What is the equilibrium market price and quantity? Demand: p = $100-2q, Supply: p = 3q

Question

ScanSolve AI Tutor · Accepted Answer

To find the equilibrium market price and quantity, we set the demand equation equal to the supply equation.

Set the demand price equal to the supply price.
Given demand: $p = 100 - 2q$
Given supply: $p = 3q$
At equilibrium, the prices are equal:
$100 - 2q = 3q$
Solve for the equilibrium quantity ( $q$ ).
$100 = 3q + 2q$ $100 = 5q$ $q = \frac{100}{5}$ $q = 20$
Substitute the equilibrium quantity ( $q$ ) into either the demand or supply equation to find the equilibrium price ( $p$ ).
Using the supply equation:
$p = 3q$ $p = 3 \times 20$ $p = 60$
The equilibrium market price is $60 and the equilibrium quantity is$ 20. Comparing this with the given options, option B matches these values.

The final answer is $\text{B}$ .

Answer