聯合生產的均衡數量及價格問題

Question

有一家公司她飼養了羊來生產羊肉跟羊皮，遵照固定比例生產過程，一頭羊生產一單位的羊肉跟一單位的羊皮，所有花費均是一起的(聯合生產)，

且羊肉的需求為Pm=308-0.5Qm，

羊皮的需求為Pss=172-2Qss，

MRm=308-Qm，

MRss =172-4Qm

MC=20+5Q

求利潤極大化時的羊肉跟羊皮生產數量以及此時的個別價格?

若改成MC=20+5Q

則利潤極大化時的羊肉跟羊皮生產數量以及此時的個別價格變成?

需要附上計算過程跟說明，謝謝你

以下是原文，上面我自己翻的，不知道有沒有誤解他的意思

Assume that a firm raises sheep in order to produce two product :meat and sheepskins. The firm products sheepskins and meat according to a fixed-proportions production process , with all costs shared jointly . Assume that the demand equation for meat is Pm=308-0.5Qm

And that the demand curve for sheepskins is Pss=172-2Qss

The corresponding marginal-revenue equations are MRm=308-Qm，MRss =172-4Qm

The marginal cost for raisimg sheep is MC=20+5Q

Assume that one sheep products one unit of meat and one sheepskin. Determine the profit-maximizing quantities of sheepskins, meat , and sheep , and the price of the meat and sheepskins

If change MC=60+10Q

And derive the same quantities and price

Answer 1

最佳解答

圖片參考：https://s.yimg.com/rk/AB01294316/o/1169914826.jpg

廠商邊際成本P=60+10Q邊際收益P=(308-Q)+(172-4Q)èP=480-5Q依邊際成本=邊際收益60+10Q=480-5Qè15Q=420èQ=28此時邊際成本P=340 羊肉市場需求線P=308-0.5QQ=28代入得羊肉價格P=294 羊皮市場需求線P=172-2QQ=28代入得羊皮價格P=116