1. There are three agents A. B. C and two items X.Y in an assignment problem. The agents' values are given in the following table.
|
|
X
|
Y
|
|
A
|
6.3
|
4.2
|
|
B
|
3.1
|
4.8
|
|
C
|
5.4
|
2.3
|
(a) Find all competitive equilibrium prices.
(b) What is the outcome of the ascending clock auction(formal version), assuming a sincere bidding behavior?
2. There are two firms f 1. fo and two workers ail. zr2 seeking to match in one-to-one fashion. The monetary values accruing to each party from a match is described in the next table. The first element indicates the value accruing to the firm and second element indicates the value accruing to the worker:
|
ω1
|
ω2 |
| f1 |
(50,-20) |
(60,-20) |
| f2 |
(30,-25) |
(50,-30) |
(a) Suppose there are (only) two salary levels 29 and 32 at which a firm and a worker can match. Assume that each firm's utility is given by the value of a worker hired minus a salary paid to that worker, and each worker's utility is given by the salary minus the cost (i.e., plus the value) of working for a firm. List the preference order for each party (i.e., the two workers and two firms) of alternatives in terms of (a match partner, salary). Find the outcome of the workers proposing deferred acceptance algorithm and that of the firms proposing deferred acceptance algorithm.
(b) Suppose now the feasible salary levels are 29. 32, and 40. Repeat the same exercise as (a).