請教一下 勞動供需的題目一題 - 經濟

※ 引述《Cupman (杯男)》之銘言：
: Consider a straw hat market consisting of 100 identical firms.
: There is an unlimited supply of straws and hence straws are free.
: The only cost incurred by each firm in production is the wage paid
: to workers. The production function of each firm is given by
: Q(L)=120L-(1/2)L^2, where Q is the number of hats produced and L is the
: number of workers hired.
: Suppose that each firm is a price taker in the product market and the
: price of a hat is $10, what is the market demand for labor?
: (MP(L)= 120-L given the production function.)
: 可以請教一下這題要怎麼推嗎?麻煩大家了謝謝!

At first, sorry that I can't type Chinese with my friend's new laptop.
Please ignore any English writing issue.


Consider an individual firm's problem. We know

Profit = Revenue - Cost = PQ-wL = 10Q(L)-wL,

where w is the wage rate. We can further get that

Profit=1200L-5L^2-wL.

From the first order condition, which is 1200-10L-w=0, we can find
this single firm's labor demand, L=120-w/10.
Since all 100 firms are identical, the market demand for labor is then

Lm=10L=1200-w.

An alternative way to figure out the representative individual firm's
labor demand is to equate MP(L) with the real wage rate, w/P.
Then, we can find

120-L = w/10 ==> L=120-w/10.

Again, it can be derived that the markt labor demand is Lm=1200-w.

If there is anything wrong or really confusing, please let me know.

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