Imagine a firm with a production function q = LK. The cost of one unit of labor is $10 and the cost of one unit of capital is $20. a) Graphical Questions: i) Draw a stylized isoquant/isocost graph identifying this firm's optimal input combination. ii) Now imagine the wage increases to $20. Draw the new isocost line and the new optimal input combination. iii) Does the amount of labor hired increase or decrease as a result of the price change? b) Calculation Questions: i) What is the formula for your marginal rate of technical substitution for L with K (MRTSLK)? (Your answer should be a mathematical formula with the variables L and K in it.) ii) If your goal is to produce 50 units, what is the optimal input combination of labor and capital before the increase in wages (w = $10)? iii) What is the optimal input combination of labor and capital after the increase in wages (w = $20)? iv ) What is the change in the amount of labor hired? v Does this production function (q = LK) reflect increasing, decreasing, or constant returns to scale