Final answer:
The function for projected revenue R(p) when selling baseball bats at price p is R(p) = p × 33.88 million. For example, if bats sell at $50 each, the projected revenue would be $1.694 billion.
Step-by-step explanation:
To find a function for projected revenue based on the price p, we must first understand the concept of revenue. Revenue is calculated by multiplying the price per unit by the number of units sold. In the context of the question, the manufacturers are willing to supply 33.88 million bats, so if all the supplied bats sell at price p, then the revenue function R(p) will be the product of the price p and the quantity supplied.
The function for projected revenue R(p) can be represented as:
R(p) = p × 33.88 million
Where p is the price at which the bats are sold. We have the information that at the equilibrium price of $80, there is a producer surplus, which is the area labeled G in Figure 3.23, as this is the amount the seller is paid over the actual cost of production.
For example, if bats are sold at $50 each, the projected revenue would be:
R(50) = 50 × 33.88 million
Revenue at $50 per bat would be $1.694 billion.