The Free-Market Innovation Machine by Baumol William J

Author:Baumol, William J.
Language: eng
Format: epub
Publisher: Princeton University Press
Published: 2014-03-14T16:00:00+00:00

c + ky =

the average cost function.

Then the firm’s total profit function is

whose first-order maximum condition yields as the profit-maximizing value of y

Marshallian consumers’ surplus at that output is given by

Thus, under the linear and parallel shift assumptions, a product innovation must increase Marshallian consumers’ surplus. Therefore, if it is successful, meaning that it increases the producer’s surplus, it must enhance welfare.

Product Innovations and Welfare: The Generally Ambiguous Result.

A graphic counterexample will suffice to prove:

PROPOSITION 9.4. Even if a product innovation is successful, it can decrease welfare.

This will happen if the innovation reduces consumers’ surplus because of its effect on the slope of the demand curve, and the sunk cost incurred by the innovation yields a negligible contribution to the producer’s surplus.

I will, once again, deal with linear average and marginal revenue curves (in the graph the marginal cost curve will also be drawn as a line segment, but that is unnecessary for the argument). However, in this case I will take the innovation not to shift the left-hand end of the revenue curves. In figure 9.2 I assume that, without the innovation, the marginal and average revenue curves are HMR1 and HAR1, respectively. With the innovation, the right-hand end of the old marginal revenue curve moves rightward, so that the new marginal revenue curve, HMR2, coincides with the old average revenue curve. Consumers’ surplus then clearly changes from triangle ABH to triangle abH, where B is the point on AR1 directly above the intersection of MC with MR1, and b is the corresponding point for MC and MR2. It is clear that if the MC curve were vertical then the second triangle would be considerably smaller than the first: the horizontal sides would be identical but the vertical side of the second triangle would be much smaller than that of the first. By continuity, this must still be true (though the difference will be smaller) if the MC curve is upward sloping but not quite vertical. Thus, in this case, the product innovation will reduce consumers’ surplus by a substantial amount (call it s), because it will raise the profit-maximizing price considerably, reduce the slope of the demand curve, and not add much to the quantity purchased. Let r represent the corresponding increment in the producer’s surplus. Then, so long as r > 0, no matter how small, the innovation will be successful on our criterion. By increasing the sunk cost, the magnitude of r can be reduced as close to zero as desired without making the innovation unsuccessful. In particular, there will be a magnitude of sunk cost beyond which s > r > 0. This proves Proposition 9.4: a successful product innovation can yield not only a negative consumers’ surplus but also a welfare loss.

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