So in this case we've been given the supply and the demand equations for 13 commodity. So the supply in question is modeled by the equation P is equal to under root of 0.1, Q plus nine minus two. And the demand equation is modeled by P is equal to under root of 25 minus 0.1. Cute! Right? So now what we are supposed to find over here simply we have to return mine like mental equilibrium be reached or we can say we have to determine the um equilibrium demand. Find the equilibrium demand for this case.
So equilibrium demand is reached when supply is equal to demand. Right? So for that I'll just take both. The equations equal to each other. Supply should be equal to demand. Right? So for that I just a body questions equal to each other that means and root of 0.1 Q plus nine minus two is equal to under root of 25 minus 0.1 Q.
Right now you can just change the decimals into factional forms so I can just write 0.1 as one upon 10-Q plus nine minus two is equal to and the root of 25 minus one upon 10-Q. Now just square buddha sides, square budo sites. So when you do that you'll get one upon 10-Q plus nine minus four times of under road one upon 10 cube plus nine plus four is equal to 25 minus one upon 10. Here right now I just need to combine all the like terms together and just simplify it. So I'm doing that I'll get one upon five q minus 12 minus four times off.
Under route one upon 10 Q Plus nine equal to zero. Okay all I can say one upon five q minus 12 is equal to four and rude, one upon 10-Q plus nine. Now you can just square both the sides. On doing that will get you squared upon 25 plus 140 for minus 24 upon five Q. Is equal to what will get on the other side.
You have to square the other side as well. Right? So on the other side we'll get That will be equal to eight upon 5 Q Plus 144. Now just uh like combine all the like terms together. And on doing that we'll get huge square upon 25 minus 20 for Q upon five minus eight upon five Q. Is a call to zero.
Now you just need to multiply both the sides by 25. So I'm doing that. What will get simply Q square upon 25 minus 32 upon five kiko to zero. Right now, I just combined these two terms together. Now, I just take the L C M s 25 we'll get you squared minus 32 times 25.
You equal to zero. You're right now. Uh further what you will get over here? Yeah, this will be five over here. Since there was a denominator. No for five.
So you just get five over here. Now, this will further give you Q square minus 160. Q is equal to zero. Or I can just characterize out cue from here. So we get q minus 160 equal to zero.
That means you will be equal to zero, or Q is equal 260. That means 162 of 160 units will help you restore equilibrium state right now, moving on to the next part, we have to find out the equilibrium price over here. So for that, I'm just going to substitute you as 160 in equation too. So just put q equal to 160 in equation too. If you want, you can just put it in the equation one as well.
So we'll get P is equal to and root of 25 minus 16. We shall give you and the root of night, and this will be equal to plus minus three. And obviously since we are finding out the price, that means we have to take the positive value. So P is equal to three. Hence the equilibrium price will be $3 Right? So this is how you find the questions based on the equilibrium conditions.
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