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At the profit-maximizing quantity, what is the total cost of producing ear buds?

Question

At the profit-maximizing quantity, what is the total cost of producing ear buds?

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Solution

To determine the total cost of producing ear buds at the profit-maximizing quantity, follow these steps:

  1. Identify the profit-maximizing quantity: This is the quantity where marginal cost (MC) equals marginal revenue (MR).

  2. Find the marginal cost (MC) and marginal revenue (MR): These can be derived from the cost function and the revenue function, respectively. The cost function typically shows the total cost (TC) as a function of quantity (Q), and the revenue function shows the total revenue (TR) as a function of quantity.

  3. Set MC equal to MR: Solve the equation MC = MR to find the profit-maximizing quantity (Q*).

  4. Calculate the total cost (TC) at Q*: Once you have the profit-maximizing quantity, substitute Q* back into the total cost function to find the total cost.

For example, if the total cost function is TC = a + bQ + cQ^2 and the total revenue function is TR = pQ (where p is the price), you would:

  • Derive MC from TC: MC = d(TC)/dQ = b + 2cQ
  • Derive MR from TR: MR = d(TR)/dQ = p
  • Set MC equal to MR: b + 2cQ = p
  • Solve for Q*: Q* = (p - b) / (2c)
  • Substitute Q* back into the TC function: TC = a + bQ* + c(Q*)^2

This will give you the total cost of producing ear buds at the profit-maximizing quantity.

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