Question

The short-run cost function of a company is given by the equation TC = 200 + 55q, where TC is the total cost, and q is the total quantity of output, both measured in thousands. What is the marginal cost function, and how is it related to the given cost function?

Answer 1

The marginal cost function, derived from the total cost function TC = 200 + 55q, is constant at 55, indicating each additional unit produced increases cost by 55,000 units of currency. This figure is important for firms in decision-making related to pricing and output.

Step-by-step explanation:

The marginal cost function is derived from the total cost (TC) function by calculating the derivative of TC with respect to the quantity (q).

In this case, the total cost function is TC = 200 + 55q. To find the marginal cost (MC), we differentiate TC with respect to q:

MC = d(TC)/dq = d(200 + 55q)/dq = 55

Therefore, the marginal cost function is constant at 55. This means that for each additional unit produced, the cost increases by 55,000 units of currency (since costs and outputs are measured in thousands).

The marginal cost is used by firms to determine the additional costs incurred when producing one more unit of output. It is crucial for decision-making such as setting price and output levels to ensure profitability.