Respuesta :
ANSWER
The market equilibrium point is x + 21y
STEP-BY-STEP EXPLANATION:
Given information
[tex]\begin{gathered} \text{supply; p = q}^2\text{ + 14q - 529} \\ \text{Demand; p = 311- 5q} \end{gathered}[/tex]At the market equilibrium, quantity demand is equal to quantity supply
The next step is to equate the two equations together
[tex]311-5q=q^2\text{ + 14q - 529}[/tex][tex]\begin{gathered} 311-5q=q^2\text{ + 14q - 529} \\ q^2\text{ + 14q - 529 - 311 + 5q = 0} \\ \text{collect the like terms} \\ q^2\text{ + 14q + 5q - 840 = 0} \\ q^2\text{ + 19q - 840 = 0} \end{gathered}[/tex]The next process is to solve for q using the general quadratic formula
[tex]\begin{gathered} x\text{ =}\frac{-b\text{ }\pm\sqrt[]{b^2\text{ - 4ac}}}{2a} \\ \end{gathered}[/tex]Where
a = 1, b = 19 and c = -840
[tex]\begin{gathered} q\text{ =}\frac{-(19)\pm\sqrt[]{19^2-\text{ 4(1 }\times-840)}}{2\text{ }\times1} \\ q\text{ = }\frac{-19\text{ }\pm\sqrt[]{361\text{ - 4(-840)}}}{2} \\ q\text{ = }\frac{-19\text{ }\pm\sqrt[]{361\text{ + 3360}}}{2} \\ q\text{ = }\frac{-19\pm\sqrt[]{3721}}{2} \\ q\text{ = }\frac{-19\pm61}{2} \\ q\text{ = }\frac{-19\text{ + 61}}{2}\text{ OR }\frac{-19\text{ - 61}}{2} \\ q\text{ = }\frac{42}{2}\text{ or }\frac{-80}{2} \\ q\text{ = 21or -40} \\ q\text{ = 21} \end{gathered}[/tex]From the above calculations, you will see that the value of q is 21 or - 40
Therefore, the market equilibrium price is 21
Recall that, the general function for the market equilibrium point is
Q(s) = x + yP
where p = price
Hence, the market equilibrium point is q(s) = x + 21y
