# Industrial Economics

I am currently struggling trying to find the short-run equilibrium price, output per firm, and profit per firm if $$190$$ firms supply the market. I am given $$p=102-1/2Q$$ and $$C(q)=5q-6q^2+3q^3$$.

First I started off with $$P=MC$$. So $$P=9q^2-12q+5$$, thus $$9q^2-12q+(5-P)=0$$.

Then, I Used the quadratic equation and came out with $$q=2/3+1/3\sqrt{p-1}$$.

Then I did $$Q=nq=190\left(2/3+1/3\sqrt{p-1}\right)$$.

Equating demand and supply I obtained $$P\approx 2.32$$ and then plugged back into $$q\approx2/3+1/3\sqrt{2.32-1}$$ to get $$q\approx1.05$$

Finally, I plugged $$q$$ and $$P$$ into $$\pi=q\cdot P-C(q)$$ and came up with $$\pi\approx 0.33$$. This just seems crazy to me! I have tried for the past few days over and over again to understand, but I am completely lost.

Any help would be greatly appreciated!

• The policy of this forum is that you should show that you have tried doing it, and be precise on what part is confusing. Otherwise, it looks like you are simply looking for someone to do your homework. Not saying that is your case, but if you update your question people can help you here. Jun 19 '19 at 4:41
• Hi Regio. I didn't know that! Okay well first I started off with P=MC. P=9q^2-12q+5. 9q^2-1212q+(5-p)=0. Used quadratic equation and came out with 2/3+1/3*sqrt(p=1). Then I did Q=nq=190(2/3+1/3*sqrt(p-1)). I solved down to 2.32....=p and then plugged back in to q=2/3+1/3*sqrt(2.32....-1) to get q=1.05.... Then I plugged q and p into q*p-C(q) and came up with .33.... This just seems crazy to me. I have tried for the past few days over and over again to understand but I am completely lost. Thanks for the help!
– jj99
Jun 19 '19 at 4:57
• I will edit that into the original question for future reference for other people if you don't mind. Jun 19 '19 at 5:04