BPP Field Exam 2010 Answers

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Question B1: Production in Teams

Relevant papers:

• Holmstrom (1982), Moral Hazard in Teams. Not on exam's reading list.
• Holmstrom (1999), Firm as Subeconomy, Not on exam's reading list.

Question B1.1

Notes about assumptions:

• The prompt does not explicitly say that everyone must receive the same share. Nonetheless, many of the relevant papers assume that this is the case. As such, will solve the problem both ways.
• The prompt also does not explicitly require a balanced budget. However, no source of funding for the agents is mentioned besides the combined output V of the individual agents. As such, I will assume that the budget balance restriction must hold.

Each agent's maximization problem

[math] \max_{e_{i}}[s_{i}\sum_{j\neq i}z(e_{j})+s_{i}z(e_{i})-e_{i}] [/math]

Note that if the agent chooses to work, his utility is [math]s_{i}\sum_{j\neq i}z(e_{j})+s_{i}z-1[/math]

If he chooses to shirk his utility is [math]s_{i}\sum_{j\neq i}z(e_{j})[/math].

Therefore, he'll work if [math]s_{i}z-1\gt 0 \iff s_{i}z\gt 1 \iff s_{i}\gt \frac{1}{z}[/math].

Note that not everyone can have [math]s_{i}\gt \frac{1}{z}[/math] because [math]\frac{N}{z}\gt 1[/math].

(a) My answer, assuming that some shares can be different.

(b) My answer, assuming that all shares must be equal.

Question B1.2

Question B1.3

Question C1: Agenda Control and Status Quo

(i)

(ii)

(iii)

(iv)