The answer is option B (p, q) = (2/3, 1/3)..
The Nash equilibrium is for Mimi to not support and Jeff to look for work. Determine the pure-strategy Nash equilibrium for this game.
Mimi and Jeff's payoff matrix is given below:
Support Mimi
No Support
Jeff Looks for Work0,00,100,-1
Jeff Loafs-10,0-5,-2
The Nash equilibrium is for Mimi to not support and Jeff to look for work. This is because this is the only point where both players are maximizing their payoffs. In this scenario, Mimi's payoff is -5 which is the highest value for Mimi if Jeff looks for work. Jeff's payoff is -1 which is the highest value for Jeff if Mimi does not support him. Hence, the answer is option B.
The mixed-strategy Nash equilibrium is for Mimi to support with probability and for Jeff to look for work with probability 0,-.To determine the mixed strategy Nash equilibrium, we need to compare the expected payoff when both players select their strategies randomly.
Mimi supports Jeff with probability p and does not support him with probability 1-p. Jeff looks for work with probability q and loafs with probability 1-q.
The expected payoffs for Mimi and Jeff are given by:
EM = -5p + (1-p)qEJ = -1q + (1-q)2p
The Nash equilibrium is found when both players maximize their payoffs simultaneously. Setting the derivatives of EM and EJ to zero, we obtain:
p = 2/3 and q = 1/3
The mixed-strategy Nash equilibrium is for Mimi to support with probability 2/3 and for Jeff to look for work with probability 1/3. Therefore, the answer is (p, q) = (2/3, 1/3).
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You are told that if you invest $11,000 per year for 23 years( all payments made at the end of each year) you will have accumulated $366,000 at the end of the period What annual rate of return is the investment offering.
Answer:
3.2%
Explanation:
this is an ordinary annuity:
future value of an ordinary annuity = annual payment x future value annuity factor
$366,000 = $11,000 x future value annuity factor
future value annuity factor = $366,000 / $11,000 = 33.2727
you can solve this in two ways:
the first is with a lot of math work in order to solve the following equation
33.2727 = [(1 + i)²³ - 1] / i
or
you can use an annuity calculator (available online) which will yield 3.2%
Close enough is good enough best characterizes which model of decision making?a. Rational model b. Satisficing model c. Incremental model d. Intuitive model
The model of decision making that is best characterized by the phrase "close enough is good enough" is the satisficing model.
So, the correct answer is B.
What's satisficing model?This model proposes that individuals make decisions by searching for options until they find one that meets their minimum requirements or thresholds. They then choose that option even if it is not the optimal or best choice.
The satisficing model contrasts with the rational model, which assumes individuals make decisions based on a thorough analysis of all available options to choose the best outcome.
The incremental model suggests that individuals make decisions based on small adjustments and improvements over time.
Finally, the intuitive model proposes that individuals make decisions based on their instincts and experiences.
Overall, the satisficing model recognizes that individuals often make decisions in a complex and uncertain environment where perfect information is not always available.
Hence, the answer of the question is B.
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Eric has decided to invest small amounts in bonds over time. This rules out purchasing a single bond. He is seeking a bond mutual fund with a yield over 4%. Which fund would you recommend?
Mutual fund name:
Ticker symbol:
Mutual fund objective:
Expense ratio:
Minimum investment:
Minimum additional investment:
Yield:
Eric has decided to invest small amounts in bonds over time. This rules out purchasing a single bond. He is seeking a bond mutual fund with a yield over 4%. Yield, fund would be recommended.
What is bonds?
Bonds are issued by governments and corporations when they want to raise money. By buying a bond, you're giving the issuer a loan, and they agree to pay you back the face value of the loan on a specific date, and to pay you periodic interest payments along the way, usually twice a year.
Bonds yield income, are think over little riskier than working capital and can help change portfolios. The first is to hold those bonds yield until their maturity date and accumulate interest commences on them. Bonds, in general, are less risky and more buttoned-up than frameworks in yield.
As a result, the significance of the bonds yield to invest small amounts in bonds over time are the aforementioned.
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Tax Structure 1
Family
A
B
C
Income
$10,000
$50,000
$100,000
Tax amount
2,000
2,000
2,000
% of income paid as
tax
[a]
[b]
[C]
The percentage of income paid as tax for A is 20%.
The percentage of income paid as tax for B is 4%.
The percentage of income paid as tax for C is 2%.
What is tax?A tax is a mandatory financial charge or some other type of levy imposed on a taxpayer (an individual or legal entity) by a governmental organization in order to fund government spending and various public expenditures (regional, local, or national).
The percentage of income paid as tax for A is:
= 2000/10000 × 100
= 20%.
The percentage of income paid as tax for B is 4%.
The percentage of income paid as tax for C is 2%.
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Given the following: lifo method 250 units left in inventory beginning inventory 200 units at $6 $1,200 purchases: april 10 400 units at $7 $2,800 may 15 250 units at $7 $1,600 july 9 200 units at $8 $1,600 october 8 100 units at $11 $1,100 the cost of ending inventory is: multiple choice $1,550 $2,300 $1,200 $3,200
The cost of ending inventory is $1550 using the last in first out method.
"Last-In, First-Out" is an abbreviation for LIFO. It is a method for computing the cost of products sold that supports the cost flow hypotheses. The premise of the LIFO technique is that the most recent things added to a company's inventory have already been sold.
Using the LIFO method, we have to calculate the cost of ending inventory.
First inventory units was 200, at the cost of $6.
200*$6=$1200
The next set of units purchased is at the cost of $7 per unit, we are left with 250 units, so we take the 50 units from the second set of the purchase.
50*$7=$350
So the value of the $1200+$350=$1550.
Therefore, the value of the ending inventory is $1550.
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Question 1 of 10
Why do managers care about soft skills when hiring for a technical job?
A. They want to know that the applicant will enjoy corporate events
and activities.
B. They want to be sure the applicant will be able to complete the
assigned tasks.
C. They want to be sure the applicant has no outside interests that
will interfere with work.
D. They want to be sure the applicant can collaborate and work well
with other team members.
D. They want to be sure the applicant can collaborate and work well
with other team members.
Explanation:
Managers do care about soft skills when hiring for a technical job as they want to be sure the applicant can collaborate and work well with other team members. The correct option is d.
What is a technical job?Technical jobs are those that require specific talents and expertise an individual possesses that help them perform a certain task or job. These skills differ from soft skills, which instead describe character and personality traits.
Technical skills are abilities an individual acquires through practice and learning, although a person may bring an inherent propensity for a certain skill. An individual who possesses a particular proficiency for coding, for instance, would have a sought-after technical skill as a job candidate at a software or technology company. Technical job skills are ideal to list on the skill section of a resume because they shine a light on abilities and strengths.
However, it is important to realize not all technical skills at an individual’s disposal should be listed.
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A private pilot wishes to insure his airplane for $200,000. The insurance company estimates that a total loss will occur with probability .002, a 50% loss with probability .01, and a 25% loss with probability .1. Ignoring all other partial losses, what premium should the insurance company charge each year to realize an average profit of $500?
The insurance company should charge an annual premium of $2,520 to realize an average profit of $500.
To determine the premium that the insurance company should charge, we need to calculate the expected value of the losses and add the desired profit margin.
Given that the private pilot wishes to insure the airplane for $200,000, and the insurance company estimates the probabilities of different loss scenarios, we can calculate the expected value of the losses.
The expected value of a loss is calculated by multiplying the loss amount by its corresponding probability and summing up all the expected losses.
Expected Loss = (Loss Amount) * (Probability)
Total Expected Loss = (0.002 * 200,000) + (0.01 * 0.5 * 200,000) + (0.1 * 0.25 * 200,000)
= 400 + 1,000 + 5,000
= 6,400
To realize an average profit of $500, the insurance company should charge a premium that covers this expected loss and includes the desired profit margin.
Premium = Expected Loss + Desired Profit
= 6,400 + 500
= 6,900
Therefore, the insurance company should charge an annual premium of $6,900 to achieve an average profit of $500.
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Question 17 of 20
Trey's bank raises the interest rate on his line of credit without providing an
explanation. Which consumer protection law has his bank violated?
Trey's bank raises the interest rate on his line of credit without providing an
explanation. The consumer protection law that his bank violated is: "The Truth in Lending Act of 1968".
What are consumer protection laws?The Truth in Lending Act of 1968 is a federal law in the United States aiming to encourage the informed use of consumer credit by requiring disclosures about its terms and prices to standardize the method in which borrowing expenses are computed and communicated.
Consumer protection laws protect consumers from faulty products and deceptive or fraudulent company activities.
It is to be noted that in the United States, a range of federal and state laws govern consumer affairs. The Federal Food, Drug, and Cosmetic Act, the Fair Debt Collection Practices Act, the Fair Credit Reporting Act, the Truth in Lending Act, the Fair Credit Billing Act, and the Gramm-Leach-Bliley Act are a few examples.
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Answer:
Credit Card Accountability, Responsability, and Disclosure Act
Explanation:
Which of the following team members would not be involved in the design of gameplay?
Consider the attached table which gives labor requirement coefficients used in the production of any and Cares for Home and foreign countries. Based on the white trade patterns for the Home and Foreign country Country Labor Coeniciant Laborcon for Candy for Cake Houl 3 origen a Foreign will export Candy and import cake Ob Foreign will export cake and import candy Oc Home will export candy and import cake d. Home will export cake and import candy e Both (a) and (d) are true
Based on the given information and trade patterns, the correct option is E - Both (a) and (d) are true. This means that both the foreign country will export candy and import cake (Option a) and the home country will export cake and import candy (Option d).
According to the labor requirement coefficients, the foreign country has a lower labor coefficient for candy production compared to the home country. This indicates that the foreign country has a comparative advantage in candy production and is likely to export candy. On the other hand, the home country has a lower labor coefficient for cake production, suggesting a comparative advantage in cake production and a likelihood of exporting cake.
Based on these comparative advantages, the trade patterns emerge. The foreign country will export candy (Option a) and import cake, while the home country will export cake (Option d) and import candy. This reflects the principle of comparative advantage, where countries specialize in producing goods in which they have a lower opportunity cost, resulting in mutually beneficial trade.
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A company has filed a registration statement with the SEC that uses a method that is only available to seasoned issuers. This registration statement is good for:
A company that filed a registration statement with the SEC, which uses method that is only available to seasoned issuers is valid for 3 years.
What is securities and exchange commission (SEC)?Securities and exchange commission refers to a government agency that is responsible for enforcing laws at the federal level inorder to protect Americas who deals in securities market.
This government agency protects:
Investors, Provides dataRegulates the marketFacilitate capital formation.Hence, a company who filed a registration statement with the SEC that uses a method that is only available to seasoned issuers. This registration statement is good for 3 years
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Clabber Company has bonds outstanding with a par value of $122,000 and a carrying value of $110,500. If the company calls these bonds at a price of $106,000, the gain or loss on retirement is:
Clabber Girl Corporation grew from the original business that was incorporated over 150 years ago. Hulman & Company began in Terre Haute, Indiana, in early 1850. Originally a wholesale grocery store, the business expanded into manufacturing with the addition of a storeroom and spice mill behind the store in 1869.
The company continued to expand and, by 1879, was manufacturing a variety of products, including spices, coffee, and baking powder, under many different brand names. By 1899, Clabber brand baking powder was introduced, and today the Clabber Girl brand, as renamed in 1923, is distributed nationwide and to many different countries around the world.
The gain or loss on retirement of the bonds can be calculated by comparing the carrying value (also known as book value) of the bonds with the price at which they are called (also known as the call price). In this case, the carrying value of the bonds is $110,500, and the call price is $106,000.
To calculate the gain or loss, subtract the call price from the carrying value.
$110,500 minus $106,000 = $4,500.
Since the carrying value is higher than the call price, there will be a loss on retirement of $4,500.
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What step of the bulletproof problem-solving process helps avoid making common decision-making biases such as confirmation bias?
Create a schedule and work plan in step four. This stage forces the issue solver to create a strategy that considers a variety of viewpoints and answers, which helps to avoid common decision-making biases like confirmation bias.
What are biases in decision-making?Cognitive mistakes known as decision-making biases produce irrational decisions. These biases can be brought on by a number of things, including the availability heuristic, which occurs when people base their decisions on the information that is most easily accessible, confirmation bias, which occurs when people only take into account evidence that confirms their beliefs, and anchoring bias, which occurs when people rely excessively on initial information.
This makes it more likely that the person solving the problem will take other viewpoints and potential solutions into account in addition to their own biases.
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2. In what type of organization is the functional manager likely to maintain project budget control? A. Weak matrix B. Balanced matrix C. Strong matrix D. Projectized
A. Weak Matrix. In a weak matrix organization, the functional manager generally has more authority and control over resources and budget, while the project manager has limited authority.
Weak matrices have been described by project managers as one in which the balance of power is critically tilted in the direction of line or function management.The shortcomings of matrix organizational structures divide loyalty among project teams. A blurry line of accountability.
Difficulty coordinating tasks and functions. Power struggle between project manager and feature manager. Deficiencies in functional organizational structures. This can lead to poor communication and independent silos. Teamwork and coordination are lacking when employees and managers are simply loyal to the team.
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what types of actions can be taken by the nlrb in response to an unfair labor practice? check all that apply.
Issue a notice to stop and comply. Order the workers' reinstatement.
In the workplace, what does it mean to be reinstated?An employee with a Mandatory Reinstatement right can return to their previous position with all of their rights and status as before they left.
When an employee is reinstated, what happens?According to case law, the simplest definition of reinstatement is "to put an employee in the same position he or she was in before being dismissed." This indicates that the worker will be reinstated with the same terms and conditions as if the dismissal had never occurred.
Can a worker fired be reinstated?The employer should immediately reinstate the employee if the initial decision to dismiss the employee as a result of a disciplinary procedure is overturned as a result of an appeal. In place of the initial decision to fire the employee, the employer may choose to impose a lesser punishment.
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Full Question = What types of actions can be taken by the NLRB in response to an unfair labor practice? Check all that apply.
Multiple select question.
Organize a labor strike or labor reduction.
Issue a cease-and-desist order.
Demand a higher wage.
Order a reinstatement of workers.
what are the factor that you need to answer your and selective attention invertors?.elaborate your answer...
links are not allowed
How do you approach Marketing design for a production?
a firm acquired an assset on 1st Apri, 1990 at a cost of Le 30,000. The useful life of the asset is expected to be 10 years. The estimated scrap value of the asset at the end of the year is Le 2,000. Show the provision for depreciation account for the first 3 years in the life of the asset using the Straight line method
Answer:
First year : Le 2100
Second year : Le 2800
Third year : Le 2800
Explanation:
Given the following :
Cost of equipment = 30,000
Useful years = 10
Salvage or scrap value = 2,000
depreciation account for the first 3 years in the life of the asset using the Straight line method :
Straight line Depreciation :
(Cost - salvage value) / useful years
First year: (April - December 1990)
April - December 1990 = 9 months
(30,000 - 2000) / 10 × 9/12
28000 / 10 × 0.75 = Le 2100
Second year:
(30,000 - 2000) / 10 × 12/12
28000/ 10 = Le 2800
Third year:
(30,000 - 2000) / 10 × 12/12
28000/ 10 = Le 2800
What is a “work point”?
Answer:
A work point is an independent entity whose location is defined in space.
Explanation:
Work points may be placed or projected onto part faces, linear edges, or onto an arc or circle. Work points can be constrained to the center points of arcs, circles, and ellipses.
what is the difference between covalent bonds and ionic bonds?
Answer:
Covalent bonding: is sharing an amount of e between two atoms.
ionic bonding: A type of chemical bonding that involves the electrostatic attraction between oppositely charged ions.
After asking coworkers to review a project plan, you receive feedback. Your coworker thinks there is a better way to display the data in the business report.You should add a
title
reference
abstract
table
Answer:
table
Explanation:
you are given a confidence interval for the population mean(µ) is 26 to 42. the sample mean used the construct this confidence interval was 34.
If the confidence interval for the population mean (µ) is 26 to 42, and the sample mean used to construct this confidence interval was 34, it suggests that the sample mean of 34 is a reasonable estimate for the population mean.
A confidence interval provides a range of values within which the true population mean is likely to fall. In this case, the confidence interval of 26 to 42 implies that we are 95% confident that the population mean falls within this range.
Since the sample mean of 34 falls within the confidence interval, it indicates that the sample mean is a plausible estimate for the population means. However, it is important to note that the confidence interval provides a range of values, and the true population mean could still be any value within that range. The sample mean serves as a point estimate, providing an estimate of the population mean based on the available data.
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A share of ownership in a company is known as which of the following?
А.Stock
B.Investment
с.Rebate
D.Bond
Answer:
Stock
Explanation:
The worth of a company is subdivided into small units known as shares. Each unit of a share represents the ownership of the company. The owners of the shares are described shareholders, and they are the owners of the company.
The term share is, at times, substituted with stock or equity. In ownership of a company, stock, shares, and equity will refer to the same things. Shareholders are also then referred to as stockholders.
Logan, Inc. Held 500 shares of treasury stock with a cost of $10 per share. In December, Logan sold 10 shares at $20 per share. The journal entry to record the sale of treasury stock using the cost method would include a (debit/credit) ________ to Treasury Stock in the amount of ________.
Answer:
Credit to treasury stock for $200
Explanation:
Based on the information given The Appropriate journal entry to record the sale of treasury stock would include CREDIT to treasury stock in the amount of $200
CREDIT to treasury stock $200
(10 shares at $20 per share)
(To record the sale of treasury stock)
arla and wendy are highline college legal studies students. they both graduate and decide to form family and immigration services, llc (fis). fis is a washington state llc that focuses on advising on immigration and family law issues. fis grows to include a staff of thirty employees. after only one year of business, fis has several clients and tripled its projected revenue. a large seattle-based law firm retains them to help grow their immigration practice. as a result of this success, fis needs to double the number of its employees to fulfill their contracts. (1) is fis subject to federal anti-discrimination laws? (2) if so, what should it consider in hiring new employees?
Yes, Family and Immigration Services, LLC (FIS) is subject to federal anti-discrimination laws. When hiring new employees, FIS should consider several factors to ensure compliance with federal anti-discrimination laws:
a. Equal Employment Opportunity: FIS must provide equal employment opportunities to all individuals, without discrimination based on protected characteristics.
They should establish fair and unbiased hiring practices and ensure that their selection criteria are job-related and non-discriminatory.
b. Non-Discriminatory Job Advertisements: FIS should ensure that their job advertisements do not contain language or requirements that discriminate against individuals based on protected characteristics.
They should focus on the qualifications and skills required for the position rather than personal attributes.
c. Fair Interview and Selection Process: FIS should conduct interviews and make hiring decisions based on the candidate's qualifications and abilities relevant to the job.
They should avoid asking questions or making decisions based on protected characteristics.
d. Reasonable Accommodations: FIS should be prepared to provide reasonable accommodations to qualified individuals with disabilities during the hiring process, as required by the ADA.
This includes making necessary adjustments to the application process or job requirements, unless it causes undue hardship.
e. Age Discrimination: When hiring new employees, FIS should also consider the ADEA, which protects individuals aged 40 and above from age discrimination.
They should avoid age-related biases and base hiring decisions solely on a candidate's qualifications and abilities.
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Which of the following choices is associated with socialism?
Karl Mars
free market
private ownership of property
Adam Smith
Answer:
Karl Mars
Explanation:
Socialism can be defined as an economic, social and political theory which asserts that the method of exchange, distribution, as well as the means of production of goods and services and ownership of properties should be controlled or regulated by the public (government) rather than the private sector. Thus, everyone living in the society has an equal share of the means of production used in producing the goods and services.
Under socialism, key industries are owned or controlled by the government. Some examples of socialist countries are Vietnam, Cuba, China, etc.
Karl Marx was a German sociologist, economist, philosopher, historian, author and political theorist. Marx was born on the 5th of May, 1818 in Trier, Germany and is famously known for his works on communism, socialism, and capitalism.
Karl Mars is the option which is associated with socialism because he believed all of human history was a struggle between rich and poor.
Why is organic manure used in soil? Explain briefly.
Explanation:
the supply plant nutrients including micronutrients they improve soil physical properties like structure of water holding capacity etc. they increase the availability of nutrients.
In class, Marcus is skilled at picking up main ideas and important details from his teachers' lectures. What is this called?
Answer:
This would observation, which is something most readers should be able to do
Explanation:
The third set of digits (two numbers) in a national drug code represents:______
a. the product strength and dosage form
b. the manufacturer
c. the cost
d. the pack size
The third set of digits (two numbers) in a national drug code represents the "pack size." Correct option is d. the pack size.
The national drug code (NDC) is a unique identifier assigned to each drug product in the United States. It consists of three sets of numbers that convey different pieces of information about the drug. The third set, which consists of two numbers, indicates the pack size of the drug.
The pack size refers to the quantity of the drug contained in a specific package or container. It represents the number of individual units, such as tablets, capsules, vials, or bottles, that are included in a single package available for purchase. The pack size information is essential for inventory management, tracking, and prescribing purposes.
For example, if the pack size is "10," it means that the package contains 10 individual units of the drug. This information helps pharmacists, healthcare providers, and consumers determine the appropriate quantity to dispense, prescribe, or purchase.
It is important to note that the product strength and dosage form, manufacturer, and cost are represented by other sets of digits in the NDC, not the third set.
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Uncertainty and International Financial Markets
Answer all parts (a)-(f) of this question.
Consider an endowment model with two periods t = 1, 2 and two countries, Home and For-
eign. Variables belonging to the Foreign country are denoted by a hat. Date 1 output in Home
and Foreign are denoted Y1 and Yb1 respectively. At date 2, there are two different states of
nature, denoted by s ∈ {1, 2}. State s occurs with probability π(s). Home output in state s
at date 2 is denoted by Y2(s) and Foreign output by Yb2(s). At date 1, countries can trade in
Arrow-Debreu (A-D) securities for each state. An A-D security for state s pays out one unit if
state s occurs and nothing otherwise. Denote p(s)
1 + r
as the price of an A-D security for state
s expressed in terms of date 1 consumption. Countries can also trade a riskfree asset whose
(gross) interest rate is denoted by 1 + r. Lifetime utility of the representative household in
both countries is given by
U = ln(C1) + βE[ln(C2(s))]
where β ∈ (0, 1) is a discount factor, C1 denotes consumption at date 1, and C2(s) denotes
consumption at date 2 in state s. The intertemporal budget constraint of the representative
household in Home (analogous for Foreign) is given by:
Y1 +
p(1)Y2(1) + p(2)Y2(2)
1 + r
= C1 +
p(1)C2(1) + p(2)C2(2)
1 + r
(a) [6 marks] Give an economic interpretation of the intertemporal budget constraint. Would
the intertemporal budget constraint look the same if there were just one riskfree asset
available to trade and no A-D securities? Explain.
(b) [7 marks] Explain why it must be the case that p(1) + p(2) = 1.
(c) [12 marks] Derive the first-order conditions for utility maximization of the representative
household in the Home country. Show that in optimum:
C2(2)
C2(1) =
p(1)
p(2)
π(2)
π(1)
(d) [5 marks] Explain why, in a global equilibrium, it must hold that:
C1 + Cb2 = Y1 + Yb1
C2(s) + Cb2(s) = Y2(s) + Yb2(s) for s=1,2
(e) [12 marks] Let x > 0 and suppose output levels at date 2 are given by:
state s=1: Y2(1) = 1 + x and Yb2(1) = 1 − x
state s=2: Y2(2) = 1 − 2x and Yb2(2) = 1 + 2x
Derive equilibrium (relative) price of A-D securities p(1)
p(2) in a global equilibrium. What
does your result imply about optimal consumption levels at date 2 in each country?
(f) [8 marks] Suppose output levels are the same as in (e) except that Yb2(2) = 1 + x. Will
equilibrium prices of A-D securities be actuarially fair? Explain.
(a) The intertemporal budget constraint represents the equality between the total resources available to the representative household at date 1 and the total consumption and investment decisions made by the household across time.
It states that the sum of the initial endowment (Y1) and the present value of future consumption and investment must equal the sum of current consumption (C1) and the present value of future consumption (C2(s)) discounted at the risk-free interest rate (1 + r). This constraint ensures that the household's consumption and investment choices are consistent with the resources available to them over time.
If there were only one risk-free asset available and no Arrow-Debreu securities, the intertemporal budget constraint would still hold. In this case, the present value of future consumption would be discounted using the risk-free interest rate, and the household's consumption and investment decisions would still need to be consistent with the available resources.
(b) The sum of the prices of the Arrow-Debreu securities for each state must equal 1 because these prices represent the probabilities of each state occurring. Since the states are mutually exclusive and exhaustive (i.e., they cover all possible outcomes), the probabilities of the states occurring must sum to 1.
(c) To derive the first-order conditions for utility maximization, we need to maximize the representative household's utility function subject to the intertemporal budget constraint. The Lagrangian for this problem is:
L = ln(C1) + βE[ln(C2(s))] - λ[(Y1 + p(1)Y2(1) + p(2)Y2(2))/(1 + r) - (C1 + p(1)C2(1) + p(2)C2(2))/(1 + r)]
Taking partial derivatives with respect to C2(1) and C2(2) and setting them equal to zero, we can solve for the optimal consumption ratios:
C2(2)/C2(1) = p(1)/p(2) * π(2)/π(1)
This equation shows that the optimal consumption ratio between date 2 states depends on the relative prices of the Arrow-Debreu securities and the relative probabilities of the states.
(d) In a global equilibrium, total consumption in each country must equal the total output in that country plus the inflow of consumption from the other country. The equation C1 + Cb2 = Y1 + Yb1 represents this equality for date 1, where C1 is the home country's consumption, Cb2 is the consumption of the home country's residents in the foreign country, Y1 is the home country's output, and Yb1 is the foreign country's output.
Similarly, for date 2, the equation C2(s) + Cb2(s) = Y2(s) + Yb2(s) represents the equality of total consumption and output between the home and foreign countries for each state s.
(e) Given the output levels provided, we can derive the equilibrium relative price of Arrow-Debreu securities (p(1)/p(2)) in a global equilibrium. Plugging the output values into the intertemporal budget constraint and solving for p(1)/p(2), we find:
p(1)/p(2) = (Y1 - Yb1 - Y2(2) + Yb2(2))/(Y2(1) - Yb2(1))
Substituting the given output levels, we get:
p(1)/p(2) = (1 - (1 + x) - (1 - 2x) + (1 + 2x))/((1 + x) - (1 - x))
Simplifying
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