推 SONGya168:學校年度後請以-標註, 非_ T修正後解鎖文 07/08 14:53
suppose that the distribution of the market next year only
depends on this year. consider only two rival companies, R and S
who manufacture a cerain product. each year, company R keeps 1/4
of its customers while 3/4 switch to S. each year, S keeps 2/3
of its customers while 1/3 switch to R. when manufacture of the product
first starts, R has 3/5 of the market while S has 2/5 of the market.
in the long run, the steady-state distribution of R of the market is ?
我有兩個問題
(1)最後一句的英文是求算 R市場在長期之下穩定均衡的分配沒錯吧?
如果(1)是對的話，我的想法如下
R S
R 1/4 3/4
S 1/3 2/3
然後明年度 R的客戶市場是 3/5*1/4 + 2/5*1/3
第三年度 R的客戶市場
[ 3/5*1/4 + 2/5*1/3 ]*1/4 + (3/5*3/4 + 2/5*2/3)1/3
依此類推，本來以為會有公比出現之類的，可是我發現好像沒有
所以我就卡住無法解下去，不知道是哪裡出問題，因此請教板上的人
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