If the market demand is given by p = 50 - 2q and the market supply is given by p = 20 + 3q, what is the value of the producer surplus at equilibrium?

• A. 60
• B. 75
• C. 120
• D. 90

Answer: (D)

Verified step by step guidance

1. Identify the equilibrium quantity and price by setting the demand function equal to the supply function: \$50 - 2q = 20 + 3q$.
2. Solve the equation for \(q\) to find the equilibrium quantity: rearrange terms to isolate \(q\) on one side.
3. Substitute the equilibrium quantity \(q\) back into either the demand or supply equation to find the equilibrium price \(p\).
4. Calculate the producer surplus, which is the area above the supply curve and below the equilibrium price. Producer surplus can be found using the formula for the area of a triangle: \(\text{Producer Surplus} = \frac{1}{2} \times \text{base} \times \text{height}\).
5. Determine the base as the equilibrium quantity \(q\), and the height as the difference between the equilibrium price and the price at which quantity supplied is zero (the intercept of the supply curve). Then plug these values into the formula to find the producer surplus.