Q1- Consider a market for a homogenous product where the demand is given by
There are two firms A and B with total cost functions TCa(qa)=5qa and TCb(qb)=0.5qb2
a) As a benevolent dictator, you would like to maximize society’s well-being. You can choose either firm to be the sole supplier of the product and the maximum price it can charge. Which firm would you pick? What price ceiling would you impose on that firm? What quantity would the firm supply? What would be its profit? What would be the consumer surplus? Show your calculations in an organized and legible way and explain your reasoning.
b) To highlight your benevolence and justify your choices, compare the results in part (a) (Quantities, Prices, Profits, and Consumer Surplus) to the results that would prevail if the two firms act as Cournot duopolists.
c) To show that things could be even worse, compare your results in part (a) to the results that would prevail if the two firms collude and act as a monopolist.