Final answer:
The task is to set up objective functions, find best responses, and determine the Nash equilibrium for two firms where firm A maximizes over price and firm B maximizes over quantity, based on their respective demand and pricing functions.
Step-by-step explanation:
The question involves setting up objective functions for two firms, finding their best responses in the context of game theory, and determining the Nash equilibrium. Firm A maximizes over price while Firm B maximizes over quantity. Each firm's objective function would be derived from their respective demand and pricing functions. To find the best response, we differentiate the profit function with respect to the firm's choice variable (price for Firm A and quantity for Firm B) and set the derivative equal to zero. This process is iterated until each firm's best response does not change given the other firm's strategy. The Nash equilibrium is the set of strategies where each firm is doing the best they can, given the strategy of the other firm.
We would proceed by setting up the profit functions for each firm taking into account the cost structures, then solve the simultaneous equations that arise from setting the derivatives of these profit functions to zero.