Question

The demand curve is P= 100 – (4/5) x Q. What price maximizes total revenues to the firms?

Answer 1

Answer

Total revenue is maximum when the marginal revenue is zero.

MR=100-2*(4/5)Q =100-(8/5)Q ........... An MR curve is a double sloped than an inverse linear demand curve

equating to zero

100-(8/5)Q=0

(8/5)Q=100

Q=100*(5/8)

Q=62.5

P=100-(4/5)*62.5=50

The price is $50

Answer 2

Total revenue (TR) is given by the equation:

TR = P x Q

Substituting the demand equation P= 100 – (4/5) x Q, we get:

TR = (100 – (4/5) x Q) x Q TR = 100Q – (4/5)Q^2

To maximize total revenue, we need to take the derivative of TR with respect to Q and set it equal to zero:

d(TR)/d(Q) = 100 - (8/5)Q = 0 100 = (8/5)Q Q = 62.5

Substituting Q = 62.5 into the demand equation to solve for P, we get:

P = 100 - (4/5) x 62.5 P = 50

Therefore, the price that maximizes total revenue for the firm is $50.