Consider a market in which the behavior of consumers is described by the inverse demand function p = 30 - 1/10q

In addition, assume there is a monopoly in this market with the following total cost function C(q) = 20q

a) Determine the monopoly price and quantity and compute the profit of the monopoly.

b) Assume the monopoly can invest in a new technology with lower costs of production. In particular, the total cost function for the new technology is given by C(q) = 10q

i) Determine the optimal price and quantity with the new technology.

ii) The new technology requires an investment of 500 dollars. Should the monopoly make the investment in the new technology?