(b)  There are two goods (quantities x and y) and two people (A and B) in the economy. A owns eight units of the x-good and none of the y-good. B owns none of the x-good, and three units of the y-good. Their preferences are described by the utility functions

 

 

and     u8 (xe,ya) = ya + logxs

 

Determine both consumers' demand functions and the market demand function, and the competitive {Walrasian) equilibrium price(s) and allocation(s).

 

(b) Consider the following game played between a boss (B) and an employee (E). The boss offers a wage, w c:: 0 . After observing the wage offer, the employee decides how much effort, e          0, to expend. The payoff functions  for the boss and the employee are (a is a constant):

 

u8 (w, e) = 2../e- w

 

=

 

  e2u E( w, e)     w - 2 + awe

i)            What is the optimal effort for the employee, as function of w?

ii)           What is the subgame perfect equilibrium choices of w and e, as function of a?

1. There are two firms in a market. Firm 1 is the "leader" and picks its quantity first. Firm 2, the "follower", observes firm 1's choice and then chooses its quantity. Profits for each firm i given by quantity choices q1 and q2 are p(q1+q2)qi - cq,, where p'(q) + p"(q) < 0 at all q 0. Show that firm 1's quantity choice is larger than its quantity choice would be if the firms chose quantities simultaneously and that its profits are larger as well.

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