Question

2. Assume the following two demand curves:

Marginal Willingness to Pay = 18 - .45 Q

Marginal Willingness to Pay = 26 – 3 Q

Solve for the following:

a)Start each curve at a price of $5 and increase the price to $7.50, what is the percent change in quantity demanded on each curve (hint: watch your signs)

b)Find the elasticity of each of these curves at this price change.

c) Are (A) and (B) elastic or inelastic.

d) Describe elastic and inelastic goods. Dose a good become more elastic over time? Explain.

Answer 1

(a)

Demand curve A

MWP = 18 - 0.45Q

At price of $5,

5 = 18 - 0.45Q

0.45Q = 13

Q = 28.89

At price of $7.50,

7.50 = 18 - 0.45Q

0.45Q = 18 - 7.50

0.45Q = 10.5

Q = 23.33

Percentage change in quantity demanded = [(23.33 - 28.89)/23.33] * 100 = -19.24%

The percentage change in quantity demanded on Demand curve A is -19.24%.

Demand curve B

MWP = 26 - 3Q

At price of $5,

5 = 26 - 3Q

3Q = 26 - 5

3Q = 21

Q = 7

At price of $7.50,

7.50 = 26 - 3Q

3Q = 26 - 7.50

3Q = 18.50

Q = 6.17

Percentage change in quantity demanded = [(6.17 - 7)/7]*100 = -11.86%

The percentage change in quantity demanded on demand curve B is -11.86%.

(b)

Percentage change in price = [(7.50 - 5)/5] * 100 = 50%

Calculate elasticity of demand curve A at this price change -

Elasticity = % change in quantity demanded/% change in price = -19.24/50 = -0.38

The elasticity of demand curve A at this price change is -0.38

Calculate the elasticity of demand curve B at this price change -

Elasticity = % change in quantity demanded/% change in price = -11.86%/50 = -0.24

The elasticity of demand curve B at this price change in -0.24

(c)

The value of elasticity of demand in case of both (A) and (B) is less than 1.

So, both (A) and (B) are inelastic.

(d)

Elastic good are those goods in case of which proportionate change in quantity demanded is greater than the proportionate change in price.

Inelastic good are those goods in case of which proportionate change in quantity demanded is less than the proportionate change in price.

A good becomes more elastic overtime because as time period increases, chances of finding substitutes of good increases that makes demand elastic. Also, as time period increases, more time becomes available to adjust demand to price change making the demand for good elastic.