Research and development activities are widely considered to have positive effects. Consider the market for innovation.

Research and development activities are widely considered to have positive effects. Consider the market for innovation. The market demand for patents is Qd=100-10P, where Q is the number of patents produced and P is the price for each patent. Suppose the market for patents is competitive and that the market supply curve is Qs=2P-8. Finally, suppose the external benefit from innovation is: MSB=8+1.5Q. This external benefit is not currently being internalized in the market.

a) Given the demand and supply curves, what is the number of patents produced by an unregulated market?

b) Is the current level of market production for patents the socially optimal number of patents? Explain your answer.

c) Find the optimal level of innovation, the DWL created by the externality, and the optimal Pigouvian subsidy.

d) Draw a figure to illustrate your answer.