Assume that annual inverse demand for a particular product is P = 150 - Q. the product is offered by a pair of bertrand competitors each with marginal cost of $75. and discount factor 9. Assume R&D is conducted at rate x, and incurs one off costs of r(x) = 10x^2 and reduces marginal cost ts to 75-x. suppose one firms decides to conduct R&D at a speed of x = 10. patent protected for T years.

Profit from each year during patent protection = (75 - (75-10))(37.5) = $375

a. what is the total surplus once patent protection expires?

b. Use the profit earned from years with patent and without patent to write total net surplus from the innovation as a function of the period of patent protection.