Assignment 8 [Key]

# Assignment 8 [Key] - Econ 102 Answer key assignment 8 Josef...

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Econ 102 - Answer key assignment 8 Josef Schroth, November 16, 2008 Question 1 1. The social planner problem is maximizing consumption. max C s . t . C Y Y 3 X X L - V L H 1/2 V 1/2 H 1 All these constraints will bind in optimum. Hence we can rewrite the planning problem as max 3 ( L - L 2 ) . The ﬁrst order condition is 1 - 2 L = 0 L = 1 2 . Then V = 1/4, X = 1/4, and C = Y = 3/4. 2. The ﬁrm maximizes its proﬁts. It uses X units of labor input to produce the consumption good. It also uses V units of labor to recruit its workforce L , where L = X + V . Note that recruiters recruit themselves in this model. The ﬁrm takes as given the prices for labor, w , and the consumption good, p . It also takes as given the productivity q of recruiters. Note that q will be determined by an aggregate search technology, but w / p is a free parameter 1

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so far. The ﬁrm problem is then max pY - wL s . t . Y 3 X X L - V L qV 3. All these constraints will bind in optimum. Hence we can rewrite the ﬁrm problem as max p 3 ( qV - V ) - wqV . The ﬁrst order condition is p 3 ( q - 1 ) - wq = 0 w p = 3 ± 1 - 1 q ² .
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Assignment 8 [Key] - Econ 102 Answer key assignment 8 Josef...

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