Question

5 60 3. Demand function of the good X is Dx = 60 -10P. Find out the price of X when demand will be : (1) 20 units (ii) 10 units (iii) 0 units.
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Answer 1

Answer:

Given, x=324−2P

P=12−23x

(i) Revenue function R(P)=Px=P(324−2P)

=8P−32P2

Revenue function R(x)=Px=(12−23x)x

12x−23x2

(ii) For maximum revenue, dPdR(P)=8−34P=0⇒P=6

and dP2d2R(P)=−34(<0)

For maximum revenue, dxdR(x)=12−3x=0 ⇒ x=4

and dx2d2R(x)=−3(<