Sand Explorers issues bonds due in 14 years with a stated interest rate of 6% and a face value of $250,000. Interest payments are made semi-annually. The market rate for this type of bond is 5%. Using present value tables, calculate the issue price of the bonds. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)
Multiple Choice
1. $200,507.
2. $274,957.
3. $335,225.
4. $250,000.
Answers
The issue price of the bonds is $274,957 (option 2) when market rate for this type of bond is 5%.
To calculate the issue price of the bonds, we need to determine the present value of the bond's future cash flows.
The bond pays semi-annual interest payments for 14 years, and the face value is $250,000. The stated interest rate is 6% and the market rate is 5%.
Using the present value of an annuity due (PVAD) table, we can find the present value factor for a 14-year period at a 5% interest rate. The present value factor is 10.1607.
Next, we calculate the present value of the bond's interest payments. Since the interest is paid semi-annually, we divide the stated interest rate by 2 to get 3% as the semi-annual interest rate.
Using the present value of an annuity (PVA) table, we find the present value factor for a 14-year period at a 3% interest rate. The present value factor is 19.0344.
Multiplying the semi-annual interest payment ($250,000 * 6% / 2 = $7,500) by the present value factor of the annuity, we get $142,757.50.
Finally, we calculate the present value of the bond's face value. Using the present value (PV) table, we find the present value factor for a 14-year period at a 5% interest rate. The present value factor is 0.5194.
Multiplying the face value of the bond ($250,000) by the present value factor, we get $129,850.
The issue price of the bonds is the sum of the present values of the interest payments and the face value:
$142,757.50 + $129,850 = $272,607.50.
Therefore, rounding to the nearest dollar, the issue price of the bonds is $274,957 (option 2).
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Related Questions
what term best describes the pridiction of the number of items a company will sell for any given commodity
Answers
The optimal market prices best describe the prediction of the number of items a company will sell for any given commodity.
What is Ideal Cost?
The ideal cost is that price tag at which the absolute benefit of the dealer is expanded. At the point when the cost is too low, the vender is moving countless units however isn't acquiring the most elevated conceivable total benefit.
For what reason is ideal cost significant?
The ideal cost is that perfect balance where it is feasible to get great benefits as indicated by the item or need that we offer. This is vital for any individual who is committed to a business action since it is a moderately basic method for getting improved results.
How would you work out ideal evaluating methodology?
Do an estimating investigation to see what they charge for comparative items and how regularly they change the cost (e.g., through limited time limits). While you surely don't have any desire to go far out of reach with your evaluating technique, you don't be guaranteed to have to offer the least cost.
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Vaughn-Williams Co. has total assets of $600,000 and stockholders' equity of $320,000. It purchased $80,000 of supplies on account and collected $50,000 on account from its customers. As a result, the company's total assets would now be __
a. $680,000
b. $360,000
c. $550,000
d. $80,000
Answers
Vaughn-Williams Co. purchased $80,000 of supplies on the account and collected $50,000 on the account from its customers. As a result, the company's total assets would now be $550,000. (Option C)
To calculate the updated total assets, we need to consider the effects of the transactions mentioned.
The purchase of $80,000 in supplies on account increases both the total assets and liabilities of the company. However, since the transaction does not involve any changes in stockholders' equity, it does not impact the equity value.
The collection of $50,000 on account from customers also affects both assets and liabilities. The increase in cash (an asset) is offset by a decrease in accounts receivable (also an asset) since the amount owed by customers is collected.
Considering these transactions, the calculation for the updated total assets would be as follows:
Total assets = Previous total assets + Purchase of supplies - Collection from customers
Total assets = $600,000 + $80,000 - $50,000
Total assets = $630,000 - $50,000
Total assets = $580,000
Therefore, the correct answer is c. $550,000.
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What are some ways to protect the confidentiality of research participants quizlet?
Answers
The ways of protecting confidentiality is:
Getting nondisclosure agreements signedlimiting participant identity accessOnly with explicit permission will participant information be disclosed.What is Confidentiality?Confidentiality describes a set of rules or a contract that limits access to or uses of specific types of information and is often done out through confidentiality clauses. Confidentiality refers to the concept and practice of keeping sensitive information private unless the owner or data custodians expressly authorizes sharing it with a third party.
In addition, confidentiality might mean:
Limiting user access to data instruments that contain participant identification.Not revealing some data sets.The confidentiality agreement is crucial to protect participants as well as the integrity of the research.To know more about Confidentiality, visit:
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you have $100,000 to invest in either stock d, stock f, or a risk-free asset. you must invest all of your money. your goal is to create a portfolio that has an expected return of 12.1 percent. assume d has an expected return of 15.6 percent, f has an expected return of 11.5 percent, and the risk-free rate is 6.3 percent. if you invest $50,000 in stock d, how much will you invest in stock f?
Answers
To determine how much you should invest in stock F, we need to find the remaining amount after investing $50,000 in stock D. you should invest approximately $37,391.30 in stock F to achieve the desired portfolio expected return of 12.1% when investing $50,000 in stock D.
Given:
Investment in stock D: $50,000
Expected return of stock D: 15.6%
Expected return of stock F: 11.5%
Risk-free rate: 6.3%
Desired portfolio expected return: 12.1%
To find the amount to be invested in stock F, we can set up the following equation:
($50,000 * 0.156) + (Amount to be invested in stock F * 0.115) = ($100,000 * 0.121)
Simplifying the equation:
$7,800 + (Amount to be invested in stock F * 0.115) = $12,100
Subtracting $7,800 from both sides:
Amount to be invested in stock F * 0.115 = $4,300
Dividing both sides by 0.115:
Amount to be invested in stock F = $4,300 / 0.115
Calculating:
Amount to be invested in stock F = $37,391.30
Therefore, you should invest approximately $37,391.30 in stock F to achieve the desired portfolio expected return of 12.1% when investing $50,000 in stock D.
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9. for sport organizations, what revenue source is the "trunk of the sport business money tree" that feeds all other income streams? a. sponsorships b. ticket sales and live attendance c. merchandise and concessions d. media rights
Answers
The revenue source that is considered the "trunk of the sport business money tree" for sport organizations is d. media rights.
Media rights refer to the fees paid by broadcasters and media companies for the rights to broadcast or stream sports events. This is often a significant source of income for sport organizations as it allows them to reach a wide audience and generate revenue through advertising and sponsorship deals.
For example, major sports leagues like the NFL and NBA earn billions of dollars from media rights deals. These funds are then used to support other income streams such as player salaries, facility maintenance, and investment in other areas of the organization. Overall, media rights play a vital role in the financial success of sport organizations.
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the process of converting sensory data into electrochemical signals is called:
Answers
The process of converting sensory data into electrochemical signals is called transduction.
This process occurs when sensory receptors in the body, such as those in the eyes or ears, detect stimuli in the environment and convert them into neural impulses. These impulses are then transmitted along sensory neurons in the form of electrochemical signals, which are interpreted by the brain to create our perception of the world around us. The conversion of sensory data into electrochemical signals is a critical component of our ability to sense and respond to our environment. It is essential for everything from basic survival instincts to complex cognitive processes like learning and memory. In conclusion, the process of converting sensory data into electrochemical signals is a fundamental aspect of human experience, and it involves a complex interplay between sensory organs, neural circuits, and the brain.
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The asset that is most susceptible to employee fraud is.
Answers
The asset in a company that is typically susceptible to fraud by the employees is known as cash.
What is an asset?An asset simply means the resource that is controlled or owned by a company.
The asset in a company that is typically susceptible to fraud by the employees is known as cash. It should be noted that an asset in a company is important as it can produce positive economic value.
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Rising interest rates have made borrowing more costly to consumers. As a result
of the most recent increase in interest rates, borrowing and consumption have
fallen throughout the economy, triggering a contractionary period. Growing
uneasy, citizens have been asking Congress to make an official statement as to
how long this contractionary period is expected to last. Which of the following is
an appropriate response?
Answers
Answer:
it depends on the measures taken to ensure that economy is stable.
Answer:
1. it is difficult to say since contractionary periods have varying lengths in different business cycles.
2. shock
3. high unemployment
4. two
5. expansion stage of the business cycle
Explanation:
just took it
a purchase of office equipment for cash is journalized as
Answers
The Office Equipment account is debited to increase its balance, reflecting the acquisition of office equipment as an asset. The Cash account is credited to decrease its balance, representing the outflow of cash for the purchase.
The journal entry would be as follows:
Office Equipment [Debit]: [Amount of the purchase]
Cash [Credit]: [Amount of the purchase]
It's crucial to remember that the specific account names and amounts mentioned in the journal entry may change depending on the particulars of the transaction and the organization's chart of accounts. For accurate and compliant financial documentation, you should also seek the advice of a qualified accountant or check the specific accounting rules that apply to your country.
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Starbucks just released study Starbucks coffee increases your life span what is the change in demand or quantity demand
Answers
Answer:
There would be a change in demand. there would be an increase in demand. the demand curve would shift rightward
Explanation:
Only a change in the price of a good leads to a change in the quantity demanded. If the price of the coffee increased, the quantity demanded would reduce and if it reduced, it would would increase
So based on the report the quantity demanded would increase. This is because most people want to live longer. This would result in the demand curve shifting rightward
What types of planning can be done to improve a nation’s economy?
A nation can undergo ____ planning or ___ planning in order to improve its economy.
Answers
Answer:
A nation can undergo long-term planning or constructive planning in order to improve its economy. Long-term planning involves setting goals and implementing policies that will have an impact over a period of several years. This type of planning may involve investments in education, infrastructure, and research and development, among other areas. Constructive planning involves implementing policies that encourage economic growth and development, such as reducing barriers to trade, promoting entrepreneurship and innovation, and investing in key industries. These types of planning can help a nation to create jobs, increase productivity, and improve living standards for its citizens. THANK YOUa firm's demand curve for labor is: group of answer choices the upward-sloping portion of its value of the marginal product curve. horizontal for the firm in perfect competition. the downward-sloping portion of its marginal product curve. the downward-sloping portion of its value of the marginal product curve.
Answers
a firm's demand curve for labor is the downward-sloping portion of its marginal product curve, option C
Demand curveIt is the graphical representation of the relationship between the price of a certain good or service and the level or amount of demand that consumers experience on it. This process analyzes the effect of prices in the market based on the law of demand, where the slope is negative.
This implies that the curve goes down, because there is an inverse relationship between price and demand: the higher the demand for a product, the lower the price.
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2. basic facts about the wto the world trade organization (wto) was built on the basis of the general agreement on tariffs and trade (gatt) and, thus, inherited many of its features. still, the wto proved to be a very distinct institution. indicate whether each property in the following table is a unique property of the wto compared to gatt. property unique property of wto yes no limits participation to a few nations oversees tariff cuts and reduction of nontariff measures enforces dispute settlements enforces binding commitments acts as a government when can japan raise tariffs on imports from a country that is a member of the wto? whenever it wants to because japan is not a member of the wto never, because japan is a member of the wto when imports from that country threaten serious injury to japanese producers whenever it wants to as long as it has no free-trade agreement with that country
Answers
The WTO enforces binding commitments and dispute settlements but doesn't limit participation or oversee tariff cuts. Japan can raise tariffs when imports threaten its producers, following WTO rules.
The General Agreement on Tariffs and Trade (GATT), from which the World Trade Organization (WTO) acquired many characteristics, also possessed a number of distinctive features. Contrary to GATT, the WTO does not restrict membership to a small number of countries and regulates the elimination of non-tariff trade restrictions. In contrast to the GATT, the WTO has a formal conflict resolution process and the authority to impose sanctions on nations that disobey WTO regulations.
Additionally, the WTO is governed by a set of legally enforceable promises, which means that nations that wish to join the organization must abide by the rules they accept. The WTO, however, does not serve as a government. When imports from a WTO member threaten to seriously harm Japanese producers, Japan may increase import duties as long as it abides by WTO rules and processes and does not have a free-trade deal with that nation.
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The images show what happened to two people who invested $1,000. gale starts with 1,000 dollars. gale has a savings account with 200 dollars and 1 percent return, mutual fund with 600 dollars and 7 percent return, and stock with 200 dollars and negative 10 percent return. the value 1 year later is 1,024 dollars with a 24 dollar profit. alex starts with 1,000 dollars. alex has a stock return with 1,000 dollars and negative 10 percent return. the value 1 year later is 900 dollars with a profit of negative 100 dollars. which investment advice would gale most likely give to alex? invest in stocks because they are less risky. put most of your money in a savings account instead. spread your investments in several different areas. stick with the stocks because they will bounce back.
Answers
The investment advice that Gale most likely to Alex is to invest in Mutual funds, as an investment in mutual funds will have a better return than any other investment.
Mutual fund: A mutual fund is a type of investment vehicle that pools money from various financial backers to buy an expanded arrangement of stocks, bonds, or different protections. The common asset is overseen by an expert asset director who pursues speculation choices for the financial backers, and the profits produced by the shared asset are conveyed among the financial backers in view of their proportionate offer in the asset. Shared reserves offer individual financial backers the advantages of enhancement, proficient administration, and liquidity, pursuing them a well-known decision for long-haul speculation objectives, for example, retirement arranging or putting something aside for a kid's schooling.
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how long does it take for tax refund to show in bank account after approved
Answers
Answer:
Assuming no issues, IRS issues tax refunds in less than 21 calendar days after IRS receives the tax return. IRS has an on-line tool, "Where's My Tax Refund", at www.irs.gov that will provide the status of a tax refund using the taxpayer's SSN, filing status, and refund amount.
Explanation:
Williams Auto has a machine that installs tires. The machine is now in need of repair. The machine originally cost $11,400 and the repair will cost $2,400, but the machine will then last two years. The labor cost of operating the machine is $0. 50 per tire. Instead of repairing the old machine, Williams could buy a new machine at a cost of $6,400 that would also last two years; the labor cost would then be reduced to $0. 25 per tire. Williams expects to install 11,400 tires in the next two years. A. Determine the total (two-years) cost for both repairing and replacing the machine
Answers
Williams should fix the equipment because it will cost less overall than to replace it.
What is labor cost?Labor expenses are an employer's total out-of-pocket expenditure for hiring employees.
Williams Auto has a machine that installs tires. Even if the equipment needs maintenance, it will only operate for another two years. Operating the machine costs $0.70 per tire in labor. Instead of repairing the old machine.
1. Total cost of Repair = Repair cost + Operating cost
= $1,700+10,700*$0.70
= $1,700 + $7,490
= $9,1902.
2. Total cost to replace = Repair cost + Operating cost
= $5,700+10,700*$0.5
= $5,700+$5,350
= $11,050
Therefore, Williams should repair the machine.
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What are good sides and bad sides of breaking news and some examples why is it bad/good?
Answers
Answer:
breaking news may have a bad news example of bad news is fake news
Answer:
In my opinion, I see that the good side of news is that it help people be more aware of what's going around, and some may contribute to the rise in support for some fundings and charity programs for example: if a breaking news about a victim of any crime for example stolen house is displayed, an interview can give a voice to the victim to speak out and maybe raise fundings to repair all stolen goods or damaged items. On the other hand, some breaking news can end up sending out the wrong message and information for example talking about untrustable information, which may later on turn out to be wrong this can cause rumors.
The trade off theory optimal capital structure is achieved when marginal tax savings equals the marginal increased bankruptcy costs from the additional unit of debt. True or False?
Answers
It is true that the trade-off theory optimal capital structure is achieved when marginal tax savings equals the marginally increased bankruptcy costs from the additional unit of debt.
What is trade-off theory?
The trade-off theory of optimal capital structure suggests that there is an optimal level of debt for a company, where the marginal tax savings from the additional debt equals the marginally increased bankruptcy costs. This means that companies must balance the benefits of using debt, such as tax deductions, with the costs, such as the risk of bankruptcy. Ultimately, the optimal capital structure is the one that maximizes the company's value.
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Six former students Ann, Bob, Carl, Dora, Ed, and Fran are the contestants in a new reality TV show. They are placed on an island. The rules of the game are as follows. Ann goes first. She is given a bag that everyone knows contains six gold coins. Ann makes a proposal of how to allocate the six coins among the six contestants including herself. The contestants (including Ann) then vote "yes" or "no" on the proposal. If the proposal gets more than half the votes then the coins are allocated according to the proposal and everyone leaves the island. If the proposal gets half or fewer than half the votes then Ann has to leave the island empty-handed and she is out of the game.
In this case, the bag of six gold coins passes to Bob. He gets to make a proposal of how to allocate the coins among the remaining contestants (that is, including Bob but excluding Ann) and the remaining contestants (that is, including Bob but excluding Ann) then vote. As before, if the proposal gets more than half the votes then the coins are allocated according to the proposal and everyone leaves the island. If the proposal gets half or fewer than half the votes then Bob has to leave the island empty-handed and is out of the game. In this case, the bag of six gold coins passes to Carl. And so on, with the same voting rules, with each failed proposal leading to expulsion of the proposer, and with the role of proposer being passed on alphabetically.
The following assumptions matter. The coins are indivisible, there is no other money on the island, and side contracts to make payments of the island are not allowed. There are no abstentions; each surviving voter must vote yes or no: whenever a voter is indifferent, she or he votes no. A player only cares about the number of gold coins she or he gets to leave the island with (and this is common knowledge). For example, leaving empty handed because your proposal fails is the same as leaving empty-handed because a successful proposal gives you no coins. Finally: it is common knowledge that all the contestants were well trained in game theory.
What proposal should Ann make and why?
Answers
By proposing an equal distribution of the coins, Ann maximizes her chances of getting a positive vote from the other contestants. Each contestant would receive the same number of coins, which eliminates any incentives for the others to reject the proposal.Ann should propose to allocate one gold coin to each contestant, including herself.
If Ann proposed to allocate more coins to herself or favored certain contestants over others, it would create a sense of inequality and potentially lead to the rejection of her proposal. Each contestant understands that if they reject the proposal, they risk being expelled from the game with no coins at all. Therefore, they would be inclined to accept an equal distribution that guarantees them at least one coin.
By proposing an equal allocation, Ann ensures that the proposal will receive more than half the votes, securing the allocation of the coins according to her proposal. This allows her to leave the island with one gold coin, as well as the other contestants.
Ann's proposal aligns with the rational behavior expected from well-trained contestants in game theory. It takes into account the self-interest of each individual and strategically addresses the voting dynamics of the game, maximizing her chances of success and leaving the island with a fair share of the coins.
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Police are investigating the site of a convenience store robbery. The glass door was
broken, and it looks as if several packages of cigarettes are missing from behind the
counter. One police officer notices a man walking past the store and gets an odd
feeling about him. He stops the man and insists on searching his pockets. Inside the
man's pockets, police find several packs of cigarettes. They arrest the man and
charge him with the crime. Unfortunately, the judge throws out the charges. What is
MOST likely the judge's reason for dismissal?
A-The man is under 18 years old.
B-The man did not have money to post bail.
C-The policeman did not have probable cause to search the man.
D-The policeman did not have enough evidence that the man was the robber.
Answers
The MOST likely judge's reason for dismissal is the policeman did not have enough evidence that the man was the robber. Thus the correct option is D.
What is Robbery?Theft or robbery is defined as the stealing of someone else's property without their permission and using force or a threat of force that exhibits fear in them to perform any action against them.
To prove a crime against someone requires one to submit enough evidence which helps to establish the claim as the justice system is based on evidence not on arguments.
In the given case, police found the activity of the men suspicious as they found cigarette packets from him. There is no evidence that he has stolen the cigarette packets might be possible he has purchased them.
So due to a lack of evidence against the person the Judge dismissal the case. Therefore, option D is appropriate.
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By default, outlook will sort messages by date and by any conversation. Conversations area
Answers
In the outlook application, the conversation means the groups of messages between the same senders or recipients.
What is the outlook application?It is an application on windows that allows to send/receive email messages, manage calendar, store names, track tasks etc
Hence, in this application, the term conversation means the groups of messages between the same senders or recipients.
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***98 POINTS *** someone please help
Answers
Answer:
There are benefits and drawbacks to command economy structures. Command economy advantages include low levels of inequality and unemployment, and the common good replacing profit as the primary incentive of production. Command economy disadvantages include lack of competition and lack of efficiency.
Explanation:
Which of the following choices incur speculative risk?
a.stocks
b.fire insurance on a house
c.options
d.life insurance
e.high interest savings account
Answers
Answer: correct option is A.
Explanation: A speculative risk can be defined as risk that is taken willingly either it results in profit or loss and the stocks involve in probability of gain and loss making it a speculative risk.
Stocks incur speculative risk. Therefore option A is correct.
What are Stocks?A stock usually referred to as equity, is a type of investment that denotes ownership in a portion of the issuing company. Shares, also known as units of stock, entitle their owners to a share of the company's assets and income in proportion to the number of shares they possess.
Common stock and preferred stock are the two primary categories of stocks.
Owners of common stock are entitled to dividends and the right to vote at shareholder meetings.
Common stockholders often do not have voting rights, while preferred stockholders typically get dividend payments ahead of time and are given preference over common investors in the event of a firm bankruptcy and asset liquidation.
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The key in using expert opinion to help forecast demand is ________; that is, comparing estimates produced by different sources. morphing indemnification simulation triangulation modeling
Answers
The key in using expert opinion to help forecast demand is triangulation; that is, comparing estimates produced by different sources.
What is triangulation?Triangulation refers to a strategy, used by researchers to test the validity through collection of information from various sources.
In other words, triangulation is a method of finding the location of an object based on measurements made from two other locations
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when you say, " i know what my dog is thinking," you are practicing introspection by analogy.
Answers
Answer:
Actually, as an AI language model, I don't possess personal experiences or a physical body, so I don't have a dog or the ability to introspect like humans do.
Explanation:
When I generate responses, I rely on patterns and information from the data I was trained on, rather than personal subjective experiences or introspection.
Introspection refers to the process of examining one's own thoughts, feelings, and experiences.
It involves self-reflection and awareness of one's mental states. While humans can engage in introspection, machines like me rely on data and algorithms to process and generate information.
So, when I respond to a statement like "I know what my dog is thinking," it's not based on my own introspection but rather the knowledge I've been trained on regarding dog behavior and communication.
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pricing is the determination of an exchange price at which the seller perceives optimum value for a good or service.
true
false
Answers
Pricing is the process of choosing an exchange rate at which the seller believes their product or service offers the best value. is true assertion
What is the value?Values are the benchmarks or ideals by which we judge the acts, traits, possessions, or circumstances of others. Values that are embraced by many include those of beauty, honesty, justice, peace, and charity.
Pricing is the process of establishing an exchange rate at which both the buyer and the seller consider a good or service to be worth the most money. The amount that buyers and sellers value are ready to accept is known as the exchange price.
Therefore, The vendor feels that their good or service is the best value. is accurate statement
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amex inc. is a worldwide company that specializes in high growth industries. it acts as a global marketer for small manufacturers of medical products, telecommunications products, and data management products. amex inc. is an example of a(n):
Answers
Amex Inc. is, given that they are a worldwide company, an example of a global conglomerate, also known as a multinational corporation (MNC).
What are global conglomerates ?A global conglomerate is a company that operates in multiple countries and specializes in a range of diverse industries. These companies often have multiple subsidiaries and brands that operate under their umbrella, and they may engage in a wide range of activities, from manufacturing and distribution to marketing and research and development.
In the case of Amex Inc., the company operates as a global marketer for small manufacturers of medical products, telecommunications products, and data management products.
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During an economic recession the federal reserve banks will most likely react by —.
Answers
To ward off a recession, the Fed has a number of monetary policy tools at its disposal. Through open market operations (OMO), like as quantitative easing (QE).
the Fed may buy additional types of assets, which can lower interest rates to boost demand and increase the amount of money in circulation. The American central bank is known as the Federal Reserve System.
It carries out five general tasks to advance the well-being of the American economy and, more broadly, the public interest.
The Federal Reserve manages the country's monetary policy to encourage maximum employment, stable prices, and moderate long-term interest rates in the U.S. economy. It also works to maintain the stability of the financial system and actively monitors and engages in domestic and international affairs in order to reduce and contain systemic risks.
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Think about a consumer with a utility function given by u=x1x2, he is facing a budget constraint: p1x1+p2x2<= I.
A) Please derive the Marshallian demand functions for x1 and x2.
B) How much of each good will the consumer purchase if I =8, p1=1 and p2=4?
Answers
Given that the consumer has a utility function given by `u = x1 * x2` and is facing a budget constraint `p1 * x1 + p2 * x2 ≤ I`.We are to derive the Marshallian demand functions for `x1` and `x2` and determine how much of each good will the consumer purchase if `I = 8`, `p1 = 1` and `p2 = 4`.Solution:The consumer’s problem is to maximize their utility function `u = x1 * x2` subject to the budget constraint `p1 * x1 + p2 * x2 ≤ I`.The Lagrangian function `L` is given by;`L = x1 * x2 + λ [I − p1 * x1 − p2 * x2]
`Differentiating the Lagrangian function with respect to `x1`, `x2` and `λ` we get;`∂L/∂x1 = x2 − λp1 = 0` …..(1)`∂L/∂x2 = x1 − λp2 = 0` …..(2)`∂L/∂λ = I − p1 * x1 − p2 * x2 = 0` …..(3)Solving the above equations for `x1`, `x2` and `λ` gives the Marshallian demand functions.`x1 = I/(2 * p1)` and `x2 = I/(2 * p2)`Therefore, the demand functions for x1 and x2 are given by;x1 = I/(2 * p1) …..(4)x2 = I/(2 * p2) …..(5) Substituting the given values, `I = 8`, `p1 = 1` and `p2 = 4` into equations (4) and (5) above;x1 = 8/(2 * 1) = 4x2 = 8/(2 * 4) = 1 The consumer will purchase `4` units of `x1` and `1` unit of `x2` if `I = 8`, `p1 = 1` and `p2 = 4`.
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The average person in the United States consumes about 2.61
gallons of oil a day. If the average lifespan is 79 years, how many
people could that oil supply for life?
Answers
Given: The average person in the United States consumes about 2.61 gallons of oil a day, the average lifespan is 79 years.
Now, we have to find the number of people that could that oil supply for life.So, we can solve the question by following these steps:First, we have to calculate the total oil consumed by one person in a lifetime.Total oil consumed by one person in a day = 2.61 gallons.Total oil consumed by one person in a year = 2.61 × 365 gallons= 952.65 gallons Total oil consumed by one person in 79 years = 952.65 × 79 = 75255.35 gallons.So, one person consumes 75255.35 gallons in a lifetime.Now, we have to calculate the number of people that could that oil supply for life. To find that, we will divide the total oil supply by the oil consumed by one person.
Total oil supply = ?Number of people that could that oil supply for life = ?So,Number of people that could that oil supply for life = Total oil supply / Oil consumed by one person So, Total oil supply = Oil consumed by one person × Number of people that could that oil supply for life Number of people that could that oil supply for life = Total oil supply / Oil consumed by one person We know that the population of the US is around 331 million people.So, 75255.35 gallons is sufficient for 75255.35 / 331 = 227 people for life. Therefore, the answer is 227.
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