ECOS3003代写、代写c/c++，Python程序

日期：2022-10-23 02:54

Problem set ECOS3003

Due date 27 Oct 2022 9am

Please keep your answers brief and concise. Excessively long and irrelevant answers will be

penalised. You can either type or neatly handwrite your answers.

Summit your answers in ONE file under PDF or Word format through the submission portal

on Canvas. Any late submission will incur a 5% penalty per day.

There are 5 short-answer problems. Total mark is 48. The problem set is worth 15% of

your final grade.

Question 1 (8 marks)

Consider the following simultaneous game (A) in normal form:

a) Calculate all the Nash equilibria of A. (4 marks)

Now consider the following game (B):

b) Do games A and B have the same Nash equilibrium/equilibria? Why or why not? (4

marks)

Question 2 (7 marks)

Tanya is an owner of Invest Co. Her utility of wealth is given by U(W) = W2 where W is her

wealth level. Tanya has been sponsored $M to invest in two potential investment projects (M

is an amount of money and simply disappears if it is not invested in a project). Investment A

pays $16 per dollar of investment or $0 with a 50% chance each. Investment B pays $9 per

dollar of investment with probability 2/3 or $0 with probability of 1/3. Which proportion of M

does Tanya want to invest in A? Explain your answer in reference to risk aversity discussed in

class. (7 marks)

Question 3 (10 marks)

DrugCo buys an input that costs $p from the market for its drug production. DrugCo knows

that 4/5 of suppliers will provide a good input that the firm can use to produce $100 value of

output and 1/5 of suppliers will provide a low quantity input that produces $60 value for the

firm. The firm is matched with a potential input supplier in the market, but cannot tell whether

it will supply a good or low quality product.

a. If DrugCo does not buy the input from the market, no production will occur. What is the

maximum price p that DrugCo is willing to pay for the input? Show your working. (2 marks)

b. Assume now that DrugCo can also buy the same input from its long-term trading partner -

Compound Corp at a price c. Compound Corp is supplying a good input for sure. What is the

most the firm is willing to pay to Compound Corp for the input if the input costs $20 from the

market? Show your working. (2 marks)

Now assume that Compound Corp can choose to supply a good input or a low-quality input.

The cost of producing a good input is $10 and that of producing a low-quality input is $5.

DrugCo will pay $25 to buy the input from Compound Corp.

c. If there are two years in which trade can occur, will Compound Corp supply a good input or

a low-quality input in the first period? In the second period? Explain your answer. (2 marks)

d. Will DrugCo sign a 2-year contract with Compound Corp or buy from the market? Explain

your answer. (2 marks)

e. Now trade can occur potentially an infinite number of times. DrugCo adopts a trigger-

strategy if Compound Corp ever supplies low-quality inputs. Both parties have a discount

factor of δ. For what value of δ will Compound Corp always supply good inputs? (2 marks)

Question 4 (8 marks)

A principal has to implement a decision that has to be a number between 0 and 1; that is, a

decision d needs to be implemented where 0 1d? ? . The difficulty for the principal is that she

does not know what decision is appropriate given the current state of the economy, but she

would like to implement a decision that exactly equals what is required given the state of the

economy. In other words, if the economy is in state s (where 0 1s? ? ) the principal would

like to implement a decision d = s as the principal’s utility Up (or loss from the maximum

possible profit) is given by = ?( ? )

2. With such a utility function, maximising utility

really means making the loss as small as possible. For simplicity, the two possible levels of s

are 0.5 and 0.8 which occur with probability 0.4 and 0.6 respectively.

There are two division managers A and B who each have their own biases. Manager A always

wants a decision of 0.3 to be implemented and incurs a disutility = (0.3 )

2. Similarly,

Manager B always wants a decision of 0.8 to be implemented and incurs a disutility =

(0.8 )2. Each manager is completely informed, so that each of them knows exactly what

the state of the economy s is.

a) The principal can opt to centralise the decision but before making her decision – given

she does not know what the state of the economy is – she asks for recommendations

from her two division managers. Centralisation means that the principal commits to

implement a decision that is the average of the two recommendations she received from

her managers. The recommendations are sent simultaneously and cannot be less than 0

or greater than 1.

Assume that the state of the economy s = 0.8. What is the report (or recommendation)

that Manager A will send if Manager B always truthfully reports s? Explain your

answer. (4 marks)

b) What if the principal instead delegates decision-making entirely to manager A (that is,

A can decide on her own d without any consultation). Does this make the principal

better or worse off than with centralisation as in part a? Provide some intuition for your

answer. (4 marks)

Question 5 (8 marks)

Consider the following workplace situation. A boss can implement an incentive scheme (I) or

not (NI). Following observing this a worker can work hard (H) or slack (S). The payoffs are as

follows. If I and H are chosen by the boss and worker, respectively, the payoffs are 25 to the

boss and 9 to the worker. If I is chosen by the boss, then L by the worker the payoffs are 12 to

the boss and 5 to the worker. If the choices are NI then H, the returns are 30 and 7 to the boss

and worker respectively. Finally following NI and L the payoffs are 17 (boss) and 11 (worker)

a) What is the subgame equilibrium of the game? Explain your answer in the context of

the principal-agent incentive contracts. (3 marks)

b) Now assume that the worker, through their union workplace agreement has a veto right

on any incentive scheme, and there is no incentive scheme currently in place. The boss

P a g e 5 | 5

and the worker can negotiate to allow for incentive scheme to be legally implemented

(and compensation/side payments can be made as part of this agreement). If the worker

has all of the bargaining power during these negotiations, will the incentive scheme be

implemented? Is the outcome surplus-maximising? Explain your answer in the context

of the value-maximisation principle? (5 marks)

Question 6 (7 marks)

Consider a version of the property‐right model studied in class involving a buyer (Simon) and

a seller (Jonny). The timing of the game is as follows. Initially the parties cannot write a

contract on investment or on sharing surplus. At this point, Jonny can make an investment that

costs either $50 (low investment) or $300 (high investment). This investment is sunk and

specific to trading with Simon. After the investment has been sunk, and contracting becomes

possible, so the parties negotiate. The ex post surplus generated is either $200 with low

investment or $500 if Jonny made a high investment. Trade occurs (or does not) between the

two parties and the game ends.

a) Draw a timeline of the game. What is the ex‐ante period and the ex‐post period in this

model? (1 mark)

b) What is the first‐best level of investment? Explain. (2 marks)

c) Now assume that property rights can be assigned to either party of an asset critical to

this production process. If Simon owns the asset he will receive 50% of the ex post

surplus. If Jonny owns the asset he will receive 90% of the ex post surplus. In this

incomplete contracting environment, who should own the asset? Explain your answer

in the context of the key predictions of the property‐rights model. (4 marks)