The Ontario Brassworks produces brazen effronteries. As you know brass is an alloy of copper and zinc, used in fixed proportions. The production function is given by: f(x1, x2) = min{x1, 2x2}, where x1 is the amount of copper it uses and x2 is the amount of zinc that it uses in production.
(a) Illustrate a typical isoquant for this production function in the graph below.
(b) Does this production function exhibit increasing, decreasing, or constant returns to scale?
(c) If the firm wanted to produce 10 effronteries, how much copper would it need? _____. How much zinc would it need? _____.
(d) If the firm faces factor prices (1, 1), what is the cheapest way for it to produce 10 effronteries? How much will this cost?
(e) If the firm faces factor prices (w1, w2), what is the cheapest cost to produce 10 effronteries?
(f) If the firm faces factor prices (w1, w2), what will be the minimal cost of producing y effronteries?