can i get some help with this question. We know that the quantity of tuna demanded and supplied is related to the price of tuna. Given that the demand function for tuna is q=(306.25-p)0.5+2.5 and the inverse supply function for tuna is p=76+3q. All quantities are in kilograms and prices in $TT. Determine the quantity of the tuna that will be demanded and supplies when the market is in equilibrium. NB 0.5 is to the power

Question

can i get some help with this question.  We know that the quantity of tuna demanded and supplied is related to the price of tuna. Given that the demand function for tuna is q=(306.25-p)0.5+2.5 and the inverse supply function for tuna is p=76+3q. All quantities are in kilograms and prices in $TT. Determine the quantity of the tuna that will be demanded and supplies when the market is in equilibrium. NB 0.5 is to the power

sasogeek · Answer

Welcome to openstudy riri :) your question is quite an interesting one but I don't seem to know how to solve it, I believe tiaph is helping you out with that one :) I hope you enjoy studying here with us, if you have any questions... ask, don't forget that, keep asking until there's no more questions to ask :) and when u see a question you can help with, take a look and try ur hands on it and help someone when you can :) you will be awarded for helping people you know ;) all the best and good luck with this one :D and hey, invite your friends here :D

anonymous · Answer

Okay. When market is in equilibrium, that means demand meets supply. so u can go ahead and equate the 2 equations p = 76 +3q Substitute the above into the demand eqn. q = (306.25 - 76-3q)^0.5 +2.5 q-2.5 = (306.25 - 76-3q)^0.5 Square both sides... q^2 -5q +6.25 = 230.25-3q q^2 -2q -224 = 0 solve this quadratic equation through factorization or through the use of a graphics calc http://www.wolframalpha.com/input/?i=x^2+-2x+-224+%3D+0 the 2 values of q are - 14 and 16 Reject -14 since the quantity of tuna cannot be negative. therefore, the quantity of tuna demanded and supplied when there is market equilibirum is 16 kg.

anonymous · Answer

OK...I don't understand one thing. The third line when you square both sides, how did 2.5 turn into 5q? Where did the q come from?

sasogeek · Answer

you see, when you have $\large (a-b)^2 , $ the expansion is given by the formula $$\large (a-b)^2 =a^2-2(ab)+b^2 $$ so that means that $\large (q-2.5)^2)=q^2-2(2.5\times q)+(2.5)^2 $ so this simplifies to $$\large q^2-5q+6.25 $$

anonymous · Answer

oh right!!! I remember learning that!! Thanks a Million guys. Got it. :D

sasogeek · Answer

:)

sasogeek · Answer

you should be here often :) i'd be glad to help anytime