※ 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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