Question

The demand for detergent in Tanzania is characterized by the following functuon P(Q) = 100 - 10Q. Firm A supplies detergent and has a cost function given by TC(Q) = 10Q²
a) assuming that firm A is a monopolist in Tanzania what is the profit maximizing quantity and price?
b) Now assume that firm A can produce for two different countries Tanzania and Kenya. Demand in kenya is given by P(Q) = 50 - 20Q. Assume firm A is a monopolist for both markets, what is the optumal price and quantity for each markets under third degree of price discrination?
c)Now assume that firm A is only active in Tanzania where it competes with firm B. Firm B cost function is CB(QB) = 40Q. Suppose that both compete in quantities . What is the equilibriam quantities and price? Show your work clearly step by step in each part.