d. Changes in input prices
The levels of input prices determine the position and slope of the isocost curves. If the relative prices of the inputs change this will affect the slope of the curves, which we have seen is given by PL/PK. If, for example, labour becomes more expensive relative to capital the slope of the isocost curves will become steeper. This will result in the point of tangency moving along the relevant isoquant, upwards and to the left, and a higher level of cost, assuming a given target output. Not surprisingly, less of the more expensive input is used than before, andmore of the input that is now relatively cheaper. The situation is illustrated in Figure 5.8. In this example it is assumed that the labour input increases in price from £400 to £500 per week. The isocost curve C0=4,000 shows the effect of the price increase and the fact that the output of 80 units can no longer be achieved at the cost of £4,000. To attain this output, assuming economic efficiency, now involves a cost outlay of about £4,400.
There are again obvious parallels in consumer theory, corresponding to the situation where product prices change. In that case it was seen that rational consumers should respond to the situation by buying less of the more expensive product. The main difference is that, because of the dual nature of the situation consumers are assumed to have a fixed budget line; therefore when a product price rises they are forced onto a lower indifference curve.
e. Expansion paths
Another application of this type of analysis is to consider what happens when the firm’s target output increases, or to express the situation in terms of its dual, when the firm’s budget increases. As the firm attains higher and higher output levels the optimal combinations of inputs involved will trace an expansion path. This is illustrated in Figure 5.9. The expansion path goes through all the points of tangency, X, Y and Z. This path can be used to determine the long-run relationships between costs and output that are examined in the next chapter. However, the graph in Figure 5.9 assumes that the prices of the inputs remain constant, or at least that their ratio remains constant, which as we shall see is not very realistic.
5.5 A problem-solving approach
It is possible to identify three main management principles that emerge from the preceding discussion of production theory. These are all key points in terms of decision-making.
5.5.1 Planning
It can be seen from Table 5.3 that in the short run the range of output for Viking Shoes associated with stage II of the production function is from 27 to 66 units per week. Under most circumstances Viking’s optimal operating output should be in this range. If we make the additional assumptions regarding the price of output and the prices of inputs in subsection 5.3.6we can conclude that optimal output is 59 units; however, it must be remembered that this output is only optimal given the choice of scale by the firm. The implication as far as planning is concerned is that the firm must ensure that it is using the best scale in order to maximize profit. For example, it may be that at the price charged customers might want to buy less than 27 units or more than 66 units, forcing the firm to operate in stage I or stage III. In this situation the firm’s scale would be too large or too small respectively. This aspect of planning, capacity planning, means that the firm must be able to have accurate forecasts of demand, and communicate the relevant information to its marketing and production departments. These two departments need to communicate with each other, so that sales forecasts by marketing people can be met by the relevant production capacity. Likewise, information relating to production constraints needs to be communicated to the marketing department, so they do not ‘oversell’ the product