Final answer:
The marginal revenue function R'(x) is the derivative of the total revenue function R(x)=8x - 0.03x², which is R'(x) = 8 - 0.06x.
Step-by-step explanation:
The student asked to find the marginal revenue function from the given total revenue function R(x)=8x−0.03x². The marginal revenue function can be found by taking the derivative of the total revenue function with respect to x, which represents the quantity of goods sold. This is applying the concept that marginal revenue is the change in total revenue from selling a small additional amount of output.
To find the marginal revenue function, R'(x), we take the derivative of R(x) with respect to x:
⌘ R(x) = 8x − 0.03x²
So R'(x) = 8 − 0.06x
This derivative function, R'(x) = 8 − 0.06x, shows the additional revenue the firm gains for each additional unit sold. In the context of perfect competition, remember that marginal revenue is the same as the price, provided the firm is a price-taker.