Rule 1 Derivative of a Constant Function fx c

The reason that fix) = 0 when fix) = c is easy to see intuitively by looking at the graph of the function fix) = c (see figure 5.18). Regardless of which poini A' is chosen. Ay — 0 for any value of Aa. Here Ay - 0 for any size of A.v.

Example 5.4 Marginal Revenue Function for a Competitive Firm

A competitive firm believes that if it sells more output there will not be a reduction in the market price. The extra revenue generated by producing and selling one more unit of output is therefore simply the price of the product. This is, of course, a sensible attitude if the firm is a small producer in a large market. Thus the extra revenue generated by an extra unit of output is constant regardless of the level of output of the firm. If we let p be market price, and MR(i/) represent marginal revenue as a function of output, it follows that dMRii/)/dq = 0 (see figure 5.19).

Figure 5.19 Total revenue and marginal revenue of a competitive firm (example 5.4)

Of course, if the firm produced a level of output equal to a substantial fraction of the output generated by all firms taken together, say one-half, then it would no longer make sense for the firm to believe that the extra revenue generated by additional sales was independent of the amount of extra output produced. In this case, if a firm's increments in output arc large relative to the size of the market, then it would be appropriate to assume rfMR(^ )/dq is negative. ■

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