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Use the following information to answer questions 1 through 4.
When the price is $6.00, the quantity demanded is 20.
When the price is $9.00, the quantity demanded is 16.
Calculate the price elasticity of demand. You must use the midpoint formula shown in your text or in the examples on Blackboard. You need to show all your work to earn credit.
Given the elasticity of demand, a 10% increase in price will cause quantity demanded to fall by what percentage? Explain your answer.
Is this demand elastic or inelastic? Explain your answer.
What is assumed about consumer income when you measure the price elasticity of demand?
Walmart advertises that it has rolled back prices. If Walmart is rolling back prices to raise revenues, should it roll back prices on products that have a price elasticity of demand that is elastic or inelastic? Explain your answer.
Example for Calculating Price
Elasticity of Demand
Given the following table, calculate the price elasticity of demand.
Price Quantity
Demanded
1.00 12
2.00 3
Formula: Ed = | [(Qd1 –Qd2) / {(Qd1+Qd2) / 2}] / [(P1 –P2) / {(P1+P2) / 2}] |
Qd is quantity demanded. P is price Ed is price elasticity of demand.
Plug the numbers into the formula
Ed = | [(12 –3) / {(12+3) / 2}] / [(1–2) / {(1+2) / 2}] |
Do some minor addition and subtraction. The colored highlights show where the
addition and subtraction was done.
Ed = | [(9) / (15 / 2)] / [(-1) / (3/2)] |
Remember that dividing by a fraction is the same as multiplying by its reciprocal.
Ed = | [9 * 2/15] / [-1 * 2/3] |
Do some multiplication. This highlights show where the multiplication was done.
Ed = | (18/15) / (-2/3) |
Remember that dividing by a fraction is the same as multiplying by its reciprocal.
Ed = | (18/15) * (-3/2) |
Simplify the first fraction so 18/15 becomes 6/5
Ed = | (6/5) * (-3/2) |
Two can be divided into the numerator 6 for the first fraction and into the 2 in the
denominator of the second fraction leaving
Ed = | (3/5) * (-3/1) |
Ed = | -9/5 |
Taking the absolute value you are left with
Ed = 9/5 or 1.8
The price elasticity of demand is the only elasticity that you take the absolute value in
the end.
A 5% change in price will cause a 9% change in quantity demanded. Or the alternative
phrasing could be a 1% change in price will cause a 1.8% change in quantity. The
ration of 9% to 5% or 1% to 1.8% In this particular example, demand is elastic since
the Ed is greater than 1 but not undefined or infinite.
Please note that if the number were plugged in as below, the final answer would be the
same. You just would have started the formula as shown below.
Formula: Ed = | [(Qd1 –Qd2) / {(Qd1+Qd2) / 2}] / [(P1 –P2) / {(P1+P2) / 2}] |
Ed = | [(3–12) / {3+12) / 2}] / [2–1) / {(2+1) / 2}] |
Example for Calculating a Price Elasticity of Supply
When the price is $8.00, quantity supplied is 6. When the price is $2.00, quantity
supplied is 4.
Es = [(Qs1 –Qs2) / {(Qs1+Qs2) / 2}] / [(P1 –P2) / {(P1+P2) / 2]
Qs is quantity supplied. P is price. Es is the price elasticity of supply.
Plugging in the numbers
Es = [(6-4) / {(6+4) / 2}] / [(8-2) / {(8+2) / 2]
Do some addition and subtraction to yield the following. The highlights show were the
addition and subtraction were done.
Es = [2 / (10 / 2)] / [6 / (10 / 2)]
Do some division. (It is just a coincidence that you have 10/2 twice.)
Es = (2/5) / (6/5)
Dividing by a fraction is the same as multiplying by its reciprocal.
Es = 2/5 * 5/6
2 will go into the numerator of the first fraction and the denominator of the second
fraction.
Es = 1/5 * 5/3
The fives will cancel each other out
Es = 1/3 or .33
In this example the elasticity of supple is inelastic since .33 is less than 1 but greater
than 0. In this example a 1% increase in price will cause a .33% increase in quantity
supplied.
Example for Calculating Income Elasticity of Demand
When consumer income is 200 their quantity demanded is 500. When their income is
300, their quantity demanded is 450. Qd is quantity demanded. I is income. Ei is
income elasticity of demand.
Ei = [(Qd1 –Qd2) / {(Qd1+Qd2) / 2}] / [(I1 –I2) / {(I1+I2) / 2}]
Plugging in the numbers:
Ei = [(500 –450) / {(500+450) / 2}] / [(200 –300) / {(200+300) / 2}]
Do some addition and subtraction. The highlights show were it was done.
Ei = [(50) / {(950) / 2}] / [(-100) / {(500) / 2}]
Divide 500 by 2 to get 250
Ei = [(50) / {(950) / 2}] / [(-100) / 250]
Dividing by a fraction is the same as multiplying by its reciprocal.
Ei = (50 *2/950) / [(-100) / 250]
Multiple 2 * 50 to get 100 and simplify -100/250 to -2/5
Ei = (100/950) / (-2)/5
Simplify 100/950 to 2/19
Ei = 2/19 / -2/5
Dividing by a fraction is the same as multiplying by its reciprocal
Ei = 2/19 * (-5/2)
The 2’s will cancel out.
Ei = -5/19 = – . 26 It is negative so the good must be an inferior good.
Example for Calculating Cross Price Elasticity of Demand
Formula: Ex = [(Qa1 –Qa2) / {(Qa1+Qa2) / 2}] / [(Pb1 –Pb2) / {(Pb1+bP2) / 2}]
Qa is quantity demanded of good A. P is price of good b. Ex is the cross price elasticity
of demand.
Good A has a quantity demanded of 12 units when the price of good B is $3.00. Good
A has a quantity demanded of 18 when the price of good B is $4.00.
Plugging in the numbers yields:
Ex = [(12 –18) / {(12+18) / 2}] / [(3 –4) / {3+4) / 2}]
Adding and subtracting yields the following. The highlights show additions and
subtractions.
Ex = [(-6) / {(30) / 2}] / [(-1) / {7) / 2}]
Dividing by 30 by 2
Ex = (-6/15) / [(-1) / {7) / 2}]
Dividing by a fraction is the same as multiplying by its reciprocal.
Ex = (-6/15) / [(-1) * (2/7)]
Anything multiplied by 1 is equal to itself. The negative sign carries over to the product
when multiplying by -1.
Ex = (-6/15) / (-2/7)
Dividing by a fraction is the same as multiplying by its reciprocal.
Ex = -6/15 * -7/2
6 divided by 2 = 3 and 2 divided by 2 = 1
Ex = -3/15 *- 7/1
Simplify again
Ex = -1/5 * -7/1
A negative number multiplied by a negative number will be a positive number.
Ex = 7/5 or 1.2
Since the cross price elasticity is positive, the goods A and B are substitutes
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