Final answer:
The total cost (TC) can be calculated by integrating the marginal cost (MC) function, resulting in TC = q^2 + 16q + C. Without additional data, the constant C remains undetermined. Marginal revenue (MR) is usually derived from changes in total revenue, which would require knowledge of the product's market price or more revenue details.
Step-by-step explanation:
Calculating Total Cost and Marginal Revenue
Given the marginal cost (MC) function MC = 2q + 16, where q represents the quantity, we can calculate the total cost (TC) by integrating the marginal cost function. Since the marginal cost is the derivative of the total cost function, this implies that:
- Find the indefinite integral (antiderivative) of the marginal cost function: TC = ∫(2q + 16)dq
- This results in TC = q^2 + 16q + C, where C is the constant of integration.
- The value for C can be determined if we know the fixed costs or total cost at zero production. Assuming C represents fixed costs, without additional information, we would keep it as C in the equation.
Hence, the total cost function (TC) will be TC = q^2 + 16q + C.
As for marginal revenue (MR), it is calculated as the change in total revenue divided by the change in quantity. If additional information about the price or total revenue at specific quantities is provided, we could use that to determine the marginal revenue function.
However, without specific data on the price or total revenue, we cannot provide the exact marginal revenue function. Yet, if we assume the firm is a price-taker in a perfectly competitive market, the marginal revenue would be equal to the market price of the product. For more complex market structures, additional information would be required to calculate MR.