A company’s marginal revenue function is given as MR(x) = 5000 - 100x. Find the total revenue function and the total revenue maximizing output.
Answers
Given : A company’s marginal revenue function is given as MR(x) = 5000 - 100x
To Find : the total revenue function and the total revenue maximizing output.
Solution:
The marginal revenue is the derivative of the revenue function
MR(x) = 5000 - 100x
integrating
R(x) = 5000x - 100x²/2 + C
=> R(x) = 5000x - 50x² + C
C is constant
at x = 0 Revenue is 0
Hence R(0) = 0 - 0 + C = 0
=> C = 0
Hence R(x) = 5000x - 50x²
Hence total revenue maximizing output is when 5000x -50x² is max
R'(x) = 5000 - 100x
R'(x) = 0
=> 5000 - 100x = 0
=> x = 50
R''(x) = - 100 < 0
Hence maximum when x = 50
total revenue maximizing output. is 50
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