Economics – Differing objectives and policies of firms | e-Consult

1. Marginal Cost and Marginal Revenue Functions:

• Marginal Cost (MC): MC is the derivative of the total cost function with respect to quantity (Q).

  MC = dTC/dQ = 2

• Marginal Revenue (MR): MR is the derivative of the total revenue function with respect to quantity (Q).

  MR = dTR/dQ = 400 - 20Q

2. Profit-Maximising Output:

To find the profit-maximising output, we set MC = MR:

2 = 400 - 20Q

20Q = 398

Q = 19.9 (approximately 20 units)

Therefore, the profit-maximising level of output is approximately 20 units.

3. Why MC = MR for Profit Maximisation:

A firm aims to maximise its profit. Profit is calculated as Total Revenue (TR) minus Total Cost (TC). The difference between TR and TC is the profit. The firm will increase profit by producing more units as long as the additional revenue gained from producing one more unit (MR) is greater than the additional cost incurred from producing one more unit (MC). However, at some point, the additional cost of producing an extra unit (MC) will equal the additional revenue (MR). Producing beyond this point will reduce profit because the cost of producing that extra unit exceeds the revenue it generates. Therefore, the firm maximises profit at the point where MC = MR. This is because at this point, the extra revenue from producing one more unit is exactly offset by the extra cost, leaving the maximum possible profit.