v**i
发帖数: 7 | 1 I came across a question in my research: Market demand D(p)=a*p^(-b), where
a is constant, b is price elasticity (constant), p is the price (decision
variable).To maximize profit L=(p-c)*D(p), we know the optimal p=bc/(b-1).
Substituting p=bc/(b-1) into L, we have L as function of b and c.Question:
How L change with regard to b and c. I got a weird result: if bc>(b-1), L
decreases with regard to b.
Thank you very much for your help! | U*****e
发帖数: 2882 | 2 nothing weird.
Take a very large b, then p is almost c. what do you want the profit to be?
where
【在 v**i 的大作中提到】
: I came across a question in my research: Market demand D(p)=a*p^(-b), where
: a is constant, b is price elasticity (constant), p is the price (decision
: variable).To maximize profit L=(p-c)*D(p), we know the optimal p=bc/(b-1).
: Substituting p=bc/(b-1) into L, we have L as function of b and c.Question:
: How L change with regard to b and c. I got a weird result: if bc>(b-1), L
: decreases with regard to b.
: Thank you very much for your help!
| v**i
发帖数: 7 | 3
where
My complete results are: if c>=1, a larger b leads to high (maximal profit);
otherwise, (maximal profit) is convex with regard to b. Here maximal profit
means the profit after substituting the optimal price.
How do we interpret the results? Why c is more than 1 or not matters?
【在 v**i 的大作中提到】
: I came across a question in my research: Market demand D(p)=a*p^(-b), where
: a is constant, b is price elasticity (constant), p is the price (decision
: variable).To maximize profit L=(p-c)*D(p), we know the optimal p=bc/(b-1).
: Substituting p=bc/(b-1) into L, we have L as function of b and c.Question:
: How L change with regard to b and c. I got a weird result: if bc>(b-1), L
: decreases with regard to b.
: Thank you very much for your help!
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