Question

For a demand curve P = 60 – 0.5Q, find the elasticity at P = 10. If the demand curve shifts parallel to the right, what happens to the elasticity at P = 10?

Answer 1

P=10

then Q is

10=60-0.5Q

0.5Q=50

Q=100

elastcity of demand =(dQ/dP)*Q

converting the inverse demand curve to normal form

P=60-0.5Q

0.5Q=60-P

Q=120-2P

dQ/dP=-2

elastcity of demand =(-2)*(10/100)

=-0.2

the elastcity of demand is -0.2 (0.2 in absolute value)

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The elasticity of demand decreases because of the shift as the increase in the demand makes the demand more inelastic at the same price level.

For example:

A parallel shift to right increases the constant in the demand function as it is a linear function; suppose the constant increases by 10 then the new demand curve is :

Q=130-2P

dQ/dP=-2 ------- slope is the same as the shift is parallel

P=10

Q=130-2*10=110

elasticity of demand=(-2)*(10/110)

=-0.181818182

=0.18 (absolute value)