Theory of the Firm Part 2

Profit Maximization

The competitive firm makes two basic choices. One is which technology (which inputs) to use to make its product, the other is how much product to produce. The choice of inputs will be covered later under a discussion of "factor markets". The present discussion relates to the second choice, how much to product.

The firm must choose that level of output that maximized its profit. Since the firm does not affect the price it receives, the revenue it receives from each incremental unit of output is constant. What is not constant is the cost of each successive unit. In the previous paper, we discussed diminishing returns and how this fact of nature affects the cost of producing successive units of output. The cost of each incremental (marginal) unit will, at some point, increase. This is the reflection of diminishing returns.

As the cost of each successive unit increases, the profit derived from it becomes progressively smaller. For a profit maximizing firm, the logical course it to produce every unit that adds to profit, but no more. The profit maximum is achieved when the contribution to profitability of the last unit produced is zero, or when the cost of producing the last unit equal the price received for it. Profit maximizing output is that level of output where price equal marginal cost (P = MC)

Average Costs

Our discussion of profit maximization has, so far, not mentioned average cost; only marginal cost. This is because the determination of the profit maximizing level of output is independent of average costs. Still, average cost are of interest, so we shall show how they relate to marginal costs.

The graph, above, shows the relationship between marginal and average variable cost (AVC). Note that, at first, marginal cost is below average variable cost and falling. This is because we are here in the region of increasing returns where marginal costs are decreasing. Since average cost is simply the sum of the marginal costs of units Q1 ….Qn divided by the number of units Qn, average changes more slowly than marginal costs. If the marginal cost number added to the average cost is below the average, then the average will fall (albeit more slowly that the marginal figure). Eventually, marginal cost starts to rise (here we are in the region of diminishing returns). As marginal cost rises, that has the effect of adding a progressively larger number to the average. As long as marginal cost is still below the average, the average will continue to fall. When marginal cost rises to equal average cost, average will stop falling and will, for the moment, neither rise nor fall. This is the minimum point of the average cost curve. Now, with marginal rising above average cost, the average cost curve starts to rise, but again more slowly than the marginal cost curve. The profit maximizing level of output is determined not by the average cost curve, but by the marginal cost curve. Where the marginal cost curve cuts the price line (marginal revenue curve) we have a condition of price equaling marginal cost (P = MC): a point of profit maximization

Average Fixed and Average Total Cost

Fixed cost is simply a "lump sum" cost a company has to pay regardless of whether they produce any output. Repaying loans (or paying bond holders) is a fixed cost. Fixed cost can be expressed as a single number, $10 million a year, for example. Average fixed cost is simply fixed cost ($10,000,000) divided by the quantity of output (Q).

Dividing fixed cost by output (Fixed/output) creates an average fixed cost curve that looks like the one above. This curve is an "asymptote" in that it runs from infinity to zero without ever really reaching those values. As we move to the right, average fixed cost get closer and closer to the horizontal (Q) axis, but never really touches it.

The graph, above, shows the relationship of average fixed cost (AFC), average variable cost (AVC) and average total cost (ATC). ATC is simply the result of adding, at each point along the Q axis, the average fixed cost (AFC) to average variable cost (AVC). This results in an average total cost curve (ATC) that gets closer and closer to AVC as Q increases.

 

 

This graph, below, is a complete representation of the firm and its profit maximizing decision. The firm's supply curve is the rising portion of the marginal cost curve. In the short run, the supply curve is the rising portion lying above the AVC curve. Here the firm is covering variable (out of pocket) expenses, but not it's fixed costs. This is not a sustainable position. In the long run the supply curve is the rising portion of the marginal cost curve lying above the ATC curve. Here, all costs are being covered.

The firm derives a profit in this situation. The profit is total revenues (rectangle 1-5-6-3) minus total costs (rectangle 1-2-3-4 the shaded area). Profit is rectangle 1-5-6-2.

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