11.14 Profit functions and technical change Suppose that a firm’s production function exhibits technical improvements over time and that the form of the function is q ¼ f(k, l, t). In this case, we can measure the proportional rate of technical change as

@ ln q

@t ¼ ft f

(compare this with the treatment in Chapter 9). Show that this rate of change can also be measured using the profit function as

@ ln q

@t ¼ PðP, v, w, tÞ

Pq $

@ ln P

@t :

That is, rather than using the production function directly, technical change can be measured by knowing the share of profits in total revenue and the proportionate change in profits over time (holding all prices constant). This approach to measuring technical change may be preferable when data on actual input levels do not exist.