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در تحقیق و توسعه در یک مدل رشد اقتصادی شومپیتر در یک منطقه خلاق
عنوان انگلیسی مقاله:
On research and development in a model of Schumpeterian economic growth in a creative region
سال انتشار : 2016
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2. The theoretical framework
2.1. Preliminaries Consider an infinite horizon, stylized region that is creative in the sense of Richard Florida. The representative creative class household in this region displays constant relative risk aversion (CRRA) and its CRRA utility function is denoted by ∫ ∞ 0 expð−ρtÞ½fCðtÞ 1−θ − 1} / (1 − θ)]dt,θ≠1, where C(t) is consumption at time t, ρN0 is the constant time discount rate, and θ≥0 is the constant coefficient of relative risk aversion.2 Following Aghion and Howitt (1992, p. 327), in what follows, we suppose that the representative creative class household is riskneutral and hence this means that θ=0. At any time t, the creative region under study possesses creative capital which we denote by R(t). The total available creative capital at any time t or R(t) either produces the final consumption good (RF(t)) or is involved in R&D (RD(t)). There is no growth in the stock of creative capital over time and hence we can write R(t)=R, ∀t. This creative capital R is supplied inelastically. The market for creative capital in our region is competitive and it clears. Hence, the market clearing condition RF(t)+RD(t)=R holds.The aggregate resource or budget constraint in our region at time t is given by C tð Þþ X tð Þþ I tð Þ ≤ O tð Þ; ð1Þ where C(t) is consumption, X(t) is total spending on machines, I(t) is total spending on R&D, and O(t) is the output of the competitively produced single final good for consumption that we shall think of as a knowledge good such as a camera or a smartphone. The price of this final good is normalized to unity at all time points and hence O(t) denotes both the output and the value of the final good. Note that the machines we have just referred to can also be thought of as inputs or as intermediate goods. There is a continuum of machines that is used to produce the single final good O(t). Each machine line or variety3 is described by ν where ν∈[0,1]. As noted in Section 1.2, the source of economic growth in our creative region is process innovations that improve the quality of existing machines. To this end, let q(ν,t) be the quality of the machine of line ν at time t. The single final good for consumption (the knowledge good) in our creative region or O(t) is produced competitively. The production function for this good is O tð Þ¼ 1 1−β ∫ 1 0 qð Þ ν;t xð Þ ν;t; q 1−βdν h iRF ð Þt β; ð2Þ where RF(t) is the creative capital input that is producing the final good at time t, q(ν,t) is the quality of the machine of line ν at time t, x(ν,t;q) is the total amount of the machine of variety ν and quality q that is used at time t, and β∈(0,1) is a parameter of the production function. Let wN0 denote the wage paid to the creative capital input RF(t) and let rN0 denote the interest rate. Since the representative creative class household in the region under study is risk-neutral, we can tell that r = ρ. 4 Notice that for a given machine line ν, only the machine with the highest or cutting edge quality is used to produce the single final good in equilibrium. This feature is the source of creative destruction in the sense of Joseph Schumpeter. In general, what this means is that when R&D leads to the invention of a higher quality machine of a particular line, the previous lower quality machine of the same line is replaced or destroyed. Our next task is to explain how new machines in our creative region are first invented and then produced.
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کلمات کلیدی:
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