Question

) Let AC(y) = 1/y+2+0.1y. Find the efficient point of production for this firm. Suppose every firm in the industry has access to the technology, find the region of economies of scope, i.e. the amount of output where production is cheaper if it is concentrated in one firm. Derive the long run, industry, average cost for this function if production is undertaken by the most cost efficient number of firms for each level of output.

Answer 1

ANSWER:

GIVEN THAT:

THE EFFICIENT POINT OF PRODUCTION FOR THIS FIRM:

1. Efficient point of production for the firm with the given average cost is the MES or minimum efficient scale.

MES is determined AC'(y) = 0

-1/y^2 + 1/10 = 0

This gives y^2 = 10

or

y = 3.1623

2. Industrial long run average cost at this output is most efficient at AC = 1/3.1623 + 2 + 0.1*3.1623

= 2.632

3. Regions for economies of scope is from 0 units to 3.1623 units.