In upcoming chapters, we will often assume that the average cost curve is U-shaped.
A: Indicate for each statement below whether you believe that the description of the firm€™s situation would lead to a U-shaped average cost curve.
(a) The firm€™s production frontier initially exhibits increasing returns to scale but, beginning at some output quantity x, it exhibits decreasing returns to scale.
(b) The firm€™s production frontier initially exhibits decreasing returns to scale but, beginning at some output quantity , it exhibits increasing returns to scale.
(c) The firm€™s production process initially has increasing returns to scale, then€”in some interval from x to €”it has constant returns to scale, followed by decreasing returns to scale.
(d) The firm€™s production process initially has increasing returns to scale, then€”in some interval from x to €” it has constant returns to scale, followed by once again increasing returns to scale.
(e) The production process for the firm has decreasing returns to scale throughout€”but, before ever producing the first unit of output, the firm incurs annually a fixed cost FC (such as a large license fee) that must be paid if production is to occur.
(f) The firm incurs the same annual FC as in (e) €” but it€™s production process initially has increasing returns to scale before eventually switching to decreasing returns to scale.
B: We will explore production processes with initially increasing and eventually decreasing returns to scale in exercises 12.5 and 12.6. Here we instead focus on exploring the impact of recurring fixed costs (like annual license fees) on the shape of cost curves. Consider, as we did in exercises 12.2 and 12.3, the Cobb-Douglas production function x = f („“,k) = A„“αkβ. In exercise 12.3B(d), you should have concluded that the cost function for this production process is

(a) In problem 12.3, this cost function was derived for the case where α+β (b) Are marginal and average cost curves for this production process upward or downward sloping? What does your answer depend on?
(c) Suppose that the firm incurs a fixed cost FC that has to be paid each period before production starts. How does this change the (total) cost function, the marginal cost function and the average cost function?
(d) Suppose that α+β (e) How does your answer differ if α+β> 1? What if α+β = 1?

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C(w, r, c)-(α β) Ααα ββ