Question

If the demand function for a commodity is given by the equation

p^2 + 16q = 1400

and the supply function is given by the equation

700 − p^2 + 10q = 0,

find the equilibrium quantity and equilibrium price. (Round your answers to two decimal places.)

equilibrium quantity
equilibrium price $

Answer 1

Answer:

q=26.92 p=31.13

Step-by-step explanation:

$p^{2} +16q=1400\\\\q=\frac{1400-p^{2} }{16} ;\\\\700-p^{2} +10q=0\\\\q=\frac{p^{2}-700 }{10} ;$

$q=q\\\\\frac{1400-p^{2} }{16} =\frac{p^{2}-700 }{10} \\\\10(1400-p^{2})=16(p^{2}-700)\\\\14000-10p^{2}=16p^{2}-11200\\\\14000+11200=16p^{2}+10p^{2}\\\\25200=26p^{2}\\\\p^{2}=\frac{25200}{26} \\\\p=+\sqrt{\frac{25200}{26}} \\\\p=31.13$

replace p in any equation and

$q=\frac{1400-p^{2} }{16} \\\\q=\frac{1400-(31.13)^{2} }{16}\\\\q=26.92$