Sarah and Sean Are Furniture Movers

Essay

Sarah and Sean are furniture movers. They are interested in adopting the efficient organizational form for a moving business. Working alone, each has a production function of yi = 3ei, where yi is income in dollars and ei is effort in hours. Working together as a team, because of the advantages of team production in moving, they are able to a achieve the production function y = 4(e1 + e2), where y is now total income. Both have utility functions given by Ui = yi/(ei + 2)2.
i)If both individuals set up independently as owner- managers, find the level of effort expended by each, the income received, and the utility level attained.
ii)If Sarah and Sean form a partnership, sharing their total income equally, what will the effort levels, income, and utilities be?
iii)What are the Pareto- optimal levels of effort, income and utility for team production by Sean and Sarah?
iv)What organizational form might Sean and Sarah adopt to achieve the solution iii)? What condition is required for this to be possible?