Q:

If the demand function for a commodity is given by the equationp^2 + 16q = 1400and the supply function is given by the equation700 − p^2 + 10q = 0,find the equilibrium quantity and equilibrium price. (Round your answers to two decimal places.)equilibrium quantity equilibrium price $

Accepted Solution

A:
Answer:Equilibrium quantity = 26.92Equilibrium price is $31.13Step-by-step explanation:Given :Demand function : [tex]p^2 + 16q = 1400[/tex]            Supply function : [tex]700 -p^2 + 10q = 0[/tex]To Find : find the equilibrium quantity and equilibrium price. Solution:Demand function : [tex]p^2 + 16q = 1400[/tex]  --ASupply function : [tex]p^2-10q=700[/tex] ---BNow to find the equilibrium quantity and equilibrium price. Solve A and BSubtract B from A[tex]p^2-10q -p^2-16q=700-1400[/tex] [tex]-26q=-700[/tex] [tex]26q=700[/tex] [tex]q=\frac{700}{26}[/tex] [tex]q=26.92[/tex] So, equilibrium quantity = 26.92Substitute the value of q in A[tex]p^2 + 16(26.92) = 1400[/tex] [tex]p^2 + 430.72 = 1400[/tex] [tex]p^2 = 1400- 430.72[/tex] [tex]p^2 = 969.28[/tex] [tex]p = \sqrt{969.28}[/tex] [tex]p = 31.13[/tex] So, equilibrium price is $31.13