Al's Authentic Anklettes sells ankle bracelets.Their demand and costs are given by Q^D = 100 - P and TC = 100 + 10Q.The profit-maximizing level of output is: A) 45 ankle bracelets. B) 47.5 ankle bracelets. C) 90 ankle bracelets. D) 10 ankle bracelets. E) no ankle bracelets.

Question

Quizplus · Accepted Answer

To find the profit-maximizing level of output, we first need to determine the marginal cost (MC) and marginal revenue (MR). From the total cost (TC) function TC = 100 + 10Q, the marginal cost (MC) is the derivative of TC with respect to Q, which is MC = 10. The demand function is given as Q = 100 - P, which can be rearranged to find the price as a function of quantity, P = 100 - Q. To find the marginal revenue (MR), we first need the total revenue (TR), which is P*Q = (100 - Q)Q. The derivative of TR with respect to Q gives MR = 100 - 2Q. Setting MR equal to MC to find the profit-maximizing quantity: 100 - 2Q = 10, solving for Q gives Q = 45. Therefore, the profit-maximizing level of output is 45 ankle bracelets.

Al's Authentic Anklettes Sells Ankle Bracelets