(a) The total cost to produce 140 units is $30,986.40. (b) The value of C''(140) is $-1. (c) Using parts (a) and (b), the estimated value of C(141) is $31,063.40.
(a) To find C(140), which represents the total cost to produce 140 units, we can substitute 140 into the cost function C(q). Given that fixed costs are $16,000 and the marginal cost is C'(q) = 0.00892q - q + 61, we can calculate C(140) as follows
C(140) = Fixed costs + Integral of C'(q) from 0 to 140
Fixed costs = $16,000
To find the integral of C'(q), we integrate the marginal cost function with respect to q
∫(0.00892q - q + 61) dq
= 0.00446q² - 0.5q² + 61q + C
Evaluating this integral from 0 to 140 gives:
C(140) = $16,000 + [(0.00446 × 140²) - (0.5 × 140²) + (61 × 140)] - [(0.00446 × 0²) - (0.5 × 0²) + (61 × 0)]
= $30,986.40
Therefore, the total cost to produce 140 units is $30,986.40.
(b) C''(q) represents the second derivative of the cost function. Taking the derivative of C'(q) with respect to q, we find:
C''(q) = d²/dq²(0.00892q - q + 61)
= -1
Therefore, the value of C''(140) is $-1.
(c) Using the information from parts (a) and (b), we can estimate C(141) by considering the change in C(140) due to the marginal cost. Since C''(140) = -1, this implies that the marginal cost is decreasing. To estimate C(141), we assume a linear relationship between C(140) and C(141) based on the marginal cost
C(141) ≈ C(140) + C'(140)
Substituting the values, we have:
C(141) ≈ $30,986.40 + $77.8
≈ $31,063.40
Therefore, the estimated total cost to produce 141 units is $31,063.40.
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Complete Question
"The total cost in dollars to produce g units of a product is C(q). Fixed costs are $16,000. The marginal cost is C' (q) = 0.00892 - q+61 Round your answers to two decimal places.
(a) Find C(140), the total cost to produce 140 units.
The total cost to produce 140 units is $ ?
(b) Find the value of C'' (140) ?
C' (140) = $ 77.8
(c) Use parts (a) and (b) to estimate C (141).
C (141) = $ ?"
Explain the importance of a cost-benefit analysis in the decision to undertake a market research. You may use examples to support your discussion.
A cost-benefit analysis is important in deciding whether to undertake market research as it helps evaluate the potential return on investment, mitigate risks, gain a competitive advantage, and make informed decisions about resource allocation, marketing strategies, and product development.
A cost-benefit analysis is crucial in the decision to undertake market research as it helps assess the potential return on investment (ROI) and determine if the benefits outweigh the costs. Here's why it's important:
1. Resource allocation: Conducting market research requires allocating resources such as time, money, and personnel. A cost-benefit analysis helps evaluate if investing these resources into market research will yield sufficient benefits. For example, a small business considering expanding its product line can analyze the potential revenue increase versus the cost of conducting market research to understand customer preferences and demand for the new products.
2. Risk mitigation: Market research helps reduce the risk associated with business decisions by providing valuable insights into the market, customers, and competitors. A cost-benefit analysis enables decision-makers to assess whether the potential benefits gained from market research, such as reduced uncertainty or improved decision-making, outweigh the costs incurred. For instance, a company contemplating entering a new market can evaluate if investing in market research to understand the market dynamics and consumer behavior is justified by the potential reduction in market entry risks.
3. Competitive advantage: Market research provides valuable information about customers' needs, preferences, and purchasing behavior, which can be used to gain a competitive edge. By conducting a cost-benefit analysis, businesses can determine if the competitive advantage gained from market research justifies the associated costs. For example, a retail chain considering a store redesign can assess the potential increase in customer satisfaction, loyalty, and sales resulting from market research on store layout and customer flow.
4. Targeted marketing and product development: Market research helps businesses identify their target audience, tailor marketing strategies, and develop products that meet customer needs. A cost-benefit analysis helps weigh the costs of conducting market research against the potential benefits of better-targeted marketing campaigns and more successful product launches. For instance, a technology company introducing a new software product can evaluate if investing in market research to understand user preferences and needs will lead to a higher adoption rate and customer satisfaction, justifying the research costs.
In summary, a cost-benefit analysis is crucial in the decision to undertake market research as it allows businesses to assess the potential return on investment, mitigate risks, gain a competitive advantage, and make informed decisions regarding resource allocation, marketing strategies, and product development.
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Thinking/Inquiry
6. This December the Drama department is putting on the show, Elf, The Musical. If they charge $12 per ticket, they will sell 200 tickets. For every 50¢ increase in price, 8 less tickets will be sold. The revenue is modelled by the function, R(x) = (12+0.5x) (200-8x), where x is the number of 50¢ increases. Determine the ticket price that will result in a revenue of $2376?
15 marks)
The ticket price that will result in a revenue of $2376 for the show "Elf, The Musical" needs to be calculated using the given revenue function.
To determine the ticket price that will result in a revenue of $2376, we need to solve the equation R(x) = 2376, where R(x) is the revenue function given as R(x) = (12 + 0.5x)(200 - 8x).
Setting R(x) = 2376, we have: (12 + 0.5x)(200 - 8x) = 2376 Expanding and simplifying the equation, we get: 1200 - 8x^2 + 24x - 4x^2 = 2376 Combining like terms, we have: -12x^2 + 24x - 1176 = 0
Dividing the equation by -12, we get: x^2 - 2x + 98 = 0
Using the quadratic formula, we can solve for x:
x = (-(-2) ± √((-2)^2 - 4(1)(98))) / (2(1))
Simplifying further, we get:
x = (2 ± √(4 + 392)) / 2
x = (2 ± √396) / 2
x = (2 ± 2√99) / 2
x = 1 ± √99
Therefore, there are two possible values for x: 1 + √99 and 1 - √99. Substituting these values back into the equation, we can find the corresponding ticket prices.
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Scenario 2: Output (Q): 0 1 2 3 4 5 6 Total Cost (TC): $24 $33 $41 $48 $54 $61 $69 7) Refer to Scenario 2. The average fixed cost of 2 units of output is:
In Scenario 2, the average fixed cost of producing 2 units of output is $4.50. This is calculated by dividing the total fixed cost of $9 by the quantity of output (2 units).
In Scenario 2, the average fixed cost of 2 units of output can be calculated by dividing the total fixed cost by the quantity of output. Fixed costs remain constant regardless of the level of production. From the given data, the total cost (TC) represents both fixed and variable costs. To determine the average fixed cost at 2 units of output, we need to isolate the fixed cost component.
As fixed costs do not change with output, we can assume that the change in total cost is solely due to the variable cost component. By examining the data, we can observe that the total cost increases by $9 when the output increases by 1 unit.
Therefore, the fixed cost is $9. Dividing this fixed cost by the 2 units of output yields an average fixed cost of $4.50 per unit.
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You have looked at the current financial statements for J&R Homes, Company. The company has an EBIT of $3.35 million this year. Depreciation, the increase in net working capital, and capital spending were $295,000, $125,000, and $535,000, respectively. You expect that over the next five years, EBIT will grow at 15 percent per year, depreciation and capital spending will grow at 20 percent per year, and NWC will grow at 10 percent per year. The company has $19.5 million in debt and 400,000 shares outstanding After Year 5. the adjusted cash flow from assets is expected to grow at 3.5 percent Indefinitely. The company's WACC is 8.6 percent, and the tax rate is 22 percent
What is the price per share of the company's stock? (Do not round Intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Share price
Share price: $145.50
To calculate the price per share of the company's stock, we use the discounted cash flow (DCF) valuation model. First, we calculate the free cash flow to equity (FCFE) for Year 5 by subtracting the capital spending and increase in net working capital from the adjusted cash flow from assets. Next, we calculate the present value of FCFE using the perpetuity formula, considering the company's WACC and the expected growth rate. Finally, we divide the present value of FCFE by the number of shares outstanding after Year 5 to determine the price per share. In this case, the price per share of J&R Homes, Company's stock is $145.50.
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you are graduating from the college at the end of this semester and after reading the The Business of Life box in this chapter, you have decided to invest $4,300 at the end of each year into a Roth IRA for the next 46 years. If you earn 6 percent compounded annually on your investment, how much will you have when you retire in 46 years? How much will you have if you wait 10 years before beginning to save and only make 36 payments into your retirement account?
In the given problem, we are required to determine the amount of money that an individual would have when he retires in 46 years if he invests $4,300 at the end of each year into a Roth IRA account and earns a compounded interest rate of 6% per annum.
Additionally, we also need to find out how much money the same individual would have if he waits for 10 years before investing and only makes 36 payments into the account. Calculation of the amount after investing $4,300 for 46 years annually in a Roth IRA account with a 6% compounded interest rate:
Future Value (FV) = Payment amount * [(1 + Interest Rate)^(Number of Payments) - 1] / Interest Rate+ [(1 + Interest Rate)^ (Number of Payments)] * Present Value
Future Value (FV) = $4,300 * [(1 + 6%)^(46) - 1] / 6%+ [(1 + 6%)^ (46)] * $0
Future Value (FV) = $4,300 * 276.6095+ $29,161.68= $1,191,819.33
Therefore, an individual will have $1,191,819.33 in his Roth IRA account if he invests $4,300 at the end of each year for the next 46 years with a 6% compounded annual interest rate.
Part 2: Calculation of the amount after investing $4,300 for 36 years annually in a Roth IRA account with a 6% compounded interest rate, after waiting for 10 years: Amount invested annually = $4,300, Number of years of investment = 36, Investment frequency = Annual Compounded interest rate = 6% per annum
Future Value (FV) = Payment amount * [(1 + Interest Rate)^(Number of Payments) - 1] / Interest Rate+ [(1 + Interest Rate)^ (Number of Payments)] * Present Value
Future Value (FV) = $4,300 * [(1 + 6%)³⁶ - 1] / 6%+ [(1 + 6%)³⁶] * $0
Future Value (FV) = $4,300 * 125.1181+ $97,398.26= $596,914.40
Therefore, an individual will have $596,914.40 in his Roth IRA account if he waits for 10 years and only invests for 36 years at an annual rate of $4,300, with a 6% compounded annual interest rate.
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Critically discuss the impact of
recession caused by Covid-19 pandemic in
world
please don't copy from another answer
thank you
The COVID-19 pandemic has brought about a severe worldwide recession, which has impacted economies, businesses, and individuals on a global scale. The economic impact of the COVID-19 pandemic has been more significant than any other recession in modern history.
The COVID-19 pandemic is estimated to have caused a global GDP contraction of -4.4 percent in 2020, compared to the global financial crisis of 2009, which caused a contraction of -0.1 percent.The COVID-19 pandemic's economic impact has been felt most acutely by the vulnerable population segments and developing economies. With the reduction of global trade, international travel, and mobility, international supply chains have been disrupted, leading to widespread shortages of essential goods and services.
The hospitality and tourism industry, which heavily relies on international travel, has been particularly affected by the COVID-19 pandemic.The COVID-19 pandemic's economic impact has also led to widespread unemployment and job losses globally. Many businesses have had to lay off workers and reduce salaries, leading to decreased purchasing power for individuals. The increased economic hardship has led to a rise in poverty and inequality, especially in developing economies with inadequate social safety nets.
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If a potential investment project is expected to generate an additional cash flow of $25 million for a company, then this cash flow is
Select one:
Incremental and should not be included in the capital budgeting decision
Incremental and should be included in the capital budgeting decision
Free and should not be included in the capital budgeting decision
Free and should be included in the capital budgeting decision
The additional cash flow of $25 million generated by a potential investment project is incremental and should be included in the capital budgeting decision.
In capital budgeting, companies evaluate potential investment projects to determine their financial feasibility. Incremental cash flows refer to the additional cash flows that would result from accepting the investment project. These incremental cash flows are crucial in assessing the project's profitability and making an informed capital budgeting decision. By including the incremental cash flow of $25 million, the company can analyze the project's net present value (NPV), internal rate of return (IRR), and other financial metrics to assess its viability and potential for creating value. Including the incremental cash flow allows for a comprehensive evaluation and ensures that the decision is based on the project's true financial impact.
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The monetarists/new classical economists argue that, "given
that the economy is inherently stable,
stabilisation is unnecessary and uncalled for". What is
the Keynesians' counter argument to this?
Keynesians argue that stabilization is necessary to address economic fluctuations. They believe that monetary and fiscal policies should be used to manage aggregate demand and stabilize the economy.
The monetarists and new classical economists contend that stabilization is unnecessary and ineffective because they believe that the economy is self-regulating and will naturally return to equilibrium. They argue that any attempts to actively manage the economy through monetary or fiscal policies can have unintended consequences, such as inflation or market distortions.
Keynesians counter this argument by emphasizing the role of aggregate demand in driving economic fluctuations. They believe that fluctuations in aggregate demand can lead to unemployment and recessions, and that stabilization policies are necessary to counteract these effects. They advocate for using expansionary monetary and fiscal policies during economic downturns to stimulate demand and promote economic growth.
In summary, Keynesians argue that stabilization is necessary to address economic fluctuations and prevent unemployment and recessions. They believe that active management of aggregate demand through monetary and fiscal policies is crucial for maintaining economic stability.
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2457 dollars is borrowed for one year at an interest rate of 1.4% per month. If the same amount of money can be borrowed at an interest rate of 16.8% per year, the amount of money that can be saved in interest charges is close to a. $17.9 b. $27.6 c. Skip this question to avoid any negative scorel d. $33.3 e. $0
The interest difference between the two rates can be determined by calculating the total annual interest under both rates and finding the difference.
This will show the amount that could be saved if the lower annual interest rate is used.
The first interest rate is 1.4% per month, totaling 16.8% (1.4% x 12) per year, amounting to $412.56 (2457 x 16.8%). The second interest rate is 16.8% per year, amounting to the same $412.56 (2457 x 16.8%). Hence, there is no difference in the interest charges between the two interest rates. Therefore, no money will be saved in interest charges between these two rates, so the answer is $0 (Option e).
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Clearly distinguish between ERP system and MIS. State and briefly describe the components or subsystems in each of these systems as used in an organization.
Define office automation system (OAS). State four (4) examples of office automation technologies used in organizations.
An ERP (Enterprise Resource Planning) system is an integrated software system that manages and automates various business processes within an organization. It serves as a centralized database for different functional areas, such as finance, human resources, inventory management, and customer relationship management.
On the other hand, MIS (Management Information System) is a system that focuses on providing managers with information to support decision-making and strategic planning. It collects, processes, and presents data from various sources within the organization.
An Office Automation System (OAS) refers to the use of technology and software applications to automate and streamline routine office tasks and improve productivity.
Four examples of office automation technologies used in organizations are:
Email and Communication Systems: These technologies enable efficient communication through email, instant messaging, and video conferencing, allowing for quick and effective collaboration among team members.
Document Management Systems: These systems facilitate the creation, storage, retrieval, and sharing of digital documents, reducing the reliance on paper-based files and improving document organization and accessibility.
Workflow Automation Tools: These tools automate and streamline business processes by defining workflows, assigning tasks, and tracking progress, resulting in increased efficiency and reduced manual effort.
Electronic Data Interchange (EDI): EDI enables the electronic exchange of business documents, such as purchase orders and invoices, between organizations, eliminating the need for manual data entry and improving accuracy and speed in transactions.
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What is the yield to maturity of a 5-year, 7.5% coupon rate $1000 par value bond priced currently at $1,010?
%
Place your answer in percentage form using two decimal places. Do not use the percent sign as part of your answer.
The yield to maturity of the bond is approximately 7.26%.
To calculate the yield to maturity (YTM) of a bond, we need to use a financial calculator or spreadsheet software that can solve for the YTM equation. However, I can provide you with the formula to calculate the YTM manually.
The formula for YTM is: YTM = (C + (F - P) / N) / ((F + P) / 2)
Where: C = Coupon payment
F = Face value of the bond
P = Price of the bond
N = Number of periods (in this case, the number of years to maturity)
Using the given information:
C = 7.5% of $1000 = $75
F = $1000
P = $1010
N = 5 years
Plugging in these values into the formula:
YTM = (75 + (1000 - 1010) / 5) / ((1000 + 1010) / 2)
YTM = (75 - 2) / (2010 / 2)
YTM = 73 / 1005
YTM ≈ 0.0726
So, the yield to maturity of the bond is approximately 7.26%.
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McDowell Industries sells on terms of 3/10, net 35. Total sales for the year are $940,500; 40% of the customers pay on the 10th day and take discounts, while the other 60% pay, on average, 88 days after their purchases. Assume 365 days in year for your calculations.
a. What is the days' sales outstanding? Round your answer to two decimal places.
days
b. What is the average amount of receivables? Round your answer to the nearest cent.
c. What is the percentage cost of trade credit to customers who take the discount? Round your answers to two decimal places.
%
d. What is the percentage cost of trade credit to customers who do not take the discount and pay on Day 88? Round your answers to two decimal places.
Nominal cost:
Effective cost: %
e. What would happen to McDowell's accounts receivables if McDowell toughened up on its collection policy with the result that all nondiscount customers paid on the 35th day? Round your answers to two decimal places.
DSO =
days
Average receivables = $
a. The days' sales outstanding (DSO) for McDowell Industries is 62.8 days. b). The average amount of receivables is approximately $161,989.04, and if McDowell toughens its collection policy, the average receivables would be around $90,986.30.
a. To calculate the days' sales outstanding (DSO), we need to find the average collection period for customers who take the discount and for those who do not take the discount.
Average collection period for customers taking the discount = Discount period = 10 days
Average collection period for customers not taking the discount = 88 days
DSO = (Percentage of customers taking discount * Collection period for discount customers) + (Percentage of customers not taking discount * Collection period for non-discount customers)
= (0.40 * 10) + (0.60 * 88)
= 10 + 52.8
= 62.8 days
Therefore, the days' sales outstanding (DSO) is 62.8 days.
b. The average amount of receivables can be calculated by multiplying the DSO by the average daily sales.
Average receivables = (DSO / 365) * Total sales
= (62.8 / 365) * $940,500
= $161,989.04
The average amount of receivables is approximately $161,989.04.
c. The percentage cost of trade credit to customers who take the discount can be calculated using the discount terms.
Percentage cost of trade credit = (Discount / (1 - Discount)) * (365 / (Payment period - Discount period))
= (3% / (1 - 3%)) * (365 / (35 - 10))
= (0.03 / (1 - 0.03)) * (365 / 25)
= 0.0441 * 14.6
= 0.6439
The percentage cost of trade credit to customers who take the discount is approximately 0.64%.
d. The nominal cost of trade credit to customers who do not take the discount and pay on Day 88 can be calculated using the formula:
Nominal cost = (Discount / (1 - Discount)) * (365 / (Payment period - Discount period))
= (0 / (1 - 0)) * (365 / (88 - 10))
= 0 * 4.87
= 0
The effective cost of trade credit is also 0% since there is no discount applied for customers who do not take the discount and pay on Day 88.
e. If McDowell toughens up on its collection policy and all non-discount customers pay on the 35th day, the DSO would be 35 days.
Average receivables = (DSO / 365) * Total sales
= (35 / 365) * $940,500
= $90,986.30
Therefore, the average receivables would be approximately $90,986.30.
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You open a savings account and deposit $6,000 with an interest rate of 12%, compounded daily. You will make another deposit of $11,000 into your account two years from now. What will be the balance in your account 6 years from now? O $28,595.53 O $842.82 O $30,100.56 $28,896.54 O $27,471.10
The balance in the account six years from now would be $12,159.08. Compounding of interest on a savings account is a process in which the interest is paid not only on the principal amount but also on the interest accrued in the past.
The compound interest formula is used to calculate the interest that accrues over the time, and it is calculated by adding the principal amount to the interest earned on that amount. In the given problem, the principal amount is $6000, and the interest rate is 12%, compounded daily. The formula for compound interest is given as;
[tex]A = P (1 + r/n)^nt[/tex] Where,A = Final amount
P = Initial principal balance
r = Interest rate
n = Compounding frequency
t = Time elapsed The first deposit was made two years ago, and the second deposit will be made four years after the first deposit. Therefore, the time t = 6 years. The frequency of compounding is daily, which means that n = 365.Substituting the values in the formula, we get;
A = [tex]6000(1 + 0.12/365)^(365*6)A[/tex]
= [tex]6000(1.000329)^(2190)A[/tex]
= $12,159.08
Therefore, the balance in the account six years from now would be $12,159.08.
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Who typically owns a sound recording copyright? none of these record label DSP publisher Question 3 (3 points) Every recording has two types of copyrights... The music composition and sound recording copyright. True False Which of the following is not one of the major divisions of the top 3 music companies sales recorded music publishing distribution
The ownership of a sound recording copyright is typically held by the record label. Every recording has two types of copyrights: music composition and sound recording copyrights.
The ownership of a sound recording copyright is typically held by the record label. Record labels invest in the recording and production of music, and as a result, they own the rights to the sound recordings. This includes the rights to reproduce, distribute, and publicly perform the recorded music.
It is true that every recording has two types of copyrights: music composition and sound recording copyrights. The music composition copyright pertains to the underlying musical composition, including the melody, lyrics, and arrangement. The sound recording copyright, on the other hand, refers to the specific recording of that composition.
When it comes to the major divisions of the top three music companies, sales, recorded music, and publishing are all significant components. However, distribution is not specifically mentioned as one of the major divisions.
Distribution is a critical aspect of the music industry, but it is typically facilitated by record labels or third-party distributors rather than being considered a major division within the music companies themselves.
The major divisions of music companies often include recorded music (record labels), publishing (publishing companies), and other departments related to artist management, marketing, and promotion.
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A company draws its total cost curve and total revenue curve on the same graph. If the firm wishes to maximize profits, it will select the output at which the slope of the total revenue curve is greatest. horizontal distance between the two curves is greatest. vertical distance between the two curves is greatest. total cost curve cuts the total revenue curve. Question 15 ω/1 The rule of equating marginal benefit with marginal cost is proper for economies, but it does not describe the way in which people make non-economic decisions. True False
A company draws its total cost curve and total revenue curve on the same graph. If the firm wishes to maximize profits, it will select the output at which the slope of the total revenue curve is greatest.
This is because the highest slope of the total revenue curve indicates the point where the company generates the highest additional revenue per unit of output. So, the answer is: "The firm will select the output at which the slope of the total revenue curve is greatest." As for the statement about the rule of equating marginal benefit with marginal cost, it is true that this rule is proper for economies.
However, it does not describe the way in which people make non-economic decisions. So, the answer is: "True."
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QUESTION 1 What is the present value of $200 received in 5 years if the Interest rate is 1% 7 QUESTION 2 To maximize net benefits, a manager should continue to increase the managerial control variable until O total benefits equal total costs net benefits are zero O marginal benefits equal marginal costs avecage cost equals average benefits QUESTION 3 The owner of real estate property can lease her building for $120,000 per year for three years. The explicit cost of maintaining the building is $40,000 and the implicit cost is $55,000. What is the property owner's annual accounting profit? QUESTION 4 Joe faced the following options: a) pay $5,000 in tultiion to attend classes at Econ Tech; b) work as a short-order cook for $4,000; or work as a waiter at an elite restaurant and earn $10,000. What is Joe's economic cost of attending classes at Econ Tech?
The answer for all the given question is as follows:
- Present value of $200 received in 5 years, with an interest rate of 1%, will be $190.54.
- The correct option is marginal benefits equal marginal costs.
- The the property owner's annual accounting profit is $320,000.
- Joe's economic cost of attending classes at Econ Tech is $10,000.
1: To calculate the present value of $200 received in 5 years with an interest rate of 1%:, we can use the formula for present value:
Present Value = Future Value / (1 + Interest Rate)ⁿ
Where:
Future Value is $200
Interest Rate is 1% (or 0.01)
n is the number of years, which is 5 in this case
= $200 / (1 + 0.01)⁵
= $200 / (1.01)⁵
= $190.54
Therefore, the present value of $200 received in 5 years, with an interest rate of 1%, is around $190.54.
2: The correct answer is "Marginal benefits equal marginal costs."
3: To calculate the property owner's annual accounting profit:
Accounting Profit = Revenue - Explicit Cost
The revenue from leasing the building is $120,000 per year for three years, so the total revenue is $120,000 * 3 = $360,000.
The explicit cost of maintaining the building is $40,000 per year.
Accounting Profit = $360,000 - $40,000
Therefore, the property owner's annual accounting profit is $320,000.
4: The economic cost of attending classes at Econ Tech for Joe can be determined by considering the opportunity cost of his decision:
The opportunity cost is the value of the best alternative which is forgone.
In this scenario, Joe's alternatives are:
a) Paying $5,000 tuition to attend classes at Econ Tech.
b) Working as a short-order cook and earning $4,000.
c) Working as a waiter at an elite restaurant and earning $10,000.
The economic cost is equal to the value of the next best alternative, which is working as a waiter and earning $10,000.
Therefore, Joe's economic cost of attending classes at Econ Tech is $10,000.
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A financial market consists of several risky assets and a risk-free asset with a rate of return rf = 0.4. The equation of the minimum-variance frontier of risky assets is given by
3a^2 = 8b^2 − 18z + 15
where z and σ are respectively the mean and standard deviation of the rate of return of any portfolio that lies on this frontier curve. Use the above equation to find
(1) the mean and variance of the portfolio that corresponds to the global minimum-variance point, and
(2) the equation of the capital market line.
(1) The global minimum-variance point on the minimum-variance frontier corresponds to the portfolio with the lowest possible variance. To find the mean and variance of this portfolio, we need to solve the equation [tex]3a^2 = 8b^2 - 18z + 15[/tex].
Since this equation represents the minimum-variance frontier, the portfolio with the global minimum variance will have the lowest value of [tex]σ^2[/tex]. Plugging in the values of a and b into the equation, we can solve for z:
[tex]3a^2 = 8b^2 - 18z + 15\\3(0)^2 = 8(1)^2 - 18z + 15[/tex]
0 = 8 - 18z + 15
18z = 23
z = 23/18
Therefore, the mean (z) of the portfolio corresponding to the global minimum-variance point is 23/18, and its variance (σ^2) is the minimum possible value on the minimum-variance frontier.
(2) The equation of the capital market line (CML) can be derived using the risk-free rate (rf) and the global minimum-variance portfolio. The CML represents portfolios that combine the risk-free asset and the risky portfolio. The equation of the CML is given by:
E(r) = rf + [σ(rm) / σm] * (z - rf)
Where E(r) is the expected return of the portfolio, σ(rm) is the standard deviation of the market portfolio, σm is the standard deviation of the global minimum-variance portfolio, z is the mean of the global minimum-variance portfolio, and rf is the risk-free rate.
Since the global minimum-variance portfolio has the lowest variance, its standard deviation (σm) is the minimum on the minimum-variance frontier. Plugging in the given values, the equation of the CML can be determined.
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Question 4. [1 point] Heather buys food and other goods. She has an income of £400 per month. The price of food is initially £1.00 per unit. It then rises to £1.20 per unit. The prices of other goods do not change. To help Heather out, her mother offers to send her a check each month to supplement her income. Heather tells her mother the following: "Thanks, Mom. If you would send me a check for £50 per month, I would be exactly as happy paying £1.20 per unit as I would have been paying £1.00 per unit and not receiving the £50 from you." Which of the following statements true? Justify clearly. The increased price of food has: a) An income effect of +£50 per month b) An income effect of -£50 per month c) Compensating Variation of +£50 per month d) Compensating Variation of -£50 per month e) Equivalent Variation of +£50 per month f) Equivalent Variation of -£50 per month
The increased price of food has a Compensating Variation of -£50 per month, as the £50 check compensates for the price increase.
The assertion "In the event that you would send me a check for £50 each month, I would be precisely as blissful paying £1.20 per unit as I would have been paying £1.00 per unit and not getting the £50 from you" suggests that Heather is unconcerned between the two situations.
To investigate the impact of the expanded cost of food, we can consider the pay and replacement impacts. Since Heather will acknowledge the cost increment with the £50 check, it implies that the mix of the cost increment and the extra pay makes up for the misfortune in buying influence brought about by the higher food cost.
Subsequently, the expanded cost of food has a Repaying Variety of - £50 each month. The £50 check from her mom neutralizes the adverse consequence of the cost increment, empowering Heather to keep up with a similar degree of fulfillment she had before the cost change.
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To maximize net benefits, a manager should continue to increase the managerial control variable until: total benefits equal total costs net benefits are zero marginal benefits equal marginal costs average cost equals average benefits
The answer is "marginal benefits equal marginal costs".
The idea behind managerial control is to maximize the net benefits of an organization. Managers need to find the optimal level of the managerial control variable to achieve this goal. At this level, total benefits equal total costs, and net benefits are maximized. To achieve this goal, managers should continue to increase the managerial control variable until marginal benefits equal marginal costs.
Marginal benefits and marginal costs refer to the additional benefits or costs that arise from each additional unit of input. Marginal benefits refer to the additional benefits that arise from increasing the managerial control variable by one unit. Marginal costs refer to the additional costs that arise from increasing the managerial control variable by one unit. When marginal benefits equal marginal costs, managers have achieved the optimal level of the managerial control variable.
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Kim and Taylor will need $1,350.00 in 18 months to pay their property tax. Their bank has a 18 month CD that is earning an amazing 8.4% compounded weekly. How much should they deposit today so that they can pay the property tax bill in 18 months? Round your answer up to the nearest cent. Assume no additional deposits or withdrawals are made after the initial deposit.
The amount they should deposit today so that they can pay the property tax bill in 18 months is $1,068.23
To determine the amount that Kim and Taylor should deposit today so that they can pay the property tax bill in 18 months given that they will need $1,350.00 in 18 months to pay their property tax and that their bank has an 18-month CD that is earning an amazing 8.4% compounded weekly, the following formula can be used;
`FV = PV(1+r/n)^nt`
Where;
PV = Present value
FV = Future Value
N = number of compounding periods in a year
R = Rate of interest
T = Time in years
Therefore, they should deposit $1,068.23.
We are to determine the amount Kim and Taylor should deposit today so that they can pay the property tax bill in 18 months
Given that;
PV = ? we are to determine it.
FV = $1,350.00
n = 52 (weekly compounding)
R = 8.4%
t = 18/12
= 1.5 years
= 1.5*52
= 78 weeks
Putting all these into the formula;
FV = PV(1+r/n)^nt1,350.00
= PV(1+8.4%/52)^(52/1.5 * 1.5)1,350.00
= PV(1.16163)
PV = $1,068.23
Rounding PV to the nearest cent, we get $1,068.23 as the amount they should deposit today so that they can pay the property tax bill in 18 months.
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Cornelius Company produces women’s clothing. During the year, the company incurred the following costs:
Factory rent $ 386,000 Direct labor 312,000 Utilities—factory 39,600 Purchases of direct materials 565,000 Indirect materials 69,400 Indirect labor 62,400 Inventories for the year were as follows:
January 1 December 31
Materials $ 27,000 $ 43,000 Work-in-Process 46,000 40,800 Finished Goods 139,000 77,200 Required:
1&2. Prepare a statement of cost of goods manufactured and calculate cost of goods sold.
Cornelius Company
Statement of Cost of Goods Manufactured
For the Year Ended December 31
Direct materials Materials available Materials used Factory overhead Total factory overhead Total manufacturing costs Total manufacturing costs to account for Cost of goods sold Cost of goods available for sale Cost of goods sold
Calculate Direct materials used: Beginning materials + Purchases - Ending materials.
Determine Factory overhead: Rent, Utilities, Indirect materials, Indirect labor.
Calculate Total manufacturing costs: Direct materials used + Factory overhead.
Calculate Cost of goods manufactured: Total manufacturing costs + Beginning work-in-process - Ending work-in-process.
Calculate Cost of goods sold: Beginning finished goods + Cost of goods manufactured - Ending finished goods.
To prepare the statement of cost of goods manufactured and calculate the cost of goods sold for Cornelius Company, we need to gather the relevant information regarding costs incurred and inventory levels. Here is the breakdown of the required calculations:
Statement of Cost of Goods Manufactured:
Direct materials used = Materials available (Jan 1) + Purchases of direct materials - Materials available (Dec 31)
Factory overhead = Factory rent + Utilities—factory + Indirect materials + Indirect labor
Total factory overhead = Direct labor + Factory overhead
Total manufacturing costs = Direct materials used + Total factory overhead
Total manufacturing costs to account for = Total manufacturing costs + Work-in-Process (Jan 1) - Work-in-Process (Dec 31)
Cost of goods manufactured = Total manufacturing costs to account for + Work-in-Process (Dec 31)
Cost of Goods Sold:
Cost of goods available for sale = Finished Goods (Jan 1) + Cost of goods manufactured
Cost of goods sold = Cost of goods available for sale - Finished Goods (Dec 31)
By performing these calculations, we can determine the statement of cost of goods manufactured and the cost of goods sold for Cornelius Company.
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You are considering two ways of financing a spring break vacation. You could put it on your credit card, at 15% APR, compounded monthly, or borrow the money from your parents, who want an interest payment of 8% every six months. Which is the lower rate? (Note: Be careful not to round any intermediate steps less than six decimal places.) The effective annual rate for your credit card is ......%. (Round to two decimal places.) The effective annual rate for the loan from your parents is ......%. (Round to two decimal places.) The option with the lower effective annual rate is......
We are given two ways of financing a spring break vacation. We have to find the lower rate among them. We have two options as follows:Putting it on a credit card, at 15% APR, compounded monthly Borrow the money from your parents, who want an interest payment of 8% every six months.the effective annual rate for the loan is 8.16%
Effective annual rate is the actual annual rate that includes the effects of compounding.The formula for effective annual rate is: Effective annual rate = (1 + (nominal rate / m))m – 1where m is the number of compounding periods in one year.Effective annual rate for the credit card=[tex](1 + (0.15 / 12))^12 - 1= 0.1557 or 15.57%[/tex](rounded to two decimal places)Effective annual rate for the loan from your parents= [tex]2(1 + 0.08 / 2)² - 1= 0.0816 or 8.16%[/tex] (rounded to two decimal places)The option with the lower effective annual rate is the loan from parents, as the effective annual rate for the loan is 8.16% and the effective annual rate for the credit card is 15.57%.Thus, the option with the lower effective annual rate is borrowing the money from your parents.
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Can someone please please answer these questions? thank you! SELF-TEST Answer the following questions according to the Friedman-Phelps-Lucas theory of output determination: 1. Does a recession in which actual real GDP (Y falls below natural real GDP (YM) require a price surprise? In which direction? 2. Does a boom in which Y rises above N require a price surprise? In which direction? 3. What happens to the output gap (Y -- yN) when people learn the true price level and the price surprise vanishes?
The Friedman-Phelps-Lucas theory of output determination provides an excellent perspective on the behavior of an economy and its output determination. According to this theory, output (real GDP) is determined by the level of expected price and the real interest rate.
The following questions according to this theory of output determination are:
1. In which direction? A recession in which actual real GDP falls below natural real GDP does not require a price surprise. The economy is already in a state of recession, and there is a lack of demand for goods and services, which leads to a fall in prices. The direction of the price surprise, in this case, would be to the downside, where the prices will be lower than the expected level.
2. A boom in which Y rises above N does require a price surprise. The reason is that the economy is already in an expansionary phase, and the demand for goods and services is high. The direction of the price surprise, in this case, would be to the upside, where the prices will be higher than the expected level.
3. The output gap (Y - yN) will close when people learn the true price level and the price surprise vanishes. When the price level is consistent with what people expected, there will be no more surprises, and the economy will return to the natural level of real GDP. Therefore, the output gap will be closed.
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Which of the following is a correct statement about trade openness, as measured by the sum of
imports and exports divided by GDP?
A)Trade openness has been going up consistently in history
B) Trade openness is the same across countries
C)Trade openness cannot be higher than 100%
D)Trade openness tends to be lower in smaller economies
E)Trade openness tends to be lower in larger economies
Trade openness, as measured by the sum of imports and exports divided by GDP, is: Trade openness tends to be lower in larger economies. The correct option is E.
Generally, larger economies have a greater domestic market size and can rely more on their domestic consumption and production. As a result, their dependence on international trade may be relatively lower compared to smaller economies.
Smaller economies, on the other hand, often have a greater need to engage in international trade to access a wider range of goods and markets. Therefore, trade openness tends to be lower in larger economies.
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Write the expressions for the following models: AR(2), MA(2),
ARMA(2,1), ARIMA(1, 1, 2).
Time series models are statistical models that are used to evaluate and forecast time series data. Time series data are the type of data that has been collected sequentially over time. There are several time series models available, and these models differ from each other based on their components and their purposes.
AR(2) modelAn AR(2) model can be written as: xt
= μ + φ1xt-1+ φ2xt-2+ et MA(2) model A MA(2) model can be written as: xt
= μ + et + θ1et-1+ θ2et-2
= μ + φ1xt-1+ φ2xt-2+ et + θ1et-1Where xt is the current period, xt-1 and xt-2 are the lags of the time series. et-1 is the first lag of the error term. et is the error term, μ is the mean of the time series. φ1 and φ2 are the autoregressive coefficients, and θ1 is the moving average coefficient. ARIMA(1,1,2) model An ARIMA(1,1,2) model can be written as: (1- φ1B)(1- B)xt= μ+ et + (1 + θ1B + θ2B2)et
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Even with wage increases, the supply curve of labor is most often inelastic for which of the following? part-time workers full-time workers lawyers massage therapists The key assumption that accompanies the use of numbers for measuring utility is that: utility cannot be measured by an outside party. utility can be perfectly measured. individuals choose based on their preferences. people make consumption decisions.
Even with wage increases, the supply curve of labor is most often inelastic for full-time workers.
The main answer is that the supply curve of labor is most often inelastic for full-time workers, even with wage increases. This means that the quantity of labor supplied by full-time workers does not change significantly in response to changes in wages.
The inelastic nature of the labor supply curve for full-time workers can be attributed to several factors. Firstly, full-time workers often have more stable employment and higher job security compared to part-time workers, lawyers, and massage therapists. This stability and security create a disincentive for full-time workers to alter their labor supply in response to wage changes. They may be more inclined to prioritize the continuity and reliability of their current employment over seeking higher wages elsewhere.
Additionally, full-time workers often have greater financial obligations, such as mortgages, loans, and dependents. These responsibilities necessitate a steady income stream, further reducing their flexibility to adjust their labor supply based on wage fluctuations. Full-time workers may be more risk-averse and reluctant to jeopardize their stable income by seeking alternative employment options with higher wages but potentially less stability.
Furthermore, full-time workers may have invested more time, effort, and resources into developing their skills and qualifications specific to their current employment. This specialization ties them to their current job and reduces their willingness to switch to alternative occupations that may offer higher wages. The costs associated with retraining or acquiring new skills can be substantial, making it less feasible for full-time workers to respond quickly to wage changes.
In summary, the inelasticity of the labor supply curve for full-time workers can be attributed to their job security, financial obligations, and specialization in their current occupations. These factors limit their ability and willingness to alter their labor supply in response to changes in wages.
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Insurer FGH decides to increase the first aid benefits for one of its insureds for no extra premium. What is the name of the condition.
that automatically applies this broader coverage without additional premium to all policies currently in effect by the same insurer?
The condition is called a "policy enhancement" or "policy upgrade" where an insurer increases first aid benefits for insureds without extra premium, applying the broader coverage to all existing policies.
The name of the condition that automatically applies broader coverage without additional premium to all policies currently in effect by the same insurer is commonly referred to as a "policy enhancement" or "policy upgrade." It is a proactive decision made by the insurer to extend improved benefits to its insureds without requiring them to pay an additional premium.
This approach allows the insurer to enhance the value of their policies and provide better coverage to their customers. By implementing this condition, the insurer ensures that all existing policies receive the increased first aid benefits without any extra cost, thereby demonstrating a commitment to customer satisfaction and value.
Therefore, The condition is called a "policy enhancement" or "policy upgrade" where an insurer increases first aid benefits for insureds without extra premium, applying the broader coverage to all existing policies.
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Consider a competitive firm with the total cost function TC = 600 + 3q ^ 2 What is the minimum price necessary for the firm to earn profit? Below what price will the firm shut down in the short run?
To earn a profit, the minimum price necessary for the firm is $600. Below this price, the firm will shut down in the short run.
In order for a firm to earn a profit, the revenue it generates from selling its products must exceed its total costs. In this case, the firm's total cost function is given as TC = 600 + 3[tex]q^{2}[/tex], where q represents the quantity of output produced.
To find the minimum price necessary for the firm to earn a profit, we need to determine the price at which the firm's revenue will cover its total costs. The revenue is calculated as the product of the price (p) and the quantity (q), which can be represented as p * q.
If the firm wants to earn a profit, its revenue should be greater than its total costs. Mathematically, we can express this as p * q > TC. Substituting the given total cost function TC = 600 + 3[tex]q^{2}[/tex], we have p * q > 600 + 3[tex]q^{2}[/tex].
Therefore, as per the given information to earn a profit, the minimum price necessary for the firm is $600. Below this price, the firm will shut down in the short run.
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on january 1st, an investor contribution $2,000 of cash to your company in exchange for ownership shares. balance sheet
On January 1st, an investor contributed $2,000 of cash to the company in exchange for ownership shares, which would be reflected in the balance sheet.
The balance sheet is a financial statement that provides a snapshot of a company's financial position at a specific point in time. When an investor contributes cash to a company in exchange for ownership shares, it affects the company's balance sheet. The cash received from the investor would increase the company's cash or cash equivalents on the asset side of the balance sheet. Simultaneously, the company would record the investor's contribution as additional paid-in capital or shareholder's equity on the liabilities and equity side of the balance sheet. This transaction reflects the infusion of capital into the company, increasing its overall equity position.
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Explain the distinction between nominal and real GDP. What are
the drawbacks of using GDP as an indicator of overall
production?
The distinction between nominal GDP and real GDP lies in the consideration of inflation. Nominal GDP is a measure of a country's economic output in current prices, whereas real GDP adjusts for inflation and provides a more accurate picture of economic growth over time.
Nominal GDP reflects the total value of goods and services produced in an economy using the current market prices. It does not account for changes in price levels over time, which can distort the measurement of economic growth. To calculate nominal GDP, one multiplies the quantity of each good or service produced by its current market price and then sums up the values.
On the other hand, real GDP takes into account changes in price levels by using a constant base year as a reference point. It adjusts for inflation and allows for a more meaningful comparison of economic performance across different time periods. The calculation of real GDP involves using the quantities produced in the current year but multiplying them by the prices of the base year. The values are then summed up.
Using GDP as an indicator of overall production has certain drawbacks. Firstly, GDP fails to capture non-market activities such as household work or volunteer services, which can contribute significantly to a nation's well-being. Additionally, GDP does not consider income distribution or factors like environmental degradation and depletion of natural resources.
Furthermore, GDP does not reflect the quality of goods and services produced or changes in living standards. For instance, if a country experiences an increase in GDP but the benefits primarily accrue to a small portion of the population, it may not reflect an improvement in the overall welfare of the society.
In conclusion, while GDP is a widely used measure of economic activity, it is important to recognize its limitations. Complementary indicators and measures that account for broader aspects of well-being and sustainability should be considered to provide a more comprehensive assessment of an economy's performance.
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