use Excel or a calculator to estimate the elasticity at each of the prices shown.( Since you do not
have a given equation for demand, you will use the equation E = (∆q/q)/( ∆p/p) or find a best fit
equation and use the formula for E as before. ) What do you notice? Where does unit elasticity
occur? Find the total revenue at each price and confirm that revenue is maximum approximately
when E = -1