I have recently been stumped on a microeconomics question where it gives a monopoly firm, its operating ATC (average total cost), price (average revenue), and quantity traded. First thing it wants me to do is to calculate marginal cost (MC). However, the information I am given is only at a single point, so how am I going to calculate it? Here it gives ATC = 30,Price= 300, and Q = 1,000,000. That's all the info the question gave me. I've had the thought that since this is where the firm is operating, then MC = MR. So if I can find MR at this quantity traded, that will be the MC. However, I am also stuck calculating MR.
Here's all the working I've been able to do: TR = AR x Q = 300 * 1000000 = 300 m. TC = ATC x Q = 30 * 1000000 = 30 m. I've also drawn a graph of ATC, AR, MR, and MC, but without knowing the y-intercept of the AR and MR functions it looks unlikely that MC = MR can be evaluated. I'm aware that the MR curve has twice the slope of demand curve, but that does not give any help with finding MR from the Price. Neither does ATC = MC since monopolies are not operating at the efficient scale.