<p>Suppose a monopolist faces the following inverse demand function : 
<span class="math-container">$p = exp(-Q)$</span>
The monopolist can produce any positive level of output with zero variable cost. Its fixed cost is <span class="math-container">$F$</span>. Find the profit-maximising output for two cases (i) when <span class="math-container">$F = 0.1$</span> and (ii) when <span class="math-container">$F= 0.5$</span>.
I tried solving it using, <span class="math-container">$MR=MC$</span>, 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!</p>

CC BY-SA 4.0
2019-03-19T19:40:47.330Z
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.
dlnB
CC BY-SA 4.0
2019-03-19T22:25:02.817Z
Can you describe the cost function? Is it  $C(q) = F$  OR  $C(q) = \begin{cases} F & \text{if } Q > 0 \\ 0 & \text{if } Q = 0 \end{cases}$ ?
Amit
CC BY-SA 4.0
2019-03-20T06:34:02.307Z
@Amit they haven't mentioned the cost function specifically, but since the variable cost is zero I think the former is the right interpretation!
Dr. Dre
CC BY-SA 4.0
2019-03-20T06:36:20.103Z
@dlnB how did you arrive at the conclusion that the profit is negative in the second case without plotting the graph?
Dr. Dre
<monopoly>
Profit Maximisation for a Monopolist
Dr. Dre
# Profit Maximisation for a Monopolist

(Asked by: username_0 on 2019-03-19)

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!

**Tags:** monopoly

> **Comments:**
> **username_1**: 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.  
> **username_2**: Can you describe the cost function? Is it  $C(q) = F$  OR  $C(q) = \begin{cases} F & \text{if } Q > 0 \\ 0 & \text{if } Q = 0 \end{cases}$ ?  
> **username_0**: @username_2 they haven't mentioned the cost function specifically, but since the variable cost is zero I think the former is the right interpretation!  
> **username_0**: @username_1 how did you arrive at the conclusion that the profit is negative in the second case without plotting the graph?  

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