PT Boekit Acem (PT BA) is the only coal mining company in Province X and is a monopsonist in the labor market. The supply of labor in Province X follows the function L = 100w, where L is the quantity supplied of labor and w is the wage rate. Labor productivity in digging coal is assumed to be constant at 2 tons per hour. Meanwhile, coal is sold at $10 per ton. a. What is the optimal number of mining workers and wage level for PT BA? (8 points) b. If the labor market is now competitive, or PT BA cannot exercise its monopsony power, calculate the optimal number of workers and the wage rate. (5 points) c. Compare the calculation results in (a) and (b), then show and explain the two conditions in one diagram. (5 points) d. In a monopsony market (as in question a), if the selling price of coal increases by 50%, will it affect the number of workers PT BA recruits? How does it affect worker wage? Explain and include calculations in your explanation. (7 points)