Refer to the following figure.What is the equation for marginal revenue?
A)MR = 4,000 - 0.005P
B)MR = 4,000- 200Q
C)MR = 4,000- 200P
D)MR = 20 - 0.01Q
E)MR = 20 -200Q

Question

Refer to the following figure.What is the equation for marginal revenue? 
A)MR = 4,000 - 0.005P 
B)MR = 4,000- 200Q 
C)MR = 4,000- 200P 
D)MR = 20 - 0.01Q 
E)MR = 20 -200Q

Quizplus · Accepted Answer

The equation for marginal revenue is based on the slope of the total revenue curve, which is twice the slope of the demand curve. In the given figure, the demand curve has a slope of (-1/200) and intercepts the price axis at 40. Thus, the equation for demand is P = 40 - 0.005Q. Twice the slope of the demand curve gives us the slope of the total revenue curve, which is -0.01. Using the point (10, 300) on the total revenue curve, we can find the y-intercept of the total revenue curve, which is 310. Therefore, the equation for total revenue is TR = 310 - 0.01Q^2. Taking the first derivative of total revenue with respect to quantity gives us the equation for marginal revenue, which is MR = 20 - 0.02Q. Simplifying this equation gives us MR = 20(1 - 0.001Q), which is of the form MR = a - bQ. Thus, the answer is D.

Refer to the Following Figure