Suppose a duopoly in a market for a differentiated good. The demands and costs of the two companies, A and B, are given by:
Qa = 200 - 2Pa + Pb
Qb 2002Pb + Pa
CTa = 550 + 46 Qa
CTb = 550 + 46 Qb
Assuming that the two companies choose their price (Bertrand model), what quantity will be produced by firm A?
Answers
In the given scenario, with the Bertrand model, there is no Nash equilibrium. Firm A's quantity produced cannot be determined as there is no unique solution in the differentiated duopoly market.
To determine the quantity produced by firm A in the Bertrand model, we need to find the Nash equilibrium, where both firms simultaneously choose their prices. In this case, we will assume that firm B has already chosen its price (Pb).
Given:
Demand for firm A: Qa = 200 - 2Pa + Pb
Demand for firm B: Qb = 200 - 2Pb + Pa
Cost function for firm A: CTa = 550 + 46Qa
Cost function for firm B: CTb = 550 + 46Qb
In the Bertrand model, each firm chooses the price that maximizes its profit, taking into account the price chosen by the other firm. The firm with the lower price captures the entire market demand.
To find the Nash equilibrium, we equate the marginal cost and marginal revenue for firm A:
MR = MC
The marginal revenue for firm A is the derivative of the demand function with respect to quantity:
MR = d(Qa)/dPa
MR = -2
The marginal cost for firm A is the derivative of the cost function with respect to quantity:
MC = d(CTa)/dQa
MC = 46
Setting MR equal to MC:
-2 = 46
This equation has no solution, which means there is no cash equilibrium in this scenario. The Bertrand model does not have a unique solution when firms have differentiated products.
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Related Questions
The WACC is used as the discount rate to evaluate various capital budgeting projects. However, it is important to realize that the WACC is an appropriate discount rate only for a project of average risk. Analyze the cost of capital situations of the following company cases, and answer the specific questions that finance professionals need to address. Consider the case of Turnbull Co. Turnbull Co. has a target capital structure of 45% debt, 4% preferred stock, and 51% common equity. It has a before-tax cost of debt of 8.2%, and its cost of preferred stock is 9.3%. If Turnbull can raise all of its equity capital from retained earnings, its cost of common equity will be 12.4%. However, if it is necessary to raise new common equity, it will carry a cost of 14.2%. If its current tax rate is 25%, how much higher will Turnbull's weighted average cost of capital (WACC) be if it has to raise additional common equity capital by issuing new common stock instead of raising the funds through retained earnings? (Note: Round your intermediate calculations to two decimal places.) O 1.15% O 1.20% 0.92% 1.01% Turnbull Co. is considering a project that requires an initial investment of $570,000. The firm will raise the $570,000 in capital by issuing $230,000 of debt at a before-tax cost of 11.1%, $20,000 of preferred stock at a cost of 12.2%, and $320,000 of equity at a cost of 14.7%. The firm faces a tax rate of 25%. What will be the WACC for this project? (Note: Round your intermediate calculations to three decimal places.) Consider the case of Kuhn Co. Kuhn Co. is considering a new project that will require an initial investment of $45 million. It has a target capital structure of 35% debt, 2% preferred stock, and 63% common equity. Kuhn has noncallable bonds outstanding that mature in 15 years with a face value of $1,000, an annual coupon rate of 11%, and a market price of $1555.38. The yield on the company's current bonds is a good approximation of the yield on any new bonds that it issues. The company can sell shares of preferred stock that pay an annual dividend of $8 at a price of $92.25 per share. Kuhn does not have any retained earnings available to finance this project, so the firm will have to issue new common stock to help fund it. Its common stock is currently selling for $22.35 per share, and it is expected to pay a dividend of $2.78 at the end of next year. Flotation costs will represent 3% of the funds raised by issuing new common stock. The company is projected to grow at a constant rate of 9.2%, and they face a tax rate of 25%. What will be the WACC for this project? (Note: Round your intermediate calculations to two decimal places.)
Answers
Turnbull Co.'s WACC will be 1.15% higher if it raises new common equity instead of using retained earnings. Kuhn Co.'s WACC for the project is 14.08%.
To determine the weighted average cost of capital (WACC) for each company case, we need to calculate the component costs and weights for each source of capital and then calculate the weighted average. Let's analyze each case separately.
Case 1: Turnbull Co.
Target capital structure:
Debt: 45%
Preferred stock: 4%
Common equity: 51%
Costs of capital:
Before-tax cost of debt: 8.2%
Cost of preferred stock: 9.3%
Cost of common equity (retained earnings): 12.4%
Cost of common equity (new common stock): 14.2%
Tax rate: 25%
Determine the component costs and weights:
Debt:
Cost of debt = 8.2%
Weight of debt = 45%
Preferred stock:
Cost of preferred stock = 9.3%
Weight of preferred stock = 4%
Common equity (retained earnings):
Cost of common equity = 12.4%
Weight of common equity = 51%
Calculate the WACC with retained earnings:
WACC with retained earnings = (Cost of debt * Weight of debt) + (Cost of preferred stock * Weight of preferred stock) + (Cost of common equity * Weight of common equity)
WACC with retained earnings = (0.082 * 0.45) + (0.093 * 0.04) + (0.124 * 0.51)
WACC with retained earnings = 0.0369 + 0.00372 + 0.06324
WACC with retained earnings = 0.10386 or 10.39%
Calculate the WACC with new common stock:
Flotation cost of new common stock = 3%
Cost of new common stock = 14.2%
Adjusted cost of new common stock = Cost of new common stock / (1 - Flotation cost of new common stock)
Adjusted cost of new common stock = 0.142 / (1 - 0.03)
Adjusted cost of new common stock = 0.142 / 0.97
Adjusted cost of new common stock = 0.1464 or 14.64%
WACC with new common stock = (Cost of debt * Weight of debt) + (Cost of preferred stock * Weight of preferred stock) + (Adjusted cost of new common stock * Weight of common equity)
WACC with new common stock = (0.082 * 0.45) + (0.093 * 0.04) + (0.1464 * 0.51)
WACC with new common stock = 0.0369 + 0.00372 + 0.0746464
WACC with new common stock = 0.1153164 or 11.53%
The difference in WACC between raising funds through retained earnings and new common stock is:
Difference = WACC with new common stock - WACC with retained earnings
Difference = 0.1153164 - 0.10386
Difference = 0.0114564 or 1.15%
Therefore, the WACC for Turnbull Co. will be 1.15% higher if it has to raise additional common equity capital by issuing new common stock instead of raising the funds through retained earnings.
Case 2: Kuhn Co.
Target capital structure:
Debt: 35%
Preferred stock: 2%
Common equity: 63%
Costs and market prices of capital:
Bonds: Face value = $1,000, Coupon rate = 11%, Market price = $1,555.38
Preferred stock: Annual dividend = $8, Price = $92.25 per share
Common stock: Price = $22.35 per share, Dividend (expected) = $2.78 per share
Flotation cost for new common stock: 3%
Expected growth rate: 9.2%
Tax rate: 25%
Determine the component costs and weights:
Debt (Bonds):
Cost of debt = Yield on existing bonds = Coupon rate / Market price of bonds
Cost of debt = 11% / $1,555.38 = 0.00707 or 0.71%
Weight of debt = 35%
Preferred stock:
Cost of preferred stock = Dividend / Price
Cost of preferred stock = $8 / $92.25 = 0.0866 or 8.66%
Weight of preferred stock = 2%
Common equity:
Cost of common equity = Dividend / Price + Growth rate
Cost of common equity = $2.78 / $22.35 + 0.092 = 0.1246 + 0.092 = 0.2166 or 21.66%
Weight of common equity = 63%
Calculate the WACC:
WACC = (Cost of debt * Weight of debt) + (Cost of preferred stock * Weight of preferred stock) + (Cost of common equity * Weight of common equity)
WACC = (0.00707 * 0.35) + (0.0866 * 0.02) + (0.2166 * 0.63)
WACC = 0.0024745 + 0.001732 + 0.1365578
WACC = 0.1407643 or 14.08%
Therefore, the WACC for Kuhn Co.'s project is 14.08%.
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the King code refers to good corporate governance and emphasizes, among other things, the concepts of transparency and accountability. Explain these concepts in the context of companies
Answers
The King Code can be explained as the code providing several benchmark standards for companies to meet in their public filings and business practices.
What is the King Code?The King Code can be understood as that which provides a number of benchmark standards for companies to meet in their public filings and business practices. Offering an overview of how companies should perform can be beneficial for standardizing industries and making an economy more appealing to foreign investors.
Companies use the King Code to guide their activities and must provide explanations when they choose to deviate from the standards set by the code.
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True or False: The APY can never be the same as the APR.
Answers
It is False that APY and APR can never be same thing.
Is it true that The APY and APR can never be the same?The Annual Percentage Rate (APR) is the interest rate charged on a loan or credit card on an annual basis.
While the Annual Percentage Yield (APY) takes into account the effect of compounding interest over the course of a year.
While it is possible for the APR and APY to be the same in simple interest scenarios, they will typically differ when compounding is involved.
For example, if a savings account has an APR of 3% and compounds interest daily, the APY will be slightly higher than 3% because the interest earned on each day's balance will be added to the principal.
Therefore, it is not accurate to say that the APY can never be the same as the APR, as this will depend on the specific terms of the loan or account and whether or not interest is compounded.
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Question 45
_______ are especially useful for relationship marketing.
o Apps
o Podcasts
o Social networking sites
o Media networks
o Wikis
Answers
Answer:social networking sites
Explanation:
Gemma and Li are both managers at Yang Accounting, a large accounting firm. Each has a very different management style. Gemma is very outgoing and constantly checking on her subordinates to see if there is any way she can help them to complete their projects. She also brings in fresh flowers for the lunchroom weekly and always remembers everyone's birthday. Li is much more introverted and communicates with his subordinates mainly through email, and he has his subordinates submit daily reports on their progress toward the weekly goals he has assigned them.
A. transformational leader
B. path-goal leader
C. task-oriented leader
D. servant leader
E. people-oriented leader
Answers
Answer:
Gemma is a people oriented leader whereas Li is a task oriented leader.
Explanation:
Gemma is good with people and the Human resources. He shows empathy towards each employee of the company by helping them and being there with them when they have any doubts or clarifications in the projects.
Li is professional. spends time to himself and cares more about the outcome of their employees work.
What is the simplest definition of accounting?
OA. The recording of financial transactions
OB. Following generally accepted principles
OC. Presenting information in reports
D. Managing all of a company's finances
Answers
Answer:
A. The recording of financial transactions.
Explanation:
Hope this helps!
If not, I am sorry.
how can interest rate on loan for rental property determine the rent
Answers
A government spends money in order to:
A. influence which products will be available to U.S. consumers.
B. make sure government programs can function properly.
C. prevent foreign businesses from competing with U.S. companies.
D. decide what each employee at a U.S. company will be paid.
BMIT
Answers
Answer:
Options A and C is not related at all. I belive It's B.
Which of these can you invest in without assuming any risk?
(1 point)
bonds
property
stocks
none
Answers
Answer:
none
Explanation:
correct
Jimmy Langenberger is the president of TemPro, Inc. , a company that provides temporary employees for not-for-profit companies. TemPro has been operating for five years; its revenues are increasing with each passing year. You have been hired to help Jimmy analyze the following transactions for the first two weeks of April: a. Billed the local United Way office $ 23,500 for temporary services provided. B. Paid $ 3,005 for supplies purchased and recorded on account last period. C. Purchased supplies for the office for $ 2,600 on account. D. Purchased a new computer for the office costing $ 3,800 cash. E. Placed an advertisement in the local paper for $ 1,400 cash. F. Paid employee wages of $ 11,900. Of this amount, $ 3,800 had been earned by employees and recorded in the Wages Payable account in the prior period. G. Issued 3,000 additional shares of common stock for cash at $ 45 per share in anticipation of building a new office. The common stock had a par value of $ 0. 50 per share. H. Received $ 12,500 on account from the local United Way office for the services provided in (a). I. Billed Family & Children's Service $ 14,500 for services rendered. J. Purchased land as the site of a future office for $ 10,000. Paid $ 3,000 cash as a down payment and signed a note payable for the balance. K. Received the April telephone bill for $ 1,950 to be paid next month.
Required:
For each of the transactions, prepare journal entries. Be sure to categorize each account as an asset (A), liability (L), stockholders' equity (SE), revenue (R), or expense (E)
Answers
Billed the local United Way office $ 23,500 for temporary services provided. Thus, option A is correct.
What is credit union?Credit union is defined as a non profit money making cooperative in which the members of that particular group can ask to borrow money from the funds available at that time with very low rate of interest. The credit union is a non profit institution but bank is a for the profit institution.
The main difference between a bank and a credit union will be that the credit union is a non profit institution but bank is a for the profit institution.
Therefore, Billed the local United Way office $ 23,500 for temporary services provided. Thus, option A is correct.
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You have been invited to give a speech at a local restaurant. The person who is hosting the event has asked you to speak for 15 minutes on a topic of your choice. Walk though the process of deciding what to talk about and discuss the reasons and methods you would use to make an effective choice.
Answers
Give me some hint please
Answer:
talk about the recipes
Explanation:
When taking notes in science and mathematics courses, you should
a. take all notes in blue or black ink pen.
b. summarize what the instructor says in your own words.
c. write down answers to worked problems.
d. use standard symbols, abbreviations, and scientific notation.
Answers
When taking notes in science and mathematics courses, you should summarize what the instructor says in your own words.
What's science? Science is a methodical enterprise that builds and organizes knowledge in the form of testable explanations and prognostications about the macrocosm.Science may be as old as the mortal species, and some of the foremost archeological substantiation for scientific logic is knockouts of thousands of times old. The foremost written records in the history of wisdom come from Ancient Egypt and Mesopotamia in around 3000 to 1200 BCE. What's mathematics? Mathematics is an area of knowledge that includes similar motifs as figures( computation and number proposition), formulas and affiliated structures( algebra), shapes and the spaces in which they're contained( figure), and amounts and their changes( math and analysis).Learn more about mathematics here:
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****Please do not copy and paste. I want a unique answer
****Please use the keyboard to answer
MGT 422
Read the following small case and answer the questions given at the end with solid explanation.
You have a long-standing consulting relationship with a large consumer products company. This company represents 50 percent of your consulting revenues and is clearly your most important client. The CEO has called to ask you to commit a significant amount of time over the next couple of months to assist with a large merger project. The company is merging with a large conglomerate whose primary business is the sale and distribution of tobacco products. The CEO is relying on you to assist in facilitating a smooth integration of the two companies. You promised yourself that because your father died of lung cancer, you would never work for a tobacco company.
Is there a way that you can accept the consulting assignment and still keep your promise to yourself? How will you handle this dilemma if you decide that you cannot work for the tobacco company?
Answers
When faced with this dilemma, there are a few possible approaches to consider:
1. Transparency and Discussion: Schedule a meeting with the CEO to have an open and honest conversation about your personal conflict of interest due to your father's experience with lung cancer. Explain your promise to yourself and the emotional significance it holds for you. Discuss potential alternative ways in which you can contribute to the merger project without directly working with the tobacco company. This could involve focusing on other aspects of the integration process or offering assistance in areas that do not involve tobacco-related products.
2. Team Delegation: If the CEO understands your conflict and agrees to explore alternative arrangements, you can suggest assigning a team member or another consultant from your firm to directly handle the aspects of the merger project related to the tobacco company. You can still contribute to the overall integration efforts by overseeing and coordinating the project, providing guidance to the assigned team member, and ensuring a smooth integration process.
3. Ethical Considerations: If the above options are not feasible, and working directly with the tobacco company goes against your personal values and promise to yourself, you may need to decline the consulting assignment. In such a case, it is important to explain your reasons sincerely to the CEO, emphasizing the personal conflict of interest and your commitment to maintaining your ethical principles. Offer assistance in finding a suitable replacement consultant who can fulfill the requirements of the project effectively.
Handling this dilemma requires careful consideration of your personal values, the impact of your decision on your professional relationship with the client, and the alternatives available to fulfill your commitments. By engaging in open communication, exploring alternative approaches, and staying true to your principles, you can navigate this situation with integrity and professionalism.
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While on a trip, the Mendoza family decided to buy a painting which cost 500. The art dealer would not accept a personal check or credit cards. What method could be used to pay for the painting
Answers
Net banking is the method could be used to pay for the painting, as the art dealer would not accept a personal check or credit cards.
What is Net banking?Netbanking, normally referred to as internet banking, is a computerized way to carry out financial written account online. Any person with a bank account can activate and use this computerized system for their financial transactions.
Net banking, ordinarily referred to as online banking, is always accessible. Customers have access to a variety of financial services through net banking, including the ability to open fixed deposits and recurring deposits, transfer funds, and examine transaction history.
Thus, net banking.
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A: Do you think the world is still suffering the effects of thefirst world war? Why do you say that?B: Should we get rid of the penny? Why? The nickel? Dime? Cashtotally? Why or why not?
Answers
A: Yes, world still experiences some effects of first World War, primarily through political boundaries and international relations. B: Yes, debate over whether to get rid of the penny, nickel, dime, or even cash entirely depends on factors such as cost-efficiency, convenience, and tradition.
The war led to the creation of new countries and the redrawing of borders, which continue to influence global politics today. Additionally, the war's economic impact contributed to the Great Depression and the rise of totalitarian regimes, whose legacies persist in various ways.
Eliminating the penny has been suggested due to its low value and the cost of production. Similarly, arguments for phasing out nickels and dimes focus on efficiency and the increased use of digital payments. However, some people still rely on cash for transactions, especially those without access to banking services.
In conclusion, while it may be beneficial to consider reducing the use of low-denomination coins, it is essential to weigh the pros and cons carefully and ensure that all populations are adequately served by our monetary system.
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Zoom has been criticized for opening up its platform for use by nonpaying users (with some restrictions). Why would Zoom do this, and why would paying customers care? 3-16. With the surge of Zoom users came a surge in scrutiny about the software's privacy and security. Why do you think Zoom developers built an insecure piece of software?
Answers
Zoom opened platform for non-paying users to expand user base; paying customers value exclusivity. Security concerns require evidence, avoiding assumptions of intentional insecurity.
There can be various reasons why Zoom decided to open up its platform for non-paying users, such as expanding its user base, increasing brand exposure, and attracting potential paying customers who may upgrade to premium features.
Paying customers may care because they might expect exclusive benefits, enhanced features, priority support, or a sense of exclusivity for their investment. As for the scrutiny regarding Zoom's privacy and security, it's important to note that building software is a complex task, and vulnerabilities can arise unintentionally due to oversight or unforeseen circumstances.
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23 points left out
:$&:$:&,&,&,,
Answers
Answer:
Is this one of the people that give free points?
Answer:
thanks. may god bless you have a nice life.
TRUE OR FALSE: A mathematics professor at a university would fall under both the Education and Training career cluster and the STEM career cluster.
Answers
Explanation: none
Kristina works at a coffee shop. She can produce 200 coffee drinks in four hours. What is her productivity for one hour?
Answers
Answer: She can produce 50 drinks in 1 hour, 200/4 = 50
Answer:
50
Explanation:
divide 200 by 4
hope this helps dont 4get to like and star
-mercury
Why do people buy and sell under futures contracts? Select ALL that apply
A. They want to take immediate advantage of the current prevailing prices.
B. They expect to make money by setting their contracts with cash payments.
C. They hope the actual price of an asset will be higher than the contracted price.
D. They value the buying and selling of derivatives on a transparent, public exchange.
Answers
When a property is financed by means of a deed of trust, to whom are the payments made? trustee trustor beneficiary grantee
Answers
In a deed of trust arrangement, the payments are made to the beneficiary (lender) rather than the trustee.
When a property is financed by means of a deed of trust, the payments are typically made to the beneficiary.
In a deed of trust arrangement, there are three parties involved: the trustor (borrower), the beneficiary (lender or creditor), and the trustee.
The trustee is a neutral third party who holds the legal title to the property until the loan is paid off or the terms of the deed of trust are fulfilled.
The trustor (borrower) makes regular payments to the beneficiary (lender) as outlined in the loan agreement.
These payments typically include principal and interest, and they are made directly to the beneficiary or their designated servicing agent.
The trustee's role is to administer the deed of trust, hold the legal title to the property, and act as an intermediary between the trustor and the beneficiary.
However, the trustee does not typically receive the payments.
Their primary responsibility is to protect the interests of both the trustor and the beneficiary and ensure that the terms of the deed of trust are followed.
Therefore, in a deed of trust arrangement, the payments are made to the beneficiary (lender) rather than the trustee.
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2. The first draft of the project charter is as follows:
Project Manager
Project Sponsor
Start Date
Project Mission
PROJECT CHARTER
Annual Clothing Drive
Talar Adams
Activities Committee
April 21
Deliver clothes to local shelters
a. Does this charter contain enough information for Talar to get started? Why or why
not?
Answers
Answer:
The charter provides some basic information about the project, such as the project manager, sponsor, start date, and mission. However, it does not provide enough details about the project's scope, objectives, budget, timeline, stakeholders, and risks. Talar needs more information to understand the project's requirements, constraints, and expectations. She also needs to define the project's deliverables, milestones, and success criteria. Without a clear and comprehensive project charter, Talar may face difficulties in planning, executing, and controlling the project, as well as communicating with stakeholders and managing their expectations. Therefore, Talar should revise the project charter to include all the necessary information and obtain approval from the project sponsor before proceeding with the project.
What does an invasion biologist study?
help me
Answers
Answer:
Invasion biology deals with invasive species. If an “invasive” species is defined as a species that spreads to the detriment of economic interests and public health, however, invasion biology could not be easily distinguished from pest management and public health sciences.
Explanation:
List qualities a good manager should have. What are the advantages and drawbacks of being in a position of authority?The qualities of a good manager are:The advantages of being a manager are:The drawbacks of being a manager are:
Answers
Jeannine and Ryan, have both been working full-time jobs for many years. They are about to adopt three siblings and are trying to decide if they are both going to keep working. What disadvantage will they likely experience if they choose a single income option?
A.
They will have higher costs for childcare.
B.
They will have a greater amount of financial income.
C.
They will have less time to spend with their new baby.
D.
They will have less disposable income.
Answers
Answer: D
Explanation:
Answer: They will have less disposable income.
Which of the principles below does Val follow when she reviews her records to make sure that recorded accounting events correspond to the actual costs?A. Time period principleB. Measurement principleC. Full disclosure principleD. Matching principle
Answers
D. Matching principle This principle helps maintain consistency and reliability in financial reporting,
Val follows the matching principle when she reviews her records to ensure that recorded accounting events correspond to the actual costs. The matching principle states that expenses should be recognized in the same period as the revenues they help generate. By applying this principle, Val ensures that costs are accurately matched with the revenues they are associated with, providing a clear and accurate representation of the company's financial performance. This principle helps maintain consistency and reliability in financial reporting, allowing for meaningful analysis and decision-making based on the recorded costs and revenues.
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Why do you think a higher percentage of those over 35 years old invest in the market compared to those under 35? Help please!
Answers
Answer:
Yes I think those over 35 invest in a market compared to people not 35, because they been though school, and have more experience in the market company.
Explanation:
office administration.Prepare for filling in order.
Answers
This (office administration) simply means to arrange the above in alphabetical order like this;
An Apple SpotA1 TaxiDriveByFine Foods LtdFirst Caribbean BankMalcolm Stephens & SonsNorth Eastern Funeral AssociationPortsmouth Police StationSt. John's Primary School21 Century Printers.What is office administration?Within a company, office administration is a collection of day-to-day operations connected to the upkeep of an office building, financial planning, record keeping and billing, personal development, physical distribution, and logistics.
Finally, administrative abilities are connected to corporate operations and enhancing office productivity. Communication and organizational abilities, as well as project management, bookkeeping, and time management skills, are among them.
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Suppose a bottle of wine costs 20 euros in france and 25 dollars in the united states. if the nominal exchange rate is .80 euros per dollar, what is the real exchange rate?
Answers
Assume that a bottle of wine costs 20 euros in France and $25 in the United States. if the nominal exchange rate is . 80 euros for one dollar. The real exchange rate is 1.
That it is the same as one. The amount of money required to buy products in the United States buys enough foreign currency to buy the same quantity of items in another nation.
what is the real exchange rate?
The nominal exchange rate (e) multiplied by the price ratio between the two nations, P/P*, yields the real exchange rate (RER) between two currencies. As a result, the RER is eP*/P. Consider Germany in relation to the United States.
Calculation:
Real exchange rate= Nominal exchange rate x domestic price /foreign price
Real exchange rate = 0.80 x25/20
Real exchange rate = 0.80 x 1.25 = 1
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The production function for a competitive firm is
Q = K.5L.5. The firm sells its output at a price of
$10, and can hire labor at a wage of $5. Capital is fixed at one unit. The profit-maximizing
quantity of labor is:
A. 2/5.
B. 1.
C. 10.
D. None of the answers are correct.
please explain in details
Answers
We can see that the profit-maximizing quantity of labor is (A) 2/5 by simplifying the expression and solving for L.
The production function for a competitive firm is Q = K.5L.5.
The firm sells its output at a price of $10, and can hire labor at a wage of $5.
Capital is fixed at one unit. The profit-maximizing quantity of labor is 2/5.
The profit-maximizing quantity of labor is 2/5.
The profit-maximizing output level for a competitive firm is where the firm's marginal cost of production equals its marginal revenue (MC = MR).
We can use the product's production function, as well as its price and the cost of one unit of input, to identify the firm's marginal cost of production and revenue. The production function for this competitive firm is Q = K.5L.5.
Capital is fixed at one unit. We can compute the total product of labor (TPL) for each quantity of labor employed (L). TPL can then be used to calculate the marginal product of labor (MPL) at each level of employment by subtracting TPL at the prior level of employment from TPL at the current level of employment. The marginal cost of production for the product produced by this competitive firm is given by the wage rate divided by the marginal product of labor (W/MPL). The marginal revenue received by the competitive firm for each product sold is constant at $10.
The profit-maximizing quantity of labor is the one at which the marginal revenue is equal to the marginal cost of production. MR = MC can be used to solve for the profit-maximizing level of L.
Thus, the profit-maximizing output level can be found by substituting the value of L into the production function.
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