The production function is given by y = 11/2, where y is the output, and L is the amount of labor input. Assume that wage rate is w so that the cost of using L unit of labor input is wL. Let p denote the unit price of the output. Note that w and p are exogenously given. (1) Find the function for the profit (in terms of p, w and L). (2) Find the optimal choice of labor input and the corresponding maximized profit (in terms of and w). (3) Suppose that both wage rate, w, and the price, p, double. How will this affect the firm's optimal decision? Explain. (4) Suppose that the government set the minimum wage > w. How will this affect the firm's optimal decision? Explain. The production function is given by y = 11/2, where y is the output, and L is the amount of labor input. Assume that wage rate is w so that the cost of using L unit of labor input is wL. Let p denote the unit price of the output. Note that w and p are exogenously given. (1) Find the function for the profit (in terms of p, w and L). (2) Find the optimal choice of labor input and the corresponding maximized profit (in terms of and w). (3) Suppose that both wage rate, w, and the price, p, double. How will this affect the firm's optimal decision? Explain. (4) Suppose that the government set the minimum wage > w. How will this affect the firm's optimal decision? Explain