A producer of fixed proportion goods X and Y (Q = Q_X = Q_Y)has marginal costs and revenues of MC = 12Q,MR_X = 54 - 6Q_X,MR_Y = 126 - 12Q_Y.The producer should produce how many units?

Question

Quizplus · Accepted Answer

To maximize profits, the producer must produce where marginal revenue equals marginal cost. First, we find the marginal revenue of X: MR_X = 54 - 6Q_X 54 - 6Q_X = MC = 12Q Solving for Q_X, we get: Q_X = (54 - MC)/6 = (54 - 12Q)/6 = 9 - 2Q Now we can substitute this value into the equation for Y's marginal revenue: MR_Y = 126 - 12Q_Y MR_Y = 126 - 12(9 - 2Q) = -6Q + 210 Setting this equal to MC: -6Q + 210 = 12Q 18Q = 210 Q = 11.67 Since Q must be an integer, the producer should produce 6 units of X and (6 units of Y to satisfy the production function).

A Producer of Fixed Proportion Goods X and Y (Q