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Introduction to Modern Economic Growth in costs, but air-conditioners became much more energy-efficient, which, they argue, was a response to higher energy prices This seems to be a clear example of the pace and the type of innovation responding to profit incentives In a related study, Popp (2002) finds a strong positive correlation between patents for energy-saving technologies and energy prices and thus confirms the overall picture resulting from the Newell, Jaffee and Stavins study Evidence from the pharmaceutical industry also illustrates the importance of profit incentives and especially of the market size on the rate of innovation Finkelstein (2003) exploits three different policy changes affecting the profitability of developing new vaccines against infectious diseases: the 1991 Center for Disease Control recommendation that all infants be vaccinated against hepatitis B, the 1993 decision of Medicare to cover the costs of influenza vaccinations, and the 1986 introduction of funds to insure vaccine manufactures against product liability lawsuits for certain kinds of vaccines She finds that increases in vaccine profitability resulting from these policy changes are associated with a significant increase in the number of clinical trials to develop new vaccines against the relevant diseases Acemoglu and Linn (2004) look at demographic-driven exogenous changes in the market size for drugs of different types and find a significant response in the rate of innovation to these changes in market sizes To sum up, the evidence suggests that profit motives and the market size are important determinants of innovation incentives and the amount and type of technological change This evidence motivates the types of models we will study, which make technological change an economic activity, responding to economic incentives 12.3 The Value of Innovation in Partial Equilibrium Let us now turn to the analysis of the value of innovation and R&D to a firm The equilibrium value of innovation and the difference between this private value and the social value (i.e., the value to a social planner internalizing externalities) will play a central role in our analysis below All of the growth models we have studied so far, as well as most of those we will study next, are dynamic general equilibrium models In fact, as emphasized at the beginning, economic growth is a process we can only understand in the context of general equilibrium analysis Nevertheless, it 545