Explain it step by step, and explain why is MRPL=MFC, explain step by step and address all the questions, thanks

The Ajax Coal Company is the only employer in its area. Its only variable input is labour, which has a constant marginal product equal to 5. Because it is the only employer in the area, the rm faces a supply curve for labour given by W = 10 + L, where W is the wage rate and L is the number of person-hours employed. Suppose the rm can sell all it wishes at a constant price of 8. a. How much labour does the firm employ, how much output does it produce, and what is the wage? b. Suppose now the firm sells a special kind of coal such that it faces a downward-sloping demand curve for its output. In particular, assume that Ajax faces the demand curve given by P = 102 1.96Q. How much labour does the rm employ, how much output does it produce, what price does it set for the output, and what is the wage? c. Assume that Ajax still faces the demand curve P = 102 1.96Q, but now further assume that Ajax has five labourers under contract to produce coal at a wage of 15. If Ajax has the option of hiring additional labourers at a higher wage without increasing the wage to the five labourers already under hire, will Ajax increase its labour force? Explain. ANSWER: a. The rm will employ workers according to MRPL = MF C . MRPL = MR'MPL. SOMRPL = 8'5 = 40 andMFC = 10 + 2L. Since MFC = MRP, L = 15 and W = 10 + L = 25, Output = 15 . 5 = 75. b. MRPL = MR . MPL. MR = 102 - 3.92Q (twice as steep as the demand curve). So MRPL = (102 - 3.92Q) . 5 = 510 - 19.6Q. Since the production function is Q = 5L (because of constant marginal product and the fact that with you cannot produce anything with 0 input), MRPL = 510 - 98L. MRPL = MFC implies 510 - 98L = 10 + 2L which solves for L = 5. W = 10 + L = 15 and Q = 5L = 25 and P = 102 - 1.96Q = 53. c. From part (b) MRPL = 510 - 98L. At L = 5, MRPL = 20. At L = 6, MRPL = -78. Since MRPL becomes negative, no matter what the wage is an extra worker will decrease profits. So Ajax will not increase its labour force