In Table 14.1, the last column indicates the predicted change in the number of firms within an industry when economic conditions change.

A: In two cases, the table makes a definitive prediction, whereas in two other cases it does not.

(a) Explain first why we can say definitively that the number of firms falls as a recurring fixed cost (i.e. license fee) increases? Relate your answer to what we know about firm output and price in the long run.

(b) Repeat (a) for the case of an increase in demand.

(c) Now consider an increase in the wage rate and suppose first that this causes the long run AC curve to shift up without changing the output level at which the curve reaches its lowest point. In this case, can you predict whether the number of firms increases or decreases?

(d) Repeat (c) but assume that the lowest point of the AC curve shifts up and to the right.

(e) Repeat (c) again but this time assume that the lowest point of the AC curve shifts up and to the left.

(f) Is the analysis regarding the new equilibrium number of firms any different for a change in r?

(g) Which way would the lowest point of the AC curve have to shift in order for us not to be sure whether the number of firms increases or decreases when w falls?

B: Consider the case of a firm that operates with a Cobb-Douglas production function f (ℓ, k) = Aℓ^αk^β where α, β > 0 and α + β < 1.

(a) The cost function for such a production process — assuming no fixed costs — was given in equation (13.45) of exercise 13.5. Assuming an additional recurring fixed cost F, what is the average cost function for this firm?

(b) Derive the equation for the output level x^∗ at which the long run AC curve reaches its lowest point.

(c) How does x^∗ change with F, w and r?

(d) True or False: For industries in which firms face Cobb-Douglas production processes with recurring fixed costs, we can predict that the number of firms in the industry increases with F but we cannot predict whether the number of firms will increase or decrease with w or r .