Final answer:
To find the utility function for a Cournot Duopoly firm with a consumer demand function of Q = a1 + bP, the firm's profit maximization problem and the demand function need to be considered.
Step-by-step explanation:
A Cournot duopoly involves two firms competing in the market by choosing their quantity of output. To find the utility function for a Cournot Duopoly firm given a consumer demand function of Q = a1 + bP, we need to consider the firm's profit maximization problem. The firm's profit can be expressed as the difference between its total revenue and total cost. The utility function can then be derived based on the firm's profit maximization problem and the demand function.