4. Consider a monopoly that uses the 3rd-degree price discrimination for two groups of consumers with the same inverse demand functions, P,(q) = P,(q) for all q. The monopoly has the total cost function C(q142) = Ci(q1) + C2(q:). Suppose that the profit-maximizing quantities are positive, q", > 0 and q", > 0. Are the optimal prices for different groups always equal, that is, p",= p"? Explain