Suppose a monopolist faces the following inverse demand function : $p = exp(-Q)$ The monopolist can produce any positive level of output with zero variable cost. Its fixed cost is $F$. Find the profit-maximising output for two cases (i) when $F = 0.1$ and (ii) when $F= 0.5$. I tried solving it using, $MR=MC$, the latter in this case is zero, so in both the cases I am getting 1 as the answer, and I am not sure if it is correct!

  • $\begingroup$ Your answer is correct. The profit-maximizing price and quantity are independent of fixed cost as fixed cost does not appear in the first-order condition. In the former case, profit is positve, while the latter corresponds to negative profit. $\endgroup$ – dlnB Mar 19 at 19:40
  • $\begingroup$ Can you describe the cost function? Is it $C(q) = F$ OR $C(q) = \begin{cases} F & \text{if } Q > 0 \\ 0 & \text{if } Q = 0 \end{cases}$ ? $\endgroup$ – Amit Mar 19 at 22:25
  • $\begingroup$ @Amit they haven't mentioned the cost function specifically, but since the variable cost is zero I think the former is the right interpretation! $\endgroup$ – Dr. Dre Mar 20 at 6:34
  • $\begingroup$ @dlnB how did you arrive at the conclusion that the profit is negative in the second case without plotting the graph? $\endgroup$ – Dr. Dre Mar 20 at 6:36

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