To explain the mystery “effectiveness of labor”( A )
z Knowledge or technology The essential feature: nonrival Î marginal cost of production is zero excludability Í the nature of the knowledge & property rights z Human capital
How to model it?
z Diminishing return of capital z Positive externality z An explicit R&D sector OR a side effect z Model the allocation of resources between conventional production sector and R&D
The determinants of the allocation of resources to R&D
z Support for basic scientific research z Private incentives for R&D and innovation Externalities of R&D: Consumer-surplus effect Business-stealing effect R&D effect z Alternative opportunities for talented individuals: rent-seeking z Learning-by-doing: AK-model 1 2. The basic R&D model Assumptions The fraction of the labor force is exogenous Generalized Cobb-Douglas function without capital Y (t) = A(t)(1− aL )L(t) γθ A&(t) = B[aL L(t)] A(t) B > 0 γ≥ 0 z γ> 1 z γ< 1 z θ> 0 z θ< 0 L&(t) = nL(t) n ≥ 0
The dynamic of knowledge accumulation A&(t) g (t) ≡= B[a L(t)]γ A(t)θ−1 A A(t) L g& A (t) = γn + (θ−1)g A (t) g A (t) Case 1: θ< 1 g& A
* g A g A
γn Interpretation of g* = : A 1−θ 1. endogenous long run growth rate 2 2. positive link with population growth 3. aL has a level effect but not a growth effect
Case 2: θ> 1 ever-increasing growth aL has a growth effect g& A g A
Case 3: θ= 1 linear growth model aL has a growth effect g& A g A
An extension with capital
3 3. The Schumpeter model
z 如何把“创新”模型化? z 如何刻画“创新部门”和“常规部门”的关系? z “创新” ―――意味着现有技术的过时 ―――来自于有风险的研究活动 ―――能够提高生产效率,也能够改善产品质量
Assumptions: z No capital accumulation z No population growth: L individuals. ∞ z Linear utility function: u(y) =