Just as economists have worked out a theory of consumers they have also developed a theory of producers. This theory explains what is behind the supply functions of markets. While this theory appears to be a general theory explaining how an enterprise behaves, in actuality explaining the behavior of any specific enterprise would be too complex a problem. Some detailed studies of particular firms such as the Ford Motor Company have been written that focus on cultural and organizational aspects of the firm these are not the typical examples of the economic theory of producers. But economics is not concerned with explaining the behavior of any specific firm; instead it is concerned with explaining the behavior of markets. In order to explain the behavior of a typical firm in a market it is not necessary to have a completely realistic and detailed model of firms. All that is required is a model that captures the market-relevant influences of the average and allows the individual differences to aveage out.
The key concept for a firm is its cost function. The cost function gives the total costs of the firm as a function of its level of production. Let q be the annual rate of output of the firm. Its cost function is total costs C given as as a function of q; i.e., C=f(q). Usually the cost function is represented as C(q). An example is shown in the graph below.
If the producer can sell the output at a price p then the revenue received is just the price p times the output q. The revenue as a function of q is shown in the above graph as a green line.
The net profit for the firm is the difference between the revenue of pq and the cost C(q). The profit is shown in the diagram above in red. A producer wants to produce at a level where the profit is the greatest ; i.e., the producer will choose a level of consumption of x such that the profit is a maximum. Note that when the profit is a maximum the slope of the profit fucntion is zero. This means that at the level of q where profit is a maximum the increase in profit from another unit of production is zero. This is equivalent to saying that the increase in revenue from another unit of production is exactly equal to the increase in cost of producing that unit.
The increase in revenue from producing another unit is just the price of the product. The increase in cost can be computed from the cost function. This increase in cost for producing another unit is called the marginal cost of another unit. The marginal cost may decrease with increasing output over some range but beyond some level of production the marginal cost goes up with increasing output. The marginal cost function is shown in the graph below.
The marginal cost function is what determines the level of output where profit is a maximum. If the market price of the product is plotted as a horizontal line, as is done in the above graph, then the profit-maximizing output is the output where the price line intersects the marginal cost function. Thus where the price line intersects the marginal cost curve gives the quantity which would be supplied at that price. If this price and quantity data are plotted in a different graph to construct the supply schedule for the firm one finds that the marginal cost curve is just being replotted. In other words,
The supply curve is exactly the same as the marginal cost curve, as least for prices above some minimum. If the price is too low the firm may find that it is most profitable to supply zero units. This would be the case if the price is so low the firm cannot avoid a loss. The upward sloping of the supply curve is just the increasing marginal cost of the increasing production.
There is another cost function that is important for a producer. It is the average cost, the total cost divided by output. The average cost function for the total cost function shown above is shown below.
The relationship of the marginal cost curve and the average cost curve is best seen geometrically from the total cost curve. Marginal cost corresponds to the slope of the total cost curve. Average cost corresponds to the slope of a line drawn between a point on the total cost curve and the origin.
When the slope of the tangent to the total cost curve is the same as the slope of the line drawn to the origin then the marginal cost and the average cost are the same. This point is where average cost is a minimum.
There is yet one more cost curve. If total cost is not zero when output is zero that level of cost is called fixed cost. This would be the level of cost in factory that would have to be paid out for maintenance, insurance, security etc.
If fixed costs are subtracted from total costs the difference is called variable costs. Variable costs include the cost of raw materials, labor, power and so forth. If the level of variable costs is divided by output the result is called average variable cost. When marginal cost is equal to average variable cost then average variable cost is at its minimum level. The three unit cost curves are shown in the graph below.
The average variable cost curve is important for determining the minimum price at which the firm will produce any output. In the graph shown below if the price were p0, which is below the minimum average variable cost then the price line of p0 crosses the marginal cost curve at an ouput of q0. At an output of q0 the firm would be making the maximum profit or the minimum loss that could be achieved with any positive amount of output.
(The crossing at the point q1 does not count because the negative slope of the marginal cost curve at that point indicates that q1 corresponds to a minimization of profit or maximization of loss.)
If the market price is not high enough to cover the variable costs then the firm is better off not producing. Thus at prices below the minimum average variable the firm produces zero. The supply curve for a firm is the same as the marginal cost curve down to the minimum average variable cost. Below that price the supply is zero.
The area under a marginal cost curve over some range of output is the same as the increase in total (and variable) cost over that range of outputs. The area under the price line over a range of outputs is the change in revenue over that range of outputs. Thus the change in profit is the same as the area between the price line and the marginal cost curve.
Since the supply curve and marginal cost curves are the same for prices above the minimum average variable cost then the area between the price line and the supply curve is the change in profit for the producers over that range of outputs. This leads to the concept of producer surplus as the area to the left of the supply curve over some range of prices.
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