Problem Set #, 1
Incentivizing Effort You are a division manager for the logging firm of Karrde Incorporated You are planning to offer a
contract to Jade Enterprises for constructing logging roads in the Myrkr Forest It is imperative that
the roads are wide enough; if the roads are wide enough, Karrdeâs profit will be 120, while it will
only be 60 if the roads are too narrow (Karrdeâs profits are 0 if it does not hire Jade) You have the
opportunity to make a take-it-or-leave-it offer to Jade, but you can not set the payment below 0 for
any outcome Whether or not the roads are wide enough depends crucially on Jadeâs effort: If Jade exerts low
effort, then the probability of success is only one third; if Jade exerts medium effort, the probability
of success is two thirds; and if Jade exerts high effort, success is guaranteed Jade Enterprises is a small concern If Jade does not take the job, its utility is 2 If Jade takes the job,
and exerts low effort, its utility is ?, where ? is the payment to Jade If Jade takes the job and
exerts medium effort, its utility is given by ? ? 1 Finally, if Jade takes the job and exerts high
effort its utility is given by ? ? 3 a) Suppose that you can observe the effort that Jade exerts, and so can write a contract where
payment is contingent on effort If you wish to incentivize low effort, what is the most
profitable contract you can offer? If you wish to incentivize medium effort, what is the most
profitable contract you can offer? If you wish to incentivize high effort, what is the most
profitable contract you can offer? Given your answers to the previous questions, which is
the most profitable contract for Karrde to offer Jade? (20 points) b) Now suppose (for the rest of this problem) you can not observe effort If you wish to write
the most profitable contract that incentivizes low effort, what contract will you write? Does
it differ from the contract for low effort in part a)? (15 points) c) If you wish to write the most profitable contract that incentivizes medium effort, what
contract will you write? How does it differ from the contract in part a) for medium effort?
(15 points) d) If you wish to write the most profitable contract that incentivizes high effort, what contract
will you write? How does it differ from the contract in part a) for high effort? (15 points) e) Consider your answers to the previous parts of this question What contract will you offer
to Jadeâthat is, what contract maximizes your profits? Does this contract incentivize the
same level of effort as the contract you offered in part a)? (10 points)
Signalling Through
Prices
Lex Chemicals has developed a new plastic usable for insulation in new homes Production costs for
the new plastic are ? = 4 per unit Demand for the insulating material is given by ? = 12 ? ?,
where ? is the price set by Lex Hence, per-period profits are given by (? ? ?)? Lex Chemicals will
have 3 periods of being the only producer of this particular type of insulation before the patent runs
out and lower cost competitors enter and take the market (For simplicity, assume no discounting of
future periods) Unfortunately for Lex, a competitor, Edge Plastics, has developed a competing product and is
considering entering the market next period The plastic develop by Edge Plastics has a production
cost of 5 There is a fixed cost of 2 for Edge Plastics to enter the market Edge, however, is uncertain of the cost structure of Lex Chemicals Edge believes there is a 50%
chance that Lex has a marginal cost of production of 8, and a 50% chance that Lex has a marginal
cost of production of 4 a) What are your per-period profits as a monopolist? What if you had the higher marginal cost
of 8? (5 points)
b) Will you attempt to signal to Edge that you are, in fact, the low cost producer? If so, what
price will you set in the first period? (20 points)