Analyse the validity of this statement: To maximise profit, you need to sell your output at the highest price. How should marginal costs be considered when determining prices?

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It is not necessary for a firm to price its products at the highest price to maximize profits. The profits earned are a function of the total revenue earned and the total costs involved in production. Usually it is seen that as the total cost of production per unit decreases as the number of units produced is increased; this is due to the fact that the fixed costs are divided over a larger number of units. The demand for most products increases as the price is decreased.

The marginal cost of a product is the amount required to produce an extra unit of the product. This is found to initially decrease as the the total number of units produced is increased, it reaches a minimum value and then starts to increase.

The profit is maximized at the point where the marginal revenue is equal to the marginal costs. The pricing of a product should be such that the number of units demanded makes the marginal cost equal to the marginal revenue.

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"To maximize profit, you need to sell your output at the highest price."  With regard to different costing systems and pricing of products, analyze the validity of this statement. How should marginal costs be considered when determining prices?

This statement is not valid.  On its face, it is impossible.  How does one set “the highest price?”  The range of possible prices for a good is essentially infinite.  Clearly, it makes no sense to set your prices to the highest level that you can imagine.  Even when we read this statement more reasonably, it is still invalid.  Firms do not simply raise their prices to maximize profits.

One way to think about this is to think about price elasticity of demand.  When a firm raises the price of its products, consumers might reduce their purchases.  We saw, for example, that people consumed less gasoline when the cost of gas was up around $4 per gallon in the United States.  The more elastic the demand for your good, the more profit you lose when you raise prices past a certain point.  Therefore, you cannot simply raise prices in order to increase your profits.

When setting prices, firms are supposed to consider their marginal costs.  The profit maximizing point for any firm is the point where its marginal revenue from selling the next unit of product is equal to the marginal cost of producing that unit.   The firm has to determine what its demand curve looks like so it can see what price it can charge at any given level of output.  It then has to set its output at the level where the price it charges brings it a marginal revenue that is equal to its marginal costs.

The statement in your question is not valid.  Firms maximize profits by getting their marginal revenues to equal their marginal costs, not by blindly increasing prices.  

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