How do chain businesses decide how to manage locations?

How do chain businesses decide how to manage locations? There are two main strategies:

owning and operating locations directly

franchising, whereby the chain enters a relationship with a local business owner who will own and operate the location, but use the branding and business format of the chain.

The propensity to franchise is the percentage of the chain’s locations that are franchised—0% if the chain owns and operates all locations directly, 100% if it franchises all its locations; most chains are somewhere in-between.
From the chain’s perspective, the strategic advantage of franchising is that it lowers the cost of managing locations. The cost of managing can be especially high when locations are geographically far away from the chain’s headquarters, and/or if the chain is organizationally young and has thus not yet developed the experience and expertise to manage remote locations. These two factors would be expected to factor into a chain’s strategic deliberations over how much to franchise.
A study decides to examine existing chains to see what factors have actually shaped their propensity to franchise. For each chain in the study, three factors are examined:

geographic dispersion: how widely the chain’s locations are situated, geographically, away from the chain’s HQ (more dispersed = the locations are on average further away from the HQ and hence most costly to own and operate directly)

organizational age: the years since the chain’s founding (older age = the chain has been around longer, and presumably developed more experience managing locations)

industry propensity to franchise: how prevalent franchising is among other chains in the chain’s industry

a) For each of these three factors, explain what influence one would expect it to have on the chain’s propensity to franchise if organizations behaved according to the assumptions of a rational adaptation perspective. Specifically, for each, choose between:

would make the propensity to franchise higher

would make the propensity to franchise lower, or
would not have any significant effect on propensity to franchise one way or another

The following applies to parts (b) and (c) of this question. The study is conducted and the following results are found:
factor observed association with propensity to franchise
geographic dispersion Positively associated: higher dispersion is associated
with higher propensity, lower dispersion is associated
with lower propensity.
organizational age No association one way or the other.
industry propensity to franchise Positively associated: higher industry propensity is
associated with higher chain propensity, lower
industry propensity is associated with lower chain
b) Based on the above study results, is there support for a rational adaptation prediction about how chain organizations would behave? If so, explain why. If not, explain why not.
c) Based on the above, is there support for an institutionalist prediction about how chains would behave? If so, explain why—and explain WHICH of the types of institutional isomorphism is supported. If not, explain why not.
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