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.How would the profit-maximizing sales quantities for bats and gloves change if the price of bats was $270? A) The quantities of bats and gloves will remain unchanged. B) The quantity of gloves will increase while the quantity of bats will decrease. C) The quantity of bats will increase while the quantity of gloves will decrease. D) The quantities of bats and gloves will both increase.

Question

Quizplus · Accepted Answer

When the price of bats increases to $270, the profit-maximizing quantity of bats will decrease because the marginal cost of producing each bat increases with the quantity produced. This means that the expanded production of bats would be less profitable than before, and the company would need to reduce its production to maintain its profit margin. On the other hand, the profit-maximizing quantity of gloves will increase because the increased price of bats will disincentivize consumers from buying as many bats, but may increase their demand for gloves as a substitute product. Therefore, the company can increase its profits by shifting its production mix towards gloves and away from bats. Overall, the quantity of gloves will increase while the quantity of bats will decrease.

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