Question

Given the total revenue function TR = 50Q - 0.5 Q2

and the total cost function TC = 2000 + 200Q - 0.2Q2 + 0.001Q3

Find the marginal revenue and the marginal cost functions

Answer 1

To obtain the Marginal revenue function, differentiate the Total revenue function w.r.t Q

$MR=\frac{dTR}{dQ}=50-Q$

To obtain the Marginal Cost function, differentiate the Total Cost function w.r.t Q

$MC=\frac{dTC}{dQ}=200-0.4Q+0.003Q^{2}$