In the Stackelberg model, suppose the first-mover has MR = 15 - Q1, the second f

Question

In the Stackelberg model, suppose the first-mover has MR = 15 - Q1, the second
firm has reaction function Q2 = 15 - Q1/2, and production occurs at zero marginal
cost. Why doesn't the first-mover announce that its production is Q1 = 30 in order to
exclude the second firm from the market (i.e., Q2 = 0 in this case)?
A) In this case, MR is negative and is less than MC, so the first-mover would be
producing less than the optimal quantity.
B) In this case, MR is negative and is less than MC, so the first-mover would be
producing too much output.
C) This is a possible outcome from the Stackelberg duopoly under these conditions.
D) We do not have enough information to determine if this is an optimal outcome for
this case.

Explanation / Answer

Should be answer B. If a firm produces Q such that MR is less than MC, then they should produce less until MC=MR. To check, you can solve this game to find the optimal result then compare it to the outcome suggested by the problem, although I don't think this is necessary. If MC1=MC2, then the Stackelberg profit will be 3/4 of monopoly profit. If monopoly profit is greater than zero, the firm will make more money by producing less output than perfect competition quantity.

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