Rewarding Sequential Innovators: Patents Prizes and Buyouts

This paper presents a model of cumulative innovation where firms are heterogeneous in their research ability. We study the optimal reward policy when the quality of the ideas and their subsequent development effort are private information. The optimal assignment of property rights must counterbalance the incentives of current and future innovators. The resulting mechanism resembles a menu of patents that, contrary to the existing literature, have infinite duration and fixed scope, where the latter increases in the value of the idea. Finally, we provide a way to implement this patent menu by using a simple buyout scheme: The innovator commits at the outset to a price ceiling at which he will sell his rights to a future inventor. By paying a larger fee, a higher price ceiling is obtained. Any subsequent innovator must pay this price and purchase its own buyout fee contract.

An Analysis of the Effect of Ghost Force Oscillation on Quasicontinuum Error

The atomistic to continuum interface for quasicontinuum energies exhibits nonzero forces under uniform strain that have been called ghost forces. In this paper, we prove for a linearization of a one-dimensional quasicontinuum energy around a uniform strain that the effect of the ghost forces on the displacement nearly cancels and has a small effect on the error away from the interface. We give optimal order error estimates that show that the quasicontinuum displacement converges to the atomistic displacement at the optimal rate O($h$) in the discrete $\ell^\infty$ norm and O($h^{1/p}$) in the $w^{1,p}$ norm for $1 \leq p < \infty.$ where $h$ is the interatomic spacing. We also give a proof that the error in the displacement gradient decays away from the interface to O($h$) at distance O($h|\log h|$) in the atomistic region and distance O($h$) in the continuum region. E, Ming, and Yang previously gave a counterexample to convergence in the $w^{1,\infty}$ norm for a harmonic interatomic potential. Our work gives an explicit and simplified form for the decay of the effect of the atomistic to continuum coupling error in terms of a general underlying interatomic potential and gives the estimates described above in the discrete $\ell^\infty$ and $w^{1,p}$ norms.Comment: 14 pages, 1 figur

Specialization and the skill premium in the 20th century

The skill premium fell substantially in the first part of the 20th century, and then rose at the end of the century. I argue that these changes are connected to the organization of production. When production is organized into large plants, jobs become routinized, favoring less skilled workers. Building on the notion that numerically controlled machines made capital more “flexible” at the end of the century, the model allows for changes in the ability of capital to do a wide variety of tasks. When calibrated to data on the distribution of plant sizes, the model can account for between half and two-thirds of the movement in the skill premium over the century. It is also in accord with a variety of industry level evidence.Technological innovations

The scale of production in technological revolutions

Many manufacturing industries, including the computer industry, have seen large increases in productivity growth rates and have experienced a reduction in average establishment size and a decrease in the variance of the sizes of plants. A vintage capital model is introduced where learning increases productivity on any given technology and firms choose when to adopt a new vintage. In the model, a rise in the rate of technological change leads to a decrease in both the mean and variance of the size distribution.Productivity

Market Structure and the Direction of Technological Change

We study a model where innovation comes in two varieties: improvements on existing products, and new products that expand the scope of a technology. We make this distinction in order to highlight how market structure can determine not only the quantity of innovation but also its direction. We study two market structures. The first is the canonical one from the endogenous growth literature, where innovations can be developed by anyone, and developers market their own innovations. We then consider a more concentrated industry, where all innovation and pricing for a given technology is monopolized. We study the implications of the different market structures for both types of innovation, focusing on differences they induce in the direction of technological change. We apply our model model to the case of a hardware/software technology and analyze which market structure offers greater profits to a monopolist who can monopolize either hardware or software. We compare social welfare across the market structures, and discuss whether one type of innovation should be subsidized over anotherMarket Strucuture, Innovation

Unemployment Insurance with Hidden Savings

This paper studies the design of unemployment insurance when neither the searching effort nor the savings of an unemployed agent can be monitored. If the principal could monitor the savings, the optimal policy would leave the agent savings-constrained. With a constant absolute risk-aversion (CARA) utility function, we obtain a closed form solution of the optimal contract. Under the optimal contract, the agent is neither saving nor borrowing constrained. Counter-intuitively, his consumption declines faster than implied by Hopenhayn and Nicolini [4]. The efficient allocation can be implemented by an increasing benefit during unemployment and a constant tax during employment.hidden savings, hidden wealth, repeated moral hazard, unemployment insurance.

Shared Rights and Technological Progress

We study how best to reward innovators whose work builds on earlier innovations. Incentives to innovate are obtained by offering innovators the opportunity to profit from their innovations. Since innovations compete, awarding rights to one innovator reduces the value of the rights to prior innovators. We show that the optimal allocation involves shared rights, where more than one innovator is promised a share of profits from a given innovation. We interpret such allocations in three ways: as patents that infringe on prior art, as licensing through an optimally designed ever-growing patent pool, and as randomization through litigation. We contrast the rate of technological progress under the optimal allocation with the outcome if sharing is prohibitively costly, and therefore must be avoided. Avoiding sharing initially slows progress, and leads to a more variable rate of technological progress.Cumulative Innovation, Patent, Licensing, Patent Pool, Litigation