Nadine sells user-friendly software. Her firm’s production function is f (x1, x2) = x1 + 2x2, where x1 is the amount of unskilled labor and x2 is the amount of skilled labor that she employs.
(a) In the graph below, draw a production isoquant representing input combinations that will produce 20 units of output. Draw another isoquant representing input combinations that will produce 40 units of output.
(b) Does this production function exhibit increasing, decreasing, or constant returns to scale?
(c) If Nadine uses only unskilled labor, how much unskilled labor would she need in order to produce y units of output?
(d) If Nadine uses only skilled labor to produce output, how much skilled labor would she need in order to produce y units of output?
(e) If Nadine faces factor prices (1, 1), what is the cheapest way for her to produce 20 units of output?
(f) If Nadine faces factor prices (1, 3), what is the cheapest way for her to produce 20 units of output?
(g) If Nadine faces factor prices (w1, w2), what will be the minimal cost of producing 20 units of output?
(h) If Nadine faces factor prices (w1, w2), what will be the minimal cost of producing y units of output?