COS2040代写、代写Python/java程序

日期：2023-04-01 07:55

COS2040 Intermediate Financial Economics

Assignment 1

Submit your work online in Canvas by 23:59 on Friday 31 March. Show all working, and explain all

reasoning, but limit your answers to a strict maximum of three pages (neatly handwritten, or typed

with one-and-a-half line spacing).

Andrew is a political consultant to the Green party. At the next election, there are two

possible outcomes. Either the Blue party will win an outright majority (call this state B),

or else the Green and Red parties will form a coalition (call this state G). In the event of

state B Andrew will earn a salary of 20, while in the event of state G his salary will be 65.

Andrew discovers that a bookmaker will allow him to place bets on a victory by the Blue

party. For every dollar that Andrew bets on a Blue victory, the bookmaker will pay him

three dollars, less the dollar that he bet, in the event of state B. However in the event of

state G, the bookmaker pays nothing and Andrew simply forfeits the dollar that he bet.

Andrew’s income consists of his salary in the relevant state, plus or minus his gains or

losses from betting. Let xB denote his income in the event of state B, and let xG denote

his income in the event of state G. Let q denote the size of the bet that he places.

(a) Write down expressions for xB and xG as functions of q. Hence derive the equation

of Andrew’s budget constraint, and an expression for its slope in the form dxG/dxB.

(3 marks.)

(b) How much would Andrew bet if he wanted to achieve complete certainty in his

income? What would his resulting income be both states? (2 marks.)

(c) Suppose that the bookmaker is risk neutral, has no administrative costs of taking

bets, and expects on average that it will break even on the bet that it offers to An-

drew. What is the probability with which the bookmaker believes that the Blue

party will win the election? (1 mark.)

(d) Given his inside political knowledge, Andrew believes the probability of a Blue

victory is π = 12 . His utility function over income is v (x) =

√

x, and he chooses q to

maximise expected utility given π = 12 . Find his optimal bundle of state-contingent

payoffs (xB, xG). (Hint: Either write a tangency condition stating that the ratio of expected

marginal utilities equals the slope of the budget constraint in (a), or use calculus to maximise

expected utility with respect to q.) To attain this, how many dollars q should he bet?

What is his resulting expected utility, and how does it compare to his utility under

the solution in (b)? Provide economic intuition for your results. (4 marks.)