<p>Under perfect competition, $p=MC$. So you may substitute this price into the demand equation to obtain the quantity.</p>

<p>A monopolist chooses output in a way such that $MR=MC$. So you have $P‘(Q)*Q+P=MC(Q)$, where $P(Q)$ is the inverse demand  equation.</p>

<p>For Cournot, it is also simple. Note that the profit function of firm i is given by $$\pi(i)=P(q_{i}+q_{-i})*q_{i}-MC(q_{i})*q_{i}$$. You just use the first order condition to solve for the price and quantitiy respectively. $q_{-i}$ denotes the output of all players except for $i$.</p>

<p>Finally, for Stackelberg I would like to know how many players/firms you have. Then, I would be able to explain it to you in a suitable way. I hope this helps.</p>

CC BY-SA 4.0
2018-05-13T08:55:52.107Z
Thanks for the answer, but I am not sure, how to use this equation `Q=1000-10*P` and `MC=50` value in these formulas. Could you please explain it with exact numbers? I have two firms.
plaidshirt
CC BY-SA 4.0
2018-05-13T21:16:51.030Z
under perfect competition, price would be $p=MC=50$. Substitute this into the demand equation to get $Q=1000-10*50=500$.
saguru
CC BY-SA 4.0
2018-05-13T21:22:28.233Z
for a monopolist: the inverse demand is $P(Q)=100-Q/10$. Hence $-1/10*Q+100-Q/10=50$. Hence, $Q=250$ and $P=75$. For the other models use the same logic, i.e. just substitute in your equations in what I told you above.
saguru
CC BY-SA 4.0
2018-05-14T07:38:26.230Z
What is the meaning of `q−i` in your equation?
plaidshirt
CC BY-SA 4.0
2018-05-14T08:02:12.910Z
In your case it would be the quantity produced by the other firm. So if you’re computing the quantity for firm 1, $i$ would be 1, $q_{-i}$ is the notation for the quantity produced by all other firms, which would in this case boil down to $q_{2}$.
saguru
CC BY-SA 4.0
2018-05-12T23:08:21.973Z
2018-05-12T23:08:21.973Z
saguru
<p>There are a given demand and <code>MC</code> value. How could I calculate quantity, price, and profit from these values in case of perfect competition, in monopoly and duopoly(Cournot and Stackelberg)?</p>

<microeconomics><econometrics><supply-and-demand>
Compute variables in perfect competition, in monopoly and duopoly
plaidshirt
# Compute variables in perfect competition, in monopoly and duopoly

(Asked by: username_0 on 2018-05-12)

There are a given demand and `MC` value. How could I calculate quantity, price, and profit from these values in case of perfect competition, in monopoly and duopoly(Cournot and Stackelberg)?

**Tags:** microeconomics, econometrics, supply-and-demand

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## 1 answers

### Answer by username_1 on 2018-05-12. Score: 1 | Accepted answer

Under perfect competition, $p=MC$. So you may substitute this price into the demand equation to obtain the quantity.

A monopolist chooses output in a way such that $MR=MC$. So you have $P‘(Q)\*Q+P=MC(Q)$, where $P(Q)$ is the inverse demand equation.

For Cournot, it is also simple. Note that the profit function of firm i is given by $$\pi(i)=P(q\_{i}+q\_{-i})\*q\_{i}-MC(q\_{i})\*q\_{i}$$. You just use the first order condition to solve for the price and quantitiy respectively. $q\_{-i}$ denotes the output of all players except for $i$.

Finally, for Stackelberg I would like to know how many players/firms you have. Then, I would be able to explain it to you in a suitable way. I hope this helps.

> **Comments:**
> **username_0**: Thanks for the answer, but I am not sure, how to use this equation `Q=1000-10*P` and `MC=50` value in these formulas. Could you please explain it with exact numbers? I have two firms.  
> **username_1**: under perfect competition, price would be $p=MC=50$. Substitute this into the demand equation to get $Q=1000-10*50=500$.  
> **username_1**: for a monopolist: the inverse demand is $P(Q)=100-Q/10$. Hence $-1/10*Q+100-Q/10=50$. Hence, $Q=250$ and $P=75$. For the other models use the same logic, i.e. just substitute in your equations in what I told you above.  
> **username_0**: What is the meaning of `q−i` in your equation?  
> **username_1**: In your case it would be the quantity produced by the other firm. So if you’re computing the quantity for firm 1, $i$ would be 1, $q_{-i}$ is the notation for the quantity produced by all other firms, which would in this case boil down to $q_{2}$.  

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