Suppose a firm's production function is given by Q=L^(1/2) * K^(1/2). The marginal product of labor and marginal product of Capital are given by:
MPL= K^(1/2)/2L^(1/2) and MPK = L^(1/2)/2K^(1/2)
A) Suppose the price of labor is w=25 and the price of capital is r=4. Derive the firm's total cost function.
B) What is the firm's marginal cost?
C) Sketch the graph of the firm's isoquant for Q=10 units of output, and on the same graph sketch the firm's iso cost line associated with the total cost of producing Q=10 units of output. Please scale the graph up to 100 units of Labor on the horizontal axis, and 100 units of Capital on the vertical axis. For the isocost line, clearly identify the vertical and horizontal intercepts. For the isoquant, clearly identify 4 combinations of labor and Capital that will produce Q=10 units.