1. Suppose that the firm's cost function is C(q) = f + c(q) and marginal cost is nondecreasing. Demonstrate that for some initial range of output, there are economies of scale.
2. Show that the cost function C(q) = f + cq where c > 0 is characterized by global economies of scale.
3. Find the range of outputs for which the cost function C(q) = f + cq2 is characterized by
(i) economies of scale, (ii) diseconomies of scale, and (iii) constant returns to scale. Are there economies of scale if f = 0?