104# AdrianW
我同意 我的推导如下
in the competitive market setting, all firms are price takers and thus are maximizing q given p. max {p*q-c(q)} => p=c'(q)
p decreases, if we assume cost function is convex then q decreases as well.
In terms of aggregate setting, its simply a shift in demand side of milk causing price to fall and supply to fall as well. thus as q_milk decreases, the demand of cows decreases.
and also i dont see why price elasticity matters. (i dont see why we should use monopolists setting as well )
we should assume that before the change of prices, the firm is already profit maximizing and thus any change of price should reduce its profits (not revenue) whether the price elasticiy of milk is elastic or inelastic if demand side of milk and technology dont change. (unless in an isoelastic curve setting and e always greater than 1, but in that setting you will never find an optimal point without constraints) There is no such thing as always elastic goods and always inelastic goods. We just operate on the elastic portion of the demand (under monopolists' setting, they would not operate on inelastic parts as they can always raise prices until they reach elastic parts) Even on the elastic portion of demand, it doesn't mean we should always raise price to raise profits (otherwise people will already do so). It is true that we should always raise price to raise "revenue" if elastic but revenue is not the same as profits unless mc=0. a rule may be important for reference is the markup formula (p-mc)/p=-1/e Anyway, the important thing is that we should assume people are already profits maximizing before the change of price of milk.
I think one potential reason the supply side of milk will change the price given the monopoly setting is that the cost function becomes more efficient, ie. c2'(q)<c1'(q) in this case you can prove p2<p1. Then why is c2'(q)<c1'(q) its hard to believe its the demand of cows causing the troubles as we are talking now about shocks to supply side of milk and we assume the demand side of milk doesnt change. So there is a supply shock of cows causing c2'(q)<c1'(q) of milk, and thus we should see that p_cows are lower now. But this is really the supply side of cows which is not about the question. (it also has an inverse relationship, ie. shocks of cows market affect the milk market)
I don't see why we should use monopolist market anyway in this question and thus the simple competitive market analysis should be enough .