Questions: Find the equilibrium point for the pair of supply and demand functions. Demand: (q=9/x ;) Supply: (q=x/16) The equilibrium point is ((12, 3/4)). (Type an ordered pair.) At the equilibrium point, the price is ( square) and the quantity is (square)

Solution Steps

To find the equilibrium point, set the demand function equal to the supply function: \[ \frac{9}{x} = \frac{x}{16} \]

Multiply both sides by \( 16x \) to clear the fractions: \[ 16x \cdot \frac{9}{x} = 16x \cdot \frac{x}{16} \] \[ 144 = x^2 \]

Take the square root of both sides: \[ x = \sqrt{144} \] \[ x = 12 \]

Substitute \( x = 12 \) back into either the demand or supply function to find \( q \). Using the supply function: \[ q = \frac{12}{16} \] \[ q = \frac{3}{4} \]

Final Answer