Copper Mine Imagine that. upon graduation. you are hired to manage a copper mine in Western Australia. Your task is to maximize prots of the mining operation by choosing the optimal level of inputs labor. L. and capital. is". In the rst few months of operation. you are only allowed to choose the level of labor you employ and must take If to be xed at It'. The production function of the mine is given by: I 2 f (a: L) = (5L + 5K 7 2K2 + LK Let the initial endowment of capital be K = '2 and let the output price be p. the price of labor be to. and the price of capital be r. I. Find an expression for Total. Average. and Marginal Value Product of labor given K xed at the initial endow- ment. Comment on the shape of the Average Value Product curve. There are no other costs besides the cm! of labor and capital. 2. Set up the prot maximization problem for the copper mine assuming you are operating under perfect compe- tition. Let r = 1. 3' Now. let p = 1 and solo: the prot maximizmion problem and obtain an expression for labor, L. as a function of at. 4. Find an expression for output. 3}. as a function of at. 5. You haven't been paying close attention to your cost of labor. After investigating. you realize that the wage you must offer has increased. Find an expression for how your choice of labor. L\" responds to a change in wage rate. Discuss the change you expect from an increase in wage rate. 6. Given your expression for how labor application changes in response to wage rate hike. what can you say about how output. g," responds to an increase in wage rate