Question

Using Calculus, calculate the elasticity of the following demand functions. After that, calculate the elasticity for the points (1, 3) and (2, 2).

The first coordinate of the points above is Q, the second is Price.

(1) Q = 10P ^ (-4)

(2) Q = 10 - P

Answer 1

(1) Q= 10P^(-4)

dQ/dP = 10[ -4. P^ (-4-1)]

= 10[ -4P^(-5) ]

= -40P^(-5)

= -40/P^5

Ep= (dQ/dP)* (P/Q)

= (-40/P^5) * (P/Q)

= (-40/P^4) * (1/Q)

At Q=1 and P=3

Ep= (-40/3^4) * (1/1)

= -40/81

= -0.49

At Q=2 and P=2

Ep= (-40/2^4) * (1/2)

= (-40/16) * (1/2)

= -40/32

= -1.25

(2) Q=10-P

dQ/dP= -1

Ep = (dQ/dP) * (P/Q)

= -1 * (P/Q)

= -P/Q

At Q=1 and P=3

Ep= -3

At Q=2 and P=2

Ep= -2/2

= -1