Question #3740

Demand function for a cola-type soft drink in general is q= 20 – 2P, where Q stand
for quantity and P stands for price.
<br>a. Calculate point elasticities at prices of 5 and 9. Is the demand curve elastic or inelastic at these points?
<br>b. Calculate arc elasticity at the interval between P = 5 and P = 6.

Expert's answer

Point elasticity (Ed).

E_{d}=δQ/δP * P/Q , where δQ/δP= -2

P_{1}=5, Q_{1}=20-2*5=10;

P_{2}=9, Q_{2}=2;

Point elasticity at the price P_{1}: E_{d1} = -2 * 5/10= -1. Unitarily elastic demand.

Point elasticity at the price P_{2}: E_{d2} = -2 * 9/2= -9. The demand curve is elastic.

Arc elasticity (Ed).

E_{d}=δQ/δP * (P_{1}+P_{2})/(Q_{1}+Q_{2} )

P_{1}=5, Q_{1}=10;

P_{2}=6, Q_{2}=8;

E_{d1}= -2/1 * 11/18= -11/9=-1.22

The demand curve is elastic.

E

P

P

Point elasticity at the price P

Point elasticity at the price P

Arc elasticity (Ed).

E

P

P

E

The demand curve is elastic.

## Comments

Assignment Expert19.10.18, 18:07Dear Muhammad Adil, please use panel to submit new questions.

Muhammad Adil19.10.18, 15:34The demand function for a cola-type soft drink in general is Q = 20 - 2P, where Q stands

for quantity and P stands for price.

a. Calculate point elasticities at prices of 5 and 9. Is the demand curve elastic or inelastic

at these points?

b. Calculate arc elasticity at the interval between P = 5 and P = 6.

c. At which price would a change in price and quantity result in approximately no change

Assignment Expert29.03.12, 17:11It's given that&

<span style="font-family: Arial, sans-serif; font-size: 14px; line-height: 24px; text-align: justify; text-indent: 27px; background-color: rgb(250, 250, 250); ">q= 20 – 2P</span><div><span style="font-family: Arial, sans-serif; font-size: 14px; line-height: 24px; text-align: justify; text-indent: 27px; background-color: rgb(250, 250, 250); ">So we can find derivative dq/dp=d(20-2p)/dp=-2</span></div>

Scott28.03.12, 12:48How do you the Q/P = -2 in the point elasticity equation?

Assignment Expert14.10.11, 18:35You are welcome. We're pleased to help you

umair19.09.11, 14:34Good .Thanks

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