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count rate minus the growth of costs. Since all the terms in the discount are positive, this implies that the discount is positive if there is learning.

As an example, suppose that the growth of output is 10 percent per year for a dynamic new product, that the discount rate is 5 percent per year, and that the learning rate is 0.3. Total marginal cost is 63 percent of the current marginal cost. In other words, because an extra unit is produced today, future units get a productivity bonus of 0.37 additional units.

Note that this additional 0.37 units is spread over a huge number of units, so there is little incentive for any individual unit to enter into a Coasean bargain with current producers. However, in a frictionless competitive world without rent-seeking and with perfect information, a Pigovian “learning curve” subsidy of 37 percent would be an efficient policy to induce higher output and move the economy down the learning curve. Another approach, which is often advocated, is for the government to purchase or subsidize early plants so as to stimulate learning.

We can also see the dangers of using learning curves to subsidize early production or choose a portfolio of projects if the learning parameters are incorrectly calculated. Suppose, for example, that the true learning parameter is 0.1 and because of the biased discussed above the estimated parameter is 0.3. With a 3 percent discount rate and a 10 percent growth rate, the learning discount is overestimated by a factor of two. (For a full set of calculations, see the background paper.)

This bias becomes particularly important in energy and global warming models that are designed to choose among different emerging technologies and where the technology is assumed to have an important learning component. For example, suppose that a policy calculation solves for future paths of solar and wind technologies based on current cost and different learning coefficients. Based on high learning rates, the model might suggest that technology A is a good bet for research and development. But this recommendation would be incorrect if the learning coefficient is based on a biased estimate of learning.

The point to emphasize here is that, in analyses that pick technologies on the basis of total discounted cost of production (as is entirely appropriate), then an upward bias in the learning rate can have a major impact on the apparent benefit of technologies with learning. The estimated costs can easily be underestimated by a factor of two. This danger is reinforced because, as shown in the first section, of the tendency to estimate learning rates in bivariate relationships, which will generally lead to strong upward biases in the learning coefficient.

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