Consider a region where people produce and consume two products, bread and olive oil. All workers are equally productive at producing bread and olive oil. The production of bread is subject to constant returns to scale, with one hour is required to produce one loaf of bread. Making olive oil at home also exhibits constant returns to scale, where one can produce one bottle of oil olive in five hours.

a. What is the opportunity cost of producing a bottle of oil olive at home for residents (as measured in terms of loafs of bread)?

b. If there is no utility of social interaction, what can we say about the residential density in this region?

c. If some of the residents are physically stronger which makes them faster in producing olive oil (instead of five hours it takes them three hours to produce a bottle), how would that change your answer to part b above?

Back to the original set up of the question above. Now, assume there is an olive oil store in town which sells a bottle of olive oil for one loaf of bread. Also: -- It takes residents 1/2 hour (i.e. 30 min.) per round-trip mile (2 miles total, 1 mile there, 1 mile back) to walk to places, -- Everyone consumes a one loaf of bread and one bottle of olive oil a day, -- Olive oil store only sells one bottle per day, -- Everyone spends 8 hours/day to work & commute (rest is sleeping + having fun at home), -- Any income left after meal and commuting expenses is allocable to rent, i.e. residents decide on their rent decisions using the leftover principle.

d. Use a martini-glass figure to show the equilibrium market area of the olive oil store. Clearly mark the origin, label your axes, and calculate the stem of the martini glass, and the slope for the arms of the martini glass and size the market area.

e. What would be the monthly rent be at 3 miles away from the olive oil store? How about at 6 miles? (as measured in terms of loafs of breads)

f. If some of the residents are more efficient at making olive oil at home (instead of five hours it takes them three hours to produce a bottle), how would that change the market area?

g. Continue from f above, how would the residential density change compare to parts d & e?