第 1 页 共 4 页
Tutor: Cheney Wan
Date: 06/11/2023
UNSW ECON3123 Organisational Economics
Problem set 4
第 2 页 共 4 页
Problem set 4
Question 1
In this question, we will consider a version of the asset ownership model where the (S)upplier makes a
cost-saving investment that does not directly increase the final value V.
As usual, there is a (S)eller and a (B)uyer. B needs a widget for production. If production is successful, then
total value is . The widget requires an asset to produce; B but S not can use the asset to
make the widget noncooperatively, so and . Further, assume that ;
the party without the asset cannot create any value noncooperatively.
S chooses investment e at cost . B chooses investment E at cost . That is, a larger
investment by S reduces the cost of investment for B. Suppose V=E; so B’s investment directly affects the
value of the transaction.
The game proceeds as usual:
1. Ownership of the machine is allocated.
2. S chooses e.
3. B chooses E.
4. B and S bargain.
5. B and S receive their payoffs.
a) Calculate each player’s outside option and , as well as the bargaining surplus, under
B-ownership.
计算双方的外部得益，以及协商盈余（资产在 B手上）
外部得益等于回报减去成本
协商盈余等于总回报减去双方的外部得益
b) Calculate each player’s outside option and , as well as the bargaining surplus, under
S-ownership.
同 a问，只是资产在 S手上
c) Under B-ownership, calculate B’s investment E choice given e. Then, calculate the equilibrium investments
e∗ and E∗ .
注意此时是算 B和 S的得益，而非外部得益，这两者的分析我们正课上说过了，实际上得益和外部得益
是有重合的地方的，按照纳什均衡，得益等于外部得益加上一半的最终盈余
d) Under S-ownership, calculate B’s investment E choice given e. Then, calculate the equilibrium investments
e∗ and E∗ .
同 C问
e) Compare total utility under B-ownership versus S-ownership.
计算资产分别在 B和 S手上时的总得益
f ) Explain, in words, why S-ownership is optimal even though only B’s investment directly affects the total
value V.
第 3 页 共 4 页
为什么在 B投资直接影响总价值的情况下，资产在 S手上为最佳，此时分析紧抓住 B的成本项进行分析，
总成本会因为双方的投资程度而变小
Question 2
We’ll consider the two-period career incentives model from lecture, and add the following feature: the
worker retires with some fixed probability at the end of the first period.
There are two tasks, one in period t=1 and one in period t=2, to be performed by a worker in a firm. In each
period, the worker chooses whether to work ( ) or shirk ( ). Working costs c for the worker in
each period. If the worker shirks in period t, he is caught with probability 0 ≤q≤1 . If caught shirking, the
worker is fired immediately and receives zero wages in that period. Otherwise, he receives a bonus for that
period.
At the end of the first period, the worker retires with fixed probability 0 hires a replacement worker for period 2.
The worker seeks to maximize his wages minus his effort costs in both
periods: + , where and for him if he retires at the
end of period 1. (Correspondingly, the replacement worker seeks to maximize his wages minus his effort costs
in the second period: .
The firm seeks to minimize wages while inducing the worker / replacement worker to choose
and .
The timing is as follows:
Step 1: The firm chooses bonus levels and .
Step 2: In the first period:
(a) the worker chooses effort and incurs cost .
(b) If the worker shirked ( ), he is caught with probability q and fired, so he receives .
Otherwise, he is paid bonus .
(c) The worker retires with probability r, in which case a replacement worker is hired.
Step 3: In the second period:
(a) the worker / replacement chooses effort and incurs cost .
(b) If the worker / replacement shirked ( ), he is caught with probability q and fired, so he
receives . Otherwise, he is paid bonus .
第 4 页 共 4 页
We’ll go through the problem set-by-step.
a) Write down the condition on that ensures the worker/replacement will choose .
分别分析有偷懒和没有偷懒的工人回报是多少，对企业来说确保工人选择不偷懒的条件就是不偷懒的总
回报大于偷懒的总回报
b) Suppose that the condition you specified in (a) is satisfied. Write down the condition on and
that ensures the worker will choose . Your answer should take the following form:
+ (1 −r) ≥ (… ).
同 a，只是注意 t2回报有了变化，因为需要假设第一阶段没有退休的概率
c) Add to both sides of your answer to (b). You should now have an inequality that takes the following
form: . This expression replaces your answer to (b); combined with your
answer to (a), it specifies conditions which and must satisfy to ensure and .
第三问是单独问，不涉及我们后面两问的作答，只是在 b问的答案上简化，不等式左右两边同时加上 c
问给的条件即可
d) What is the firm’s optimal choice of and ? What is the corresponding total wage
?
How does this answer change with the retirement rate r?
最佳选择就是让工人不偷懒，所以直接取 a问和 b问的答案即可，然后加和，就是企业的最小工资，看
此时这个最小工资的等式怎样随着退休率变化，分析部分我们 week8的内容里会讲，此处其实为劳动经
济学的内容，通过工资支付时间的不同来激励员工
e) Explain, in words, why total wages increase as the retirement rate r increases.
d问已经分析，只不过 d问只是答案