ECO - A cable company is considering a new suburban market

A cable company is considering a new suburban market. The expected average fixed cost per home is $700. The monthly demand for residential cable in the city has been estimated to be given by q(p) 180 2p , where q is expressed in thousands of households and p is the price (or charge) per month. The operator estimates a marginal cost of $20 per month per household.

1) What is the quantity of households that would subscribe at a price of $0?

2) a. Without competition in the market, what price would this cable company charge per month?
b. What is the price elasticity of demand at this price?
c. In this case, how long would the cable company need to wait to cover fixed cost?
(Hint: you need to think about how much the operator generates profits per month.)
d. Over this period of time, how much consumer surplus would be generated?