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Organisational Economics Problem Set 4 Solution

发布时间：2022-11-25

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Organisational Economics

Problem Set 4 Solution

Question 1

duced) is given by

2 2 8 2

a) Under ��-ownership, �� can produce the w1idget and final good w1ithout the help of ��. So:

and so the surplus from bargaining is �� (= ��). 0 1 2

c) ��Under �� ownership (noting that �� = ��), ��’s payoff is��_�� = ��_�� + ₂ = �� − ₂ (��

�� 8 ��∗ = 0, ∗

− ��). So, choosing

giving ��

= 1.

�� 1 2

d) U��nder ��-ownership (noting that �� = ��), ��’s payoff is ��_�� = ��_�� + ₂ = ₂ − ₂ (��

− ��). So, choosing

��∗ =�� 2 + 2 .

�� = �� + ��2 = 4�� + 14 − 81 ��2

Similarly (anticipating the best response of ��),

’s payoff will be

∗

and so

e) Under ��-ownership, total payoffs are thus 1 2 1

In contrast, under �� ownership, total payoffs is then given by

. By comparing total payoffs under each ow2nership stru8cture, w8 e find that ��-ownership optimal.

bargaining surplus they can hope to share in. Facing this situation, they naturally have no reason to put in any effort at all. This lack of cost-saving effort decreases total utility.

for this is to increase ��, thereby making effort cheaper for �� so that indeed a higher �� will be exerted

are motivated to produce a good of high quality, which leads to some cost saving effort, higher quality product, and higher total payoffs.

a) ��In period 2, the worker seeks to maximize his period-2 payoff ��[��₂ − ��₂]. (Remember that ��₁ and

�� − �� ≥ (1 − ��)�� ,

i.e., ��₂ ≥ ��/��. 2 2

If the worker works (��₁ = 1), then his payoff is ��₁ − �� + (1 − ��)(��₂ − ��). (Here, we used the fact that

he will retire with probability ��. Thus, the probability that he remains with the firm in the second

1 ��(��₁ + (1 − ��)(��₂ − ��)) ≥i.e��..,

This can be rearranged to become ��₁ + (1 − ��)��₂ ≥ ��((1 − ��) + 1/��).

d) Notice that the RHS of Equation (1) is increasing in ��₂. Consequently, to minimize ��₁ + ��₂, the firm

1 2 = ��(1/�� + (1 − ��)∗+ ��/��). ∗ ∗ (2)

It follows that the firm can minimize ��₁ +��₂ by choosing ��₂ = ��/�� and ��₁ +��₂ = ��(1/��+(1−��)+��/��). That is, ��∗1 = ��(1/�� + (1 − ��) + ��/��) − ��/�� = ��(1/�� − (1 − ��)(1/�� − 1)) = ��(1 + ��(1/�� − 1)).

e) Remember that to induce the worker to work in the second period, the firm has to give the worker some surplus in the second period. As the retirement rate increases, the worker (in period 1) anticipates that he is less likely to receive this surplus in the second period – if he is not caught shirking. Thus the worker requires more surplus in the first period to be willing to work in the second period, and the firm has to pay the worker higher wages in the first period (and thus, higher total wages).