Innovation Equation

Macro

The equation is mainly from the Ramsey Model, trying to figure out the behavior of the R&D sector. (Research and Development).

$$\frac{\dot{N}}{N}=\theta L_R$$

Resource Constraint of Labor

$$L=L_Y+L_R$$

How does a market economy allocate labor across the 2 activities?

When an entrepreneur develops a new product, the entrepreneur becomes a monopolistic producing that product.

Let $V$ denote the value of an invention. $\dot{N}$ is the number of new products.

Cost of R&D = $W{L}_R$

We assume free entry into the R&D sector.

$$\dot{N}V=W{L}_R$$ $$PV=\frac{{\pi }_i}{1+r}+\frac{{\pi }_i}{(1+r{)}^2}\cdots =$$

Combining two equations, we could get that:

$$\theta N{L}_{R}V=W{L}_R⟹\theta NV=W$$

We will use this equation to determine $L_R$