Saturday, March 22, 2008

Firms' Goals and Pricing

Walter Nicholson. Intermediate Microeconomics and Its Application Third Edition. Dryden Press, 1983.

I have decided to treat myself to review some basic economics this evening. It's been 20 years since I looked at my last economics textbook. What better way to brush up than my 1983 copy of Walter Nicholson's Intermediate Microeconomics and Its Application textbook? In this blog I will briefly review his thoughts on costs.

Costs (chapter 9)

Economists view historical costs as sunk costs. The implicit cost of a machine is what someone else would pay for it, i.e., its "rental rate". To minimize production costs firms choose inputs such that the rate of technical substitution is equal to the ratio of input costs. Thus if wages are w and machinery rental rates are v then:

Rate of Technical Substitution = wage rate/rental rate = w / v

That is, the rate of technical substitution is the rate at which one input may be traded off against another in the production process while holding output constant and that rate is the same rate at which they are traded in the open market.

In other words, the rate of technical substitution of labor for capital is the ratio of the

marginal product (labor)/ marginal product (capital)

so that each input should provide the same additional output per dollar spent and if they don't, firms will trade some of the less productive input for the more productive.

Short versus Long Run

In the short run production capacity is fixed. In the long run production can be curtailed. Fixed costs are fixed in the short run.

Short run average total costs = (total costs) / (total output)


Short run marginal costs = (change in total costs) / (change in output)

In the very short run price purely rations demand. This is because supply cannot be increased. But generally in the longer run there is a supply response to changing demand. In the short run (longer than very short run) the number of firms is fixed but firms can adjust the amount they are producing.

Theoretically, marginal and average costs ought to increase in response to increases in output but most studies fail to show increasing average or marginal costs but rather find that marginal and average costs are constant over large ranges of output.

Long Run

In the long run all productive inputs are variable. Nicholson makes the point that some factors may be difficult to alter even in the long run. The rate of technical substitution must equal the ratio of the input prices.

The long run total cost curve is found by considering all short run total cost curves and choosing the lowest one for each possible output level. "The locus of all these cost minimizing choices is called the long-run total cost curve..."

Under the assumption of constant returns to scale, the long term total cost curve is a straight line and average and marginal costs are constant and equal (equal because of the assumption of constant returns to scale which means that the marginal cost equals the average cost).

If there is a fixed input, average costs fall as variable inputs are added, but then rise again as the fixed input causes diminishing marginal productivity.

At the minimum piont of the Long Run Average Total Cost Curve the Long Run Marginal Cost Curve = Long Run Average Total Cost Curve = Short Run Average Total Cost Curve = Short Run Marginal Cost Curve

In reality, many empirical studies find declining long run average costs for smaller size with a flattening minimum average cost beyond a threshhold.

Changes in input prices will tilt the total cost lines. Changing input prices will change the isoquants on which the total cost curves are based and change the ratios of inputs.

No comments: