Calculus/Managerial Economics Question

8. If the demand equation is given by QD = 10 – 2P, write the corresponding marginal revenue (MR) equation.

a. MR = 10 – 4P
b. MR = 5 – 2Q
c. MR = 5 – Q
d. MR = 10 – Q

I know the answer is C ( I have a key), but I cannot understand why. Trying to study for a test tomorrow. Anyone care to help explain the process of arriving at that answer?

Thank you,
Travis

The marginal revenue is the derivative of revenue with respect to quantity.
Furthermore, revenue = price * quantity.

Let P = price, Q = quantity, R = revenue.

Q = 10 - 2P, so Q^2 = 10Q - 2PQ = 10Q - R, so R = (10Q - Q^2)/2.

Marginal revenue = dR/dQ = (10 - 2Q)/2 = 5 - Q, choice C.

Lord bless you on your test tomorrow!