THE MAXIMUM PROFIT POSITION (Under conditions of perfect competition).
In the derivation of the supply curve of the individual firm the assumption of perfect competition plays an important part. It is the implication of this assumption that there are many firms on the market and that the individual firm cannot exert any influence on price irrespective of the quantity it offers for sale. This also means that it can sell ANY quantity of this product at this price.
In a diagram this means that the demand curve for the firm is perfectly elastic (ie parallel to the x-axis – the horizontal axis). MR5 in the chart below is such a demand curve.
This demand curve can also be referred to as the sales curve.
In the chart below (Figure 1) the curves ATC (average total cost) – sometimes referred to as AFC (average full cost per unit) shows the changes in the average total cost per unit at different levels of production Q; and the AVC the average variable cost per unit. The Average Constant or Fixed costs do not appear here.
The problem that the economist needs to resolve here, is to determine the quantity the firm will offer for sale at different prices, in order to maximize its profit as a given price level.
To start off, let us have a look at the price P5.
P5 can be regarded as a possible market price – and as been explained the firm can sell any quantity at the ruling price. Note however that that decision will impact on the cost structure of the firm. So at P5 the firms sales curve or demand for the product (or in fact the marginal return earned) is represented by MR5.
In the solution of the problem as stated, the principle used to take the decision is encapsulated in the “economic motive” and that is to maximize profit . Profit can in this case be defined as the difference between total expenditure and total income . To determine the quantity produced and sold to produce maximum profit one needs to find the point where the difference is the greatest. Since both price and costs are known, this point should be relatively easy to establish.
Let us look at a point depicted here as “f” . At quantity Q1 -this is where MC cuts the P5 demand curve on its downward slope at volume Q1. The cost per unit of the product would be Q1f (or P5). The average full (total) cost of the quantity is above the marginal cost – the full cost per unit is also above the full revenue at that point - the firm would operate at a loss per unit – if one multiplied the loss per unit by the quantity produced and sold one will arrive at the total loss.
The firm at this point however does not have to contend itself with the loss. AFC/ATC runs downward from here (“g”) to the right. This clearly shows that the loss per unit for greater levels of output (greater than Q1) becomes steadily smaller; it follows that the firm will improve its position by producing more than (f) or Q1. Why is “g” so high? (how is ATC calculated?)
The figure does also show that at point “h” with an output level at Q6 the total cost per unit exactly matches the returns. At this point normal profit is made (perhaps one can explain normal profit here: One can get normal profit and economic profit (previously called excess profit). Normal profit is the profit made by all firms under perfect competition in a situation of perfect equilibrium.
It is also the point at which existing firms have no reason to leave a particular market and at which point there is no inducement for new firms to enter a particular market. Economic profit is the amount by which the difference between costs and receipts exceeds normal profit. (If the difference is negative we have a loss).
If there is no difference we have NORMAL PROFIT. You can thus see that NORMAL PROFIT is part of the cost structure of a firm and is added to the costs as a variable cost item.
OK, now we are at a point, a production output level where normal profits are made. However the entrepreneur, who determines the behavior of the firm is not interested in normal profit – he is interested in maximum profit. The curve ATC (AFC Average Full Cost) – the Mancosa Economics Study Guide just refers to it as AC (Average total cost per unit) and a price of MR5 shows that this is indeed possible. This is because the difference between P5 and ATC does not only become positive at quantity levels above Q6 it also increases in size as Q moves to the right (production quantity increases). This means that the profit per unit is increasing. The maximum profit per unit is achieved where AFC (ATC) reaches its minimum. This is at an output level of Q4 or point “d” . Here the profit per unit amounts to “dP5” – the difference between d and MR5. Since the quantity produced increases from “Q6” to “Q4” together with the profit per unit the total profit (which sits way above this graph) also increases. This point is thus preferred by the entrepreneur.
For levels of output greater than this profit per unit decreases again until normal profit is again made at point “I” – production level Q7. If production is further increased, losses are made because costs exceeed income.
It can now be asked whether the output where profit per unit is the maximum, is perhaps the output the entrepreneur will decide on. The entrepreneur again is not interested in profit per unit, but total profit (which has already been defined as the difference between total receipts and total costs). In principle it should be possible to increase total profit by producing and selling a greater quantity even if this is done at a smaller profit per unit , provided costs do not rise too rapidly. Here we now reach the most important point in the analysis for the answer to the problem “what quantity should be produced and sold?” and whether or not total profit can be increased by expanding output – this answer is found in Marginal Costs.
With an output of “d” or Q4 MARGINAL COSTS (which at this stage is equal to Average Full (Total) costs) are Q4d. Marginal costs are, in other words lower than the price of the product. In accordance with the significance of the concept of marginal costs this means that the cost of one extra unit produced is lower than the additional income obtained when that unit is sold. Thus, whatever the size of the profit made at such a stage, this means that profit can be increased by selling one more unit. The increase in profit thus obtained is equal to price minus the marginal cost.
The same conclusion can be made for any point to the right of d. The difference between marginal cost and price (price of course being the income per unit of output) for as long as the price obtained is higher than the cost of producing that additional unit. This is not the case for all outputs – point “I” has already been mentioned. At an output level to the right of “e” the marginal cost is higher than the price obtained for that additional unit. It costs more to produce than to sell – In this case the firm would benefit by producing less.
So increase output where marginal cost is less than price, decrease output where marginal cost is more than price – maximum profit can only be achieved where price equals marginal cost. Output = Q5
At price P5, is Q5 the optimum production and sales point - In other words “e”
That is why marginal cost concept is so critical in the analysis microeconomic problems – one would not have been able to solve the problem without this tool.
The quantity a firm will produce for sale on the market at a certain price in a condition of perfect competition is determined by the intersection of the rising part of the marginal cost curve with the perfectly elastic sales curve at this price.
Charl Heydenrych ©2011
Adapted from:
Van den Bogaerde, F. 1983. Elements of Price Theory. J.L van Schaik, Pretoria
Other sources consulted:
http://ingrimayne.com/econ/International/MonoComp.html