If the demand function for a commodity is given by equation p^2+12q=18 and the supply function is given by the equation 700-p^2+6q=0, find the equilibrium quantity and price
Hmm. I get a negative value for q.
Is there maybe a typo?
To find the equilibrium quantity and price, we need to solve the given demand and supply equations simultaneously.
Given:
Demand function: p^2 + 12q = 18
Supply function: 700 - p^2 + 6q = 0
Step 1: Solve one of the equations for one variable.
Let's solve the demand equation for p^2:
p^2 = 18 - 12q
Step 2: Substitute the value of p^2 from the demand equation into the supply equation.
700 - (18 - 12q) + 6q = 0
Step 3: Simplify and solve for q.
700 - 18 + 12q + 6q = 0
682 + 18q = 0
18q = -682
q = -682 / 18
q ≈ -37.9
Step 4: Substitute the found value of q into the demand or supply equation to solve for p.
Using the demand equation:
p^2 + 12(-37.9) = 18
p^2 - 454.8 = 18
p^2 = 18 + 454.8
p^2 ≈ 472.8
p ≈ √472.8
p ≈ 21.75
Step 5: Check the solution by substituting the found values of p and q into the other equation.
Using the supply equation:
700 - p^2 + 6(-37.9) = 0
700 - 21.75^2 - 227.4 = 0
700 - 472.5625 - 227.4 = 0
0 ≈ 0 (approximately)
Step 6: Interpret the solution.
The equilibrium price is approximately p = $21.75, and the equilibrium quantity is q ≈ -37.9 units. However, in this context, a negative quantity does not make sense. It is likely that there was an error made during the calculations, or there might be another issue with the given equations.
Please note that equilibrium price and quantity should always be positive values. Double-check the given equations or seek further clarification if needed.