Dan is the owner of a price-taking company that manufactures sporting goods. One

Question

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 CB(QB, QG) = 100QB + QB2 + QBQG and the marginal cost is MCB = 100 + 2QB + QG, where QB is the output level for bats and QG is the output level for gloves. Dan's cost function for baseball gloves is CG(QB, QG) = 50QG + QG2 + QGQB, and the marginal cost is MCG = 50 + 2QG + QB. The price of a baseball bat is $240 and the price of a baseball glove is $150. If he only produced gloves, what would Dan's profit be if he produces the profit-maximizing quantity?

Explanation / Answer

If Dan is owning a price taking company, it means that the company runs in perfect competition where Marginal Revenue equals Price of good.

Here Price of gloves = $150

thus MR of glove = $150

and Price of Bat = $240 = MR of bat

We also know that at profit maximization, MR equals MC

Thus MC of gloves = MR of gloves

50 + 2QG + QB = 150

QB = 100 - 2QG .... eq i

and MC of bats = MR of bats

100 + 2QB + QG = 240

QB = 70 - QG/2 ..... eq ii

From eq i and eq ii

100 - 2QG = 70 - QG/2

200 - 4QG = 140 - QG

3QG = 60

QG = 60/3 = 20

Hence Dan would produce 20 units of gloves.

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.