A friend of mine just asked this question and I showed how far we understand. Ca

Question

A friend of mine just asked this question and I showed how far we understand. Can you explain in easy terms how you finish this.

Suppose the demand curve for coffee is P= 10 - 2Q and P = $6. Calculate the absolute value of the price elasticity of demand at the $6 price.

A) 6.00
B) 1.50
C) 1.00
D) 0.66
E) 0.16


This is what we got...beside the question are what we dont understand

ED = -(dQ/dP x P/Q) why is there a minus in front of this
P= 10 - 2Q ,
if P= $6 ,
6 = 10 -2Q
Q =2
P/Q = 6/2= 3
and
from
P= 10 - 2Q
Q =1/2(10-P) we get it to here....but do not understand how they did
the next step...ie dQ/Dp = - 1/2. please in easy terms

dQ/dP = -1/2
ED = -(-1/2 x 3) = 3/2 = 1.5
answer : B) 1.50

Explanation / Answer

ED = -(dQ/dP x P/Q)
P= 10 - 2Q ,
if P= $6 ,  

6 = 10 -2Q

Q =2

P/Q = 6/2= 3
and

from

P= 10 - 2Q

Q =1/2(10-P)

dQ/dP = 1/2 [d(10)/dP - dP/dP]                  [d(10)/dP =0 , as 10 is constant ][dP/dP = 1]

dQ=dP = 1/2 [0-1]
dQ/dP = -1/2
ED = -(-1/2 x 3) = 3/2 = 1.5

answer : B) 1.50

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