If price of an article decreases from Rs P
1
​
to Rs 190, when quantity demanded increases from 5000 units to 5200 units, and if point elasticity of demand is -0.8 find P
1
​
?

Using the mid-point / linear definition often applied in such examinations for price elasticity of demand (E
d
​
):

E
d
​
=
ΔP
ΔQ
​
×
Q
1
​

P
1
​

​

Given:

Initial Quantity, Q
1
​
=5000

Final Quantity, Q
2
​
=5200

ΔQ=5200−5000=200

Initial Price = P
1
​


Final Price, P
2
​
=190

ΔP=190−P
1
​


Elasticity, E
d
​
=−0.8

Substitute these values into the formula:

−0.8=
190−P
1
​

200
​
×
5000
P
1
​

​

−0.8=
5000
200
​
×
190−P
1
​

P
1
​

​

−0.8=
25
1
​
×
190−P
1
​

P
1
​

​

−0.8×25=
190−P
1
​

P
1
​

​

−20=
190−P
1
​

P
1
​

​

Cross-multiplying gives:

−20×(190−P
1
​
)=P
1
​

−3800+20P
1
​
=P
1
​

20P
1
​
−P
1
​
=3800
19P
1
​
=3800
P
1
​
=
19
3800
​
=200
Thus, the original price P
1
​
is Rs. 200.