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I'm studying Mathematical Economics and there's this question that I'm unable to understand.

Q. Suppose a firm faces a demand curve for its product $P = 32 - 2Q$, and the firm's costs of production and marketing are $C(Q) = 2Q^2$. Find the following:

(f) What would the competitive price and quantity be, assuming $C(Q) = 2Q^2$ represented the industry cost function?

Actually the question has 5 more parts but I was only stuck on this last one (f). In the other parts I calculated Profit formula, price and quantity that maximize total revenue and the price and quantity that maximize profit (if by any chance these are related to the last part)

Any help will be appreciated!

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  • $\begingroup$ Take the derivative of your cost function (which is marginal costs) and set it equal to price. Then solve. $\endgroup$ – Joseph Apr 29 '18 at 22:27
  • $\begingroup$ Hi, Welcome to Economics SE! we have a policy regarding homework questions where we require that you show some work before an answer is provided. More on this topic here: economics.meta.stackexchange.com/questions/1465/… $\endgroup$ – EconJohn Apr 30 '18 at 3:31
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Well, it's very straightforward question. You have a cost function, from which you can get a Supply Curve, by taking its first derivative. You'll find competitive price and quantity when the supply curve you got meets the demand curve.

First, our supply curve: $$P = 4Q$$ Then, the demand curve:

$$ P = 32- 2Q$$

Competitive $Q$ is:

$$ 32 - 2Q = 4Q $$ $$Q = \frac{32}{6} \approx 5.333$$

So, competitive price is: $$ P = 32 - 2 * 5.333 \approx 21.333$$

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    $\begingroup$ Thank you so much! I hd completely forgotten that marginal cost curve is also your supply curve. $\endgroup$ – M. Asbaat Amar May 2 '18 at 15:26

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