a firm has a propietary technology and demand for the technology is given by Q_d=5-4P

where Q_d is the quantity demanded for the licenses of the technology per year and P is the price of the licenses.

1. Suppose according to the intellectual property law patents expire after 20 years and the interest rate is 4%. What is the private velue of the patent?
2. What is the total deadweight loss of the patent ovr its life
3. what is the total consumer surpluss generated by the patent over its life (including the time after the patent expires)