Question

The demand function for your large pizza is estimated by the equation Q = 5,000 - 25P + 4M +10P_A - 15P_T. Moreover, currently P = 10, P_A = 15, M = 500, P_T = 100. Is the current price, P = $10, the best price you can charge to maximize your revenues?  If it is not, what price should you charge to maximize revenue?

Answer 1

it is not the price where revenue is maximum because demand is inelastic and the revenue is maximum at P=$113

------------------------

the demand equation given is

Q = 5,000 - 25P + 4M +10P_A - 15P_T

P = 10, P_A = 15, M = 500, P_T = 100

Q=5000-25*10+4*500+10*15+-15*100

Q=5400

Q=5000-25P+4*500+10*15+-15*100

Q=5650-25P

the inverse demand curve is

Q=5650-25P

25P=5650-Q

P=226-0.04Q

the revenue is maximum at elastcity=-1 or unit elastic

elastcity=(dQ/dP)*Q

=(-0.04)*(10/5400)

=-0.00007407407

the demand is inelastic so need to increase price to make it unit elastic.

revenue is maximum when MR=0

Total revenue =P*Q=226Q-0.04Q^2

MR=dP/dQ=226-0.08Q

equating to zero

226-0.08Q=0

0.08Q=226

Q=226/0.08=2825

P=226-0.04*2825=113

the revenue is maximum at P=$113 and the P=$10 the revenue is lnot maximum.