The inverse demand for boccie balls is given by ??=80-??P=80-Q. Boccie balls can be produced at a constant marginal and average total cost of $20.
a. If the boccie ball industry were perfectly competitive, what quantity would be sold, and what price would prevail in the market?
Q =
P = $
The Correct Answer and Explanation is :
To find the equilibrium price and quantity in a perfectly competitive market, we set price (P) equal to marginal cost (MC) because firms in perfect competition produce where P = MC. Here’s the step-by-step solution:
Step 1: Use the Inverse Demand Function
The inverse demand function is given as:
[
P = 80 – Q
]
Where (P) is the price and (Q) is the quantity.
Step 2: Marginal Cost and Perfect Competition
In perfect competition, price equals marginal cost. The marginal cost is given as (MC = 20).
Set (P = MC):
[
80 – Q = 20
]
Step 3: Solve for Quantity ((Q))
Rearranging the equation:
[
Q = 80 – 20
]
[
Q = 60
]
Step 4: Find the Market Price ((P))
Substitute (Q = 60) back into the demand function:
[
P = 80 – Q
]
[
P = 80 – 60
]
[
P = 20
]
Final Answer:
- Quantity ((Q)): 60 boccie balls
- Price ((P)): $20
Explanation:
In a perfectly competitive market, price is determined by the intersection of the demand curve and the supply curve. Since marginal cost is constant at $20, the supply curve is horizontal at this price. The market equilibrium occurs where the demand curve intersects this price, leading to a quantity of 60.
Perfect competition ensures allocative efficiency because firms produce at a level where price equals marginal cost. Here, the market price of $20 reflects the marginal benefit consumers receive from the last unit consumed, which matches the marginal cost of production. This balance maximizes social welfare, as no resources are wasted, and consumer and producer surplus are optimized.
If the industry were not perfectly competitive (e.g., monopolistic), the price would likely be higher, and the quantity sold lower, resulting in a deadweight loss.