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The Manhattan Metaphor

机译：曼哈顿隐喻

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Fixed operating costs draw a sharp distinction between endogenous growth based on horizontal and vertical innovation: a larger number of product lines puts pressure on an economy’s resources; greater productivity of existing product lines does not. Consequently, the only plausible engine of endogenous growth is vertical innovation whereby progress along the quality or cost ladder does not require the replication of fixed costs. Is, then, product variety expansion irrelevant? No. The two dimensions of technology are complementary in that using one and the other produces a more comprehensive theory of economic growth. The vertical dimension allows endogenous growth unconstrained by endowments, the horizontal provides the mechanism that translates changes in aggregate variables into changes in product-level variables, which ultimately drive incentives to push the technological frontier in the vertical dimension. We show that the potential for exponential growth due to an externality that makes entry costs fall linearly with the number of products, combined with the limited carrying capacity of the system due to fixed operating costs, yields logistic dynamics for the number of products. This desirable property allows us to provide a closed-form solution for the model’s transition path and thereby derive analytically the welfare effects of changes in parameters and policy variables. Our Manhattan Metaphor illustrates conceptually why we obtain this mathematical representation when we simply add fixed operating costs to the standard modeling of variety expansion.
机译：固定的运营成本在基于横向创新和纵向创新的内生增长之间形成了鲜明的区别：大量产品线给经济资源带来压力；现有产品线的更高生产力无法实现。因此，内在增长的唯一可能的引擎是纵向创新，在纵向创新中，沿着质量或成本阶梯的进步不需要重复固定成本。那么，产品品种扩展是否无关紧要？不能。技术的两个方面是相辅相成的，因为使用一个和另一个可以产生更全面的经济增长理论。垂直维度允许内生性增长不受end赋的约束，水平维度提供了将总变量的变化转换为产品水平变量的变化的机制，最终推动了将技术前沿推向垂直维度的动机。我们表明，由于外部性导致指数增长的潜力，使进入成本随产品数量线性下降，再加上由于固定运营成本而导致的系统承载能力有限，因此产生了针对产品数量的物流动态。这种理想的属性使我们能够为模型的过渡路径提供封闭形式的解决方案，从而通过分析得出参数和政策变量变化的福利影响。我们的曼哈顿隐喻从概念上说明了为什么当我们简单地将固定运营成本添加到品种扩展的标准模型中时，为什么获得这种数学表示。

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