Dan is the owner of a price-taking company that manufactures sporting goods.One particular facility Dan owns produces baseball bats and baseball gloves.His cost function for baseball bats is C_B(Q_B,Q_G)= 100Q_B + Q_B² + Q_BQ_G and the marginal cost is MC_B = 100 + 2Q_B + Q_G,where Q_B is the output level for bats and Q_G is the output level for gloves.Dan's cost function for baseball gloves is C_G(Q_B,Q_G)= 50Q_G + Q_G² + Q_GQ_B,and the marginal cost is MC_G = 50 + 2Q_G + Q_B.The price of a baseball bat is $240 and the price of a baseball glove is $150.What is the profit-maximizing sales quantity for baseball gloves? A) 10 B) 20 C) 30 D) 60

Question

Quizplus · Accepted Answer

To find the profit-maximizing sales quantity for baseball gloves, we need to set the marginal revenue (MR) equal to the marginal cost (MC) for baseball gloves. Given the price of a baseball glove is $150, which is a price-taking scenario, the MR for baseball gloves is also $150. The marginal cost (MC) for baseball gloves is given by MC = 50 + 2Q + Q_bats. Without the specific output level for bats (Q_bats), we directly compare the MR and MC for gloves. Since we don't have the exact relationship between the output of bats and gloves, we look for an answer that could potentially satisfy the MR = MC condition based on the given MC formula. However, without additional information or a specific formula linking bats and gloves production, we cannot accurately calculate the exact quantity based solely on the provided information. The correct answer, therefore, hinges on understanding the principle of profit maximization (MR = MC) and recognizing the limitations of the information provided regarding the relationship between the production of bats and gloves.

Dan Is the Owner of a Price-Taking Company That Manufactures