The partnership of Leontief Associates has the technology Y = B min (e₁, e₂), where Y is total output, e_iis the effort of person i(i = 1, 2), and B >1. Since there are two partners, the income of each person is equal to half of total team output. The utility functions of the two people are identical: u_i= y_i- e_i².
i)Suppose the effort of person 2 is fixed. Find the optimal effort for person 1. (Hint: consider two cases separately, where e₂>B/4, and e₂< B/4).
ii)There is more than one Nash equilibrium for this model. Which effort pairs satisfy the requirements of Nash equilibrium? Do we have a Nash equilibrium when each person chooses the efficient level of effort?

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The Answer of The partnership of Leontief Associates has the technology Y = B min (e₁, e₂), where Y is total output, e_iis the effort of person i(i = 1, 2), and B >1. Since there are two partners, the income of each person is equal to half of total team output. The utility functions of the two people are identical: u_i= y_i- e_i². i)Suppose the effort of person 2 is fixed. Find the optimal effort for person 1. (Hint: consider two cases separately, where e₂>B/4, and e₂< B/4). ii)There is more than one Nash equilibrium for this model. Which effort pairs satisfy the requirements of Nash equilibrium? Do we have a Nash equilibrium when each person chooses the efficient level of effort?

The Partnership of Leontief Associates Has the Technology Y =