Question

If Q = 400 – 2P, at what price is revenue maximized at?

For the demand equation P = 36 - 2Q, what Price will maximize total revenue?

If TC=40+6QTC=40+6Q and EP=−3EP​=−3 what is the optimal price to be charged?

If TC=75+15QTC=75+15Q and EP=−2EP​=−2 is P=$30 the optimal price?

Answer 1

If Q = 400 – 2P, at what price is revenue maximized at?

Answer:

The revenue is maximum when marginal revenue =0

the inverse demand curve is

Q=400-2P

2P=400-Q

P=200-0.5Q

TR=P*Q=200Q-0.5Q^2

MR changes in total revenue and a change in function is found by differentiation

MR=dTR/dQ=200-Q

equating to zero

200-Q=0

Q=200

P=200-0.5*200=$100

the revenue is maximum at P=$100

For the demand equation P = 36 - 2Q, what Price will maximize total revenue?

ANswer

TR=P*Q

TR=36Q-2Q^2

MR=dTR/dQ=36-4Q

equating to zero

36-4Q=0

4Q=36

Q=9

P=36-2*9=$18

the total revenue is maximum when P=$18

If TC=40+6Q and EP =−3 what is the optimal price to be charged?

answer

the formula is

P=MC/(1+(1/E))

P=price

MC=marginal cost

E=elastcity

A marginal cost is a change in total cost and a change in function found by differentiation

MC=dTC/dQ=6

P=6/(1+(1/(-3)))

=$9

the optimum price is $9

If TC=75+15Q and EP =−2 is P=$30 the optimal price?

answer

Yes,

MC=dTC/dQ=15

P=15/(1+(1/(-2)))

=$30

the optimum price is $30