# Write a short note on profit maximization of a firm under a)p=mc b)mc must be non-decreasing q⁰

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Write a short note on profit maximization of a firm under

a) p = mc

b) mc must be non-decreasing q⁰

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A firm always wishes to maximize its profit. The firm would like to identify the quantity q0, the firm’s profits are less at q0 For profits to be maximum, the following conditions must hold at q0

1. The price P must equal MC (P = MC): Profit is the difference between total revenue and total cost. Both total revenue and total cost increase as output increases. As long as the change in total revenue is greater than the change in total cost, profits will continue to increase.

The change in total revenue per unit increase in output is the marginal revenue and the change in total cost per unit increase in output is the marginal cost.

Therefore, we can conclude that as long as marginal revenue is greater than marginal cost, profits are increasing and as long as marginal revenue is less than marginal cost, profits will fall. It follows that for profits to be maximum, marginal revenue should be equal to marginal cost.

For the perfectly competitive firm, we have established that the MR=P. So the firm’s profit-maximizing output becomes the level of output at which P = MC.

2. Marginal cost must be non-decreasing at q0: It means that the marginal cost curve cannot slope downwards at the profit-maximizing output level. This can be explained with the help of diagram: In the given diagram, at output levels q1 and q4 the market price is equal to the marginal cost. However, at the output level q1, the marginal cost curve is downward sloping. The q1 is not profitmaximizing output level.

If we observe all output levels left to the q1 the market price is lower than the marginal cost. But the firm’s profit at an output level slightly smaller than q1 exceeds that corresponding to the output level q1 Therefore, q1 cannot be a profit-maximizing output level.