Answer:
Yes we should go with this project because it has a positive NPV of $4,350
Explanation:
We need to calculate the net present value of the machine to decide whether to invest in the machine or not.
As per Given Data
Costs $270,000
Cash Inflows
Year 2 $100,000
Year 3 $150,000
Year 4 $75,000
Interest Rate = 6%
Net Present Value
As we know Net Present value is calculated by discounting each years cash flows using using the Weighted Average cost of Capital.
Year Cash Inflows Discount factor 13% Present values
Year 0 $(270,000) (1+6%)^-0 $(270,000)
Year 2 $100,000 (1+6%)^-2 $89,000
Year 3 $150,000 (1+6%)^-3 $125,943
Year 4 $75,000 (1+6%)^-4 $59,407
Net present value $4,350
On March 15, American Eagle declares a quarterly cash dividend of $0.045 per share payable on April 13 to all stockholders of record on March 30.
Required:
Record American Eagle's declaration and payment of cash dividends for its 226 million shares. (If no entry is required for a particular transaction/event, select "No Journal Entry Required" in the first account field. Enter your answers in dollars, not in millions (i.e. $5.5 should be entered as 5,500,000).)
Answer and Explanation:
The journal entries are shown below:
On March 15
Dividend Dr $10,170,000 (226 million shares × $0.045 per share)
To Dividend payable $10,170,000
(Being the dividend is declared)
For recording this we debited the dividend as it increased the balance of dividend and credited the dividend payable as it increased the liabilities
On March 30
No journal entry is required for recording of dividend
On April 13
Dividend payable $10,170,000
To cash $10,170,000
For recording this we debited the dividend payable as it decreased the liabilities and credited the cash as it reduced the assets
(Being the dividend payable is recorded)
Costs of $6,500 were incurred to acquire goods and make them ready for sale. The goods were shipped to the buyer (FOB shipping point) for a cost of $350. Additional necessary costs of $700 were incurred to acquire the goods. No other incentives or discounts were available. What is the buyer’s total cost of merchandise inventory?
Answer:
Total cost of merchandise inventory = $7,550
Explanation:
The total cost of merchandise inventory, is the sum total of all the costs incurred in the acquisition of the goods, and it is calculated as shown below:
cost of goods = $6,500
cost of shipping = $350
Additional necessary cost = $700
∴ Total cost of merchandise inventory = cost of goods + cost of shipping + Additional necessary cost
Total cost of merchandise inventory = 6,500 + 350 + 700 = $7,550
Brainliest for anyone if they get this CORRECT.
Answer:
UR FACE
Explanation:
magic
Answer:
6
Explanation:
Find the percentage for 24% of 25.
That's how I did mine.
General cultural factors driving global business are
A. the rise of a global workforce, global economies of scale, and global production and operations.
B. growth of a global village spurred by television, the Internet, and computerization.
C. the rise of the global workforce, political stability, and a global knowledge base.
D. global communication and transportation technologies, a global knowledge base, and global social norms.
E. the development of global markets, political stability, and a global workforce.
Answer:
D. global communication and transportation technologies, a global knowledge base, and global social norms.
Explanation:
Global business management process involves identifying, analyzing and planning a business at the international level.
General cultural factors driving global business are global communication and transportation technologies, a global knowledge base, and global social norms.
When starting up a business with the intention to break into the global market successfully, it is important and necessary to ensure the cultural factors driving a business are well managed.
The business should ensure it creates a medium for effective communication by using both the traditional and digital media such as television, radio, billboards, blogs etc. Efficient means of transportation or logistics should be developed for smooth export of their goods and services.
Also, having a well informed knowledge of their niche is key to the success of the business.
Lastly, the business should abide with the global social norms.
On January 1, 2021, Swifty Corporation had 106000 shares of its $5 par value common stock outstanding. On June 1, the corporation acquired 10300 shares of stock to be held in the treasury. On December 1, when the market price of the stock was $13, the corporation declared a 15% stock dividend to be issued to stockholders of record on December 16, 2021. What was the impact of the 15% stock dividend on the balance of the retained earnings account?
Answer:
Decrease by $186,615
Explanation:
The impact of the 15% stock dividend on the balance of the retained earnings account is shown below:-
Shares = 106000 - 10300
= 95,700
Dividend of 15% = 95,700 × 15%
= $14,355
Value of shares = Dividend × Market price of the stock
= $14,355 × $13
= $186,615
So, the retained earning will decrease by $186,615
The following account balances are taken from the December 31, 2018, financial statements of ABZ Advertising Company. The company uses accrual basis accounting. Advertising Revenue $ 58,322 Cash 51,907 Accounts Receivable 8,426 Interest Expense 2,530 Accounts Payable 5,500 Operating Expenses 47,241 Deferred Revenue 1,476 Equipment 22,746 Income Tax Expense 2,916 The following activities occurred in 2019: Performed advertising services on account, $69,000. Received cash payments on account, $13,400. Received deposits from customers for advertising services to be performed in 2020, $4,500. Made payments to suppliers on account, $5,500. Incurred $56,450 of operating expenses; $48,950 was paid in cash and $7,500 was on account and unpaid as of the end of the year. What is the balance of Accounts Receivable at December 31, 2019
Answer:
Check the explanation
Explanation:
Particulars Amt
Opening Cash 51907
Add: Cash Received (13400+4500) 17900
Less: Payment to supplier 5500
Less: Operating Expenses Paid 48950
Closing Cash Balance 15357
How are foreign exchange rates determined
Answer:
Currency prices can be determined in two main ways: a floating rate or a fixed rate. A floating rate is determined by the open market through supply and demand on global currency markets. ... 5 Therefore, most exchange rates are not set but are determined by on-going trading activity in the world's currency markets.
Answer: market forces for. a p e x
Explanation:
just did that bro
A Company manufactures clay molded pottery on an assembly line. Its standard costing system uses two cost categories, direct materials and conversion costs. Each product must pass through the Molding Department and the Finishing Department. Direct materials are added at the beginning of the production process. Conversion costs are allocated evenly throughout production. Data for the Assembly Department for August 2017 are: Work in process, beginning inventory: 3000 units Direct materials (100% complete) Conversion costs (40% complete) Units started during August 695 units Work in process, ending inventory: 500 units Direct materials (100% complete) Conversion costs (65% complete) Costs for August: Standard costs for Assembly: Direct materials $15 per unit Conversion costs $35.50 per unit Work in process, beginning inventory: Direct materials $12,400 Conversion costs $9450 What is the balance in ending work-in-process inventory
Answer:
Ending work-in-process inventory is $19,037.50
Explanation:
First Determine the Equivalent Units in ending work-in-process inventory in terms of direct materials and conversion costs
Direct materials ( 500 units × 100%) = 500 units
Conversion costs (500 units × 65%) = 325 units
Then determine the Value of ending work-in-process inventory
Direct materials ( 500 units × $15) = $ 7,500.00
Conversion costs (325 units × $35.50) = $ 11,537.50
Total = $19,037.50
Conclusion
Therefore, ending work-in-process inventory is $19,037.50
Your aunt is about to retire, and she wants to sell some of her stock and buy an annuity that will provide her with income of $53,000 per year for 30 years, beginning a year from today. The going rate on such annuities is 7.25%. How much would it cost her to buy such an annuity today
Answer:
Present Value= $641,494.12
Explanation:
Giving the following information:
Cash flow= $53,000 per year
Number of years= 30 years
Interest rate= 7.25%
First, we need to calculate the final value of the annuity:
FV= {A*[(1+i)^n-1]}/i
A= annual flow
FV= {53,000*[(1.0725^30)-1]} / 0.0725
FV= $5,237,351.32
Now, we can determine the present value:
PV= FV/(1+i)^n
PV= 5,237,351.32/ (1.0725^30)
PV= $641,494.12
Consider two ways of commuting in a crowded city: taking public transportation, such as subway and buses, or driving your own car.
A person who chooses to take public transportation in a crowded city imposes a _________ externality on drivers. A policy implication of this result is a _________ those who take public transportation.
Persons who choose to drive their own cars to get around in a crowded city impose a _______ externality on other drivers. A policy implication of this result is a ________ those who drive their own cars.
Answer:
Positive; Subsidy for
Negative; Tax on
Explanation:
An externality is the economic term that describes a cost or benefit incurred or received by a third party, over which said party has no control over its development.
When externalities result in a benefit for a certain group they are said to be positive and when it is detrimental it is said to be negative.
Taking public transportation in a crowded city is benefitial to drivers making this a positive externality. In order to encourage people to take public transportation, a subsidy for those who take transportation may be adopted.
On the other hand, people who choose to drive their own car impose a negative externality and may encourage a tax on those who drive their own car.
The single milling machine at Stout Manufacturing was severely overloaded last year. The plant operates eight hours per day, five days per week, and 50 weeks per year. Management prefers a capacity cushion of 15 percent. Two major types of products are routed through the milling machine. The annual demand for product A is 3000 units and 2000 units for product B. The batch size for A is 20 units and 40 units for B. The standard processing time for A is 0.5 hours/unit and 0.8 hours/unit for B. The standard setup time for product A is 2 hours and 8 hours for product B. How many new milling machines are required if Stout does not resort to any short-term capacity options
Answer:
If we assumes we setup machine for product A x times, and B y times, the total hours required is 0.5*3000 + 0.8*2000+ 2*x + 8 *y = 3100+2x+8y. Notice that due to the capacity restriction x has to be no smaller than 150 hours (3000/20) and y has to be no smaller than 50 hours (2000/40). so total required hours must exceed 3100+2*150+8*50=3800. The management prefer a 15% capacity cushion, which means the total duration prepared for the processing should be at least 3800*(1+15%)=4370 hours.
If one machine operates eight hours per day, five days per week and 50 weeks a year, it operates 5*8*50 = 2000 hours in total.
That's why we need 2 more machines ( 3 machines in total since 4370 > 2*2000).
Oriole Tire Co. just paid an annual dividend of $1.70 on its common shares. If Oriole is expected to increase its annual dividend by 3.10 percent per year into the foreseeable future and the current price of Oriole’s common shares is $19.65, what is the cost of common stock for Oriole? (Round intermediate calculations to 4 decimal places, e.g. 0.1555 and final answer to 2 decimal places, e.g. 15.25%.)
Answer:
Cost of common stock is 12.02%
Explanation:
The cost of common stock can be computed from share price formula given below:
share price=do*(1+g)/r-g
do is the dividend just paid which is $1.70
g is the expected dividend growth per year which is 3.10%
r is the cost of common stock which is unknown
share price is $19.65
by changing the subject of the formula:
r=do*(1+g)/share price+g
r=1.70*(1+3.10%)/19.65+3.10%
r=1.7527/19.65+3.10%
r=0.0892+3.10%=12.02%
The company's cost of capital which is also the cost of common stock is 12.02%
The required reserve ratio is 0.05. If the Federal Reserve buys $1,000,000 worth of bonds from a bond dealer who has her account at Bank XYZ above and she deposits the entire $1,000,000 into a checking account at Bank XYZ, what will be the new required and excess reserves for this bank (assume no new loans are made)? (Remember that required reserves are found by applying the required reserve ratio to the amount of total checkable deposits.)
Missing information:
total deposits in bank XYZ = $4,000,000
total reserves = $3,800,000
Answer:
the required reserve = $250,000
excess reserves = $4,550,000
Explanation:
required reserve ratio = 5%
the Fed buys $1,000,000 worth of bonds
the $1,000,000 are deposited entirely in bank XYZ
total checkable deposits will increase to $5,000,000
the required reserve = $5,000,000 x 5% = $250,000
excess reserves = total checkable deposits - total loans - required reserves = $5,000,000 - $200,000 - $250,000 = $4,550,000
Grab Manufacturing Co. purchased a 10-ton draw press at a cost of $183,000 with terms of 4/15, n/45. Payment was made within the discount period. Shipping costs were $4,300, which included $270 for insurance in transit. Installation costs totaled $12,900, which included $3,700 for taking out a section of a wall and rebuilding it because the press was too large for the doorway. The capitalized cost of the 10-ton draw press is: Multiple Choice $192,880. $190,880. $196,380. $197,880.
Answer:
$192,880
Explanation:
According to the scenario, computation of the given data are as follow:-
Cost of 10-ton draw press is $183,000 and if the cost paid before 15 days, there will be a 4% discount.
Discount Value is
= Cost of Draw Press × Discount Rate
= $183,000 × 4%
= $7,320
Total Capitalized Amount is
= (Total Cost of Draw Press - Discount Value) + Shipping Cost + Installation Cost
= ($183,000 - $7,320) + $4,300 + $12,900
= $175,680 + $4,300 + $12,900
= $192,880
According to the analysis, the capitalized cost of the 10-ton draw press is $192,880.
Because any cost which incurred for using an asset should be capitalized.
To encourage employee ownership of the company's common shares, KL Corp. permits any of its employees to buy shares directly from the company through payroll deduction. There are no brokerage fees and shares can be purchased at a 12% discount. During May, employees purchased 10,000 shares at a time when the market price of the shares on the New York Stock Exchange was $12 per share. KL will record compensation expense associated with the May purchases of:
Answer:
Dr Cash 105,600
Dr Compensation Expense 14,400
Cr Common Stock 10,000
Cr Paid-In Capital – Excess of Par 110,000
Explanation:
KL Corp Journal entry
Dr Cash 105,600
Dr Compensation Expense 14,400 (10,000*12*12%)
Cr Common Stock 10,000 (10,000*1)
Cr Paid-In Capital – Excess of Par 110,000
(10,000*(12-1))
The five-step procedure designed by ethics consultant Leonard H. Bucklin of Corporate-Ethics. US for investigating and solving ethics problems is known as a. the Bucklin Method. b. the Ethical Investigation Protocol. c. Business Process Pragmatism. d. Ethical Decision Determination.
The correct answer is C. Business Process Pragmatism
Explanation:
Leonard H. Bucklin was a recognized American attorney mainly known for his texts about laws, ethics, and related topics. In the field of Corporate-Ethics Bucklin designed a method with five different stages to deal with ethical problems. This method was known as the Business Process Pragmatism as it was a systematic approach to deal with ethical issues in business. Moreover, this method involved inquiring about the problem, discussing important aspects and possible solutions, deciding or selecting the best solution, justifying the solution, and evaluating the outcome.
11. a. Suppose David spends his income M on goods x1 and x2, which are priced p1 and p2, respectively. David’s preference is given by the utility function
(1, 2) = √1 + √2.
(i) Derive the Marshallian (ordinary) demand functions for x1 and x2. (25 marks)
(ii) Show that the sum of all income and (own and cross) price elasticity of demand
for x1 is equal to zero. (25 marks) b. For Jimmy both current and future consumption are normal goods. He has strictly convex and strictly monotonic preferences. The initial real interest rate is positive. If the real interest rate falls, in each of the following cases, argue what will happen to his period 2 consumption level? Clearly illustrate your argument on a graph.
(i) He is initially a borrower. (25 marks)
(ii) He is initially a lender. (25 marks)
Answer:
Explanation:
D
Wayne Industries is building a new prototype riding lawnmower especially for women. The marketing strategy for the product has been developed and presented. The lawnmower is now being tested rigorously. This step will ensure that the product meets all the CPSC product specifications and leaves little chance for any product liability issues. Which step int he new product development process is this?
A) After this stage, no changes can be made in any aspect of the product design, features, or composition.
B) At this stage, the functional features and the intended psychological characteristics are combined.
C) The new product at this stage can be distributed through a full-scale roll-out immediately.
D) The new lawnmower is at the introductory stage of the lifecycle.
E) The new-product idea is at the last stage of the development process.
Answer:
The answer is option E) The new-product idea is at the last stage of the development process.
Explanation:
The are several stages in the development of a new product idea. Beginning with initial idea generation all the way to the final evaluation stage.
The new prototype riding lawnmower especially for women designed by Wayne Industries is at the last stage of the development process.
The last stage of the development process also known as the Evaluation phase is characterized by:
Presenting the marketing strategy developed for the product.ensuring that the product meets all the CPSC product specifications and leaves little chance for any product liability issues.We can consider the case where wine producers in Chile ask the government to tax imported wines from France with a tax. They consider that this tax would increase both the State's tax revenue and employment in the Chilean wine industry. What kind of economic argument is this in relation to international trade? Do you agree or not with the argument presented by wine producers in Chile? If the state government adopts this position, does it consider it to be good economic policy or not? Briefly explain your answers using the concepts of international trade discussed in your Textbook.
Answer:
If the Government executes taxes on lavender trade from France (therefore creating French wine beloved than national wine), the local wine manufacturers would take pleasure in such a strategy because it would create French wine much economical (since it'll value extra) and therefore doubtless growth in local wine drinking. This might additional because additional service chances within the national wine region and conjointly rise the Government's government revenue (income from taxes on the wine trade). Such a procedure is hidden wanting i.e. an advocate procedure in expressions of Global trade wherever the govt. is protective the benefits of the native wine manufacturers by heavy imports.
If the Chilean wine trade isn't terribly inexpensive in relations of value, feature etc. and remains at an emergent phase then it's vital to safeguard the local trade from global competition.
Samco signed a 5-year note payable on January 1, 2018, of $ 475 comma 000. The note requires annual principal payments each December 31 of $ 95 comma 000 plus interest at 9%. The entry to record the annual payment on December 31, 2021, includes A. a debit to Interest Expense for $ 17 comma 100. B. a debit to Interest Expense for $ 42 comma 750. C. a credit to Cash of $ 137 comma 750. D. a credit to Notes Payable for $ 95 comma 000.
Answer:
Option A, a debit to Interest Expense for $ 17 comma 100 is correct
Explanation:
The principal amount on 1st January 2021 needs to be established since that would be the amount left after 2018,2019,2020 principals have been repaid
Principal at 1st January 2021=$475,000-($95,000*3)=$190000
Interest on principal in 2021=$190000 *9%=$17100
Total repayment in 2021=principal plus interest=$95,000+$17,100=$ 112,100.00
The $95,000 would be a debit to notes payable not credit hence option is wrong.
Only option A,a debit of $17,100 to interest expense is correct
Carlos is a 25% owner of CEBJ Builders, a company that specializes in residential construction. The other 75% of CEBJ is owned by his three brothers. During the year, Carlos spends 1,800 hours managing the operations of CEBJ. He also is the 100% owner of four rental properties and spends 125 hours a year maintaining the properties, more than any other individual. During the current year, the four properties generate a loss of $18,500. His adjusted gross income before considering the rental loss is $118,000.
What amount of the loss can Carlos deduct from the current year?
Answer:
$99,500
Explanation:
Adjusted gross income before considering the rental loss $118,000.
Less generated a loss of $18,500
Adjusted gross income $99,500
Carlos qualifies under the real estate professional exception due to the fact that he spends more than 50% of his personal service time in real property trade and the amount of time spent in real property trade is higher than 750 hours, he is as well the sole owner and spends more than 100hours.
Therefore the rental activity is not considered passive and he is allowed to offset the $18,500 loss against his active and portfolio income which is why Carlos'sadjusted gross income after considering the loss is $99,500 ($118,000 -$18,500)
You should meet with your academic adviser at least once a __________.
Group of answer choices
Answer:
Once a Semester
Explanation:
Advisors can help you decide if you want to minor in something, and what the requirements are. They can ensure you're odds of graduating in four years is on track, or give you special permissions to take certain classes.
Southern Rim Parts estimates its manufacturing overhead to be $318,000 and its direct labor costs to be $1,060,000 for year 1. The first three jobs that Southern Rim worked on had actual direct labor costs of $65,000 for Job 301, $90,000 for Job 302, and $175,000 for Job 303. For the year, actual manufacturing overhead was $399,000 and total direct labor cost was $834,000. Manufacturing overhead is applied to jobs on the basis of direct labor costs using predetermined rates.Required:a. How much overhead was assigned to each of the three jobs, 301, 302, and 303?b. What was the over- or underapplied manufacturing overhead for year 1?
Answer:
a. Job 301 = $19,500
Job 302 = $27,000
Job 303 = $52,500
b. Overhead applied for the year = $250,200
Under-applied overhead = $148,800
Explanation:
a. The computation of overhead was assigned to each of the three jobs, 301, 302, and 303 is shown below:-
Overhead application rate = Budgeted Overhead ÷ Application Base
Application base = Budgeted Overhead ÷ Budgeted Direct Labor costs
= $318,000 ÷ $1,060,000
= 0.3
Overhead assignment to jobs = Budgeted rate × Labor Cost
Job 301
= 0.3 × $65,000
= $19,500
Job 302
= 0.3 × $90,000
= $27,000
Job 303
= 0.3 × $175,000
= $52,500
b. The computation of over- or underapplied manufacturing overhead for year 1 is shown below:-
Overhead applied for the year = Total direct labor cost × Overhead rate
= $834,000 × 0.3
= $250,200
Under-applied overhead = Actual overhead - Applied overhead
= $399,000 - $250,200
= $148,800
• Why has the stock market declined so much?
We need a passage or something. not just the question
Melrose Company has an investment in bonds issued by Roscoe Industries that are classified as available-for-sale securities. The bonds were purchased at par. At December 31, Year 2, the Investment in Roscoe bonds account had a debit balance of $200,000, representing its amortized cost, and its Fair value adjustment account had a credit balance of $5,000. On December 31, Year 3, the amortized cost of those bonds had not changed, but the fair value of those bonds was $225,000.
Which of the following will be included in the related journal entry dated December 31, Year 3?
a. Debit to Fair value adjustment for $20,000.
b. Credit to Fair value adjustment for $20,000.
c. Debit to Fair value adjustment for $30,000.
d. Credit to Fair value adjustment for $30,000.
Answer:
c. Debit to Fair value adjustment for $30,000.
Explanation:
The Journal entry is shown below:-
On Dec 31,
Fair value adjustment account Dr, $30,000 ($225,000 + $5,000 - $200,000)
To Unrealized holding gain on available for sale securities $30,000
(Being unrealized holding gain is recorded)
Here we debited the fair value adjustment account as it decreased the liabilities and we credited the unrealized holding gain on available for sale securities as it increased the gain so the same is recorded .
A manufacturing company prepays its insurance coverage for a three-year period. The premium for the three years is $2,700 and is paid at the beginning of the first year. Eighty percent of the premium applies to manufacturing operations and 20% applies to selling and administrative activities. What amounts should be considered product and period costs respectively for the first full year of coverage?
Answer:
$720 and $180
Explanation:
According to the scenario, computation of the given data are as follows:
Premium for 3 years = $2,700
So, premium for 1 year = $2,700 ÷ 3 = $900 per year
Manufacturing operation percentage = 80%
Selling and administrative operation percentage = 20%
So, Premium for manufacturing operation = $900 × 80% = $720
And Premium for selling and admin operation = $900 × 20% = $180
Which of the following scenarios are potential candidates for the Chi-square test? Check all that apply. Group of answer choices Is there a relationship between gender and pet ownership? Is there a relationship between martial status (single, married, divorced, widowed) and political party affiliation (Democrat, Independent, Republican)? Is there a relationship between amount of credit card debt and employment status (unemployed, employed part-time, employed full-time)?
Answer:
A. Is there a relationship between gender and pet ownership?
B. Is there a relationship between marital status (single, married, divorced, widowed) and political party affiliation (Democrat, Independent, Republican)?
Explanation:
The chi squared test is a test in statistics used to establish the relationship between categorical variables. It seeks to compare the observed results in an experiment to the expected results. The test assumes that the variables being compared are independent of each other.
Categorical variables are descriptive and qualitative in nature. Numerical variables, on the other hand, deal with numbers. The amount of credit card debt is a numerical value, and therefore, does not qualify as a chi squared variable.
A translation adjustment (or translation gain) that is a consequence of translation of a functional currency that is different from the reporting currency should be:_______.
A. Included in net income in the period in which it occurs.
B. Deferred and amortized over a period not to exceed 40 years.
C. Deferred until a subsequent year when a loss occurs and offset it against that loss.
D. Included as a separate item in the equity section of the balance sheet.
Answer:
d
Explanation:
wild guess
Margie Company produces a single product and has provided the following data concerning its most recent month of operations: Selling price $ 88 Units in beginning inventory 0 Units produced 5,200 Units sold 4,900 Units in ending inventory 300 Variable costs per unit: Direct materials $ 12 Direct labor $ 23 Variable manufacturing overhead $ 2 Variable selling and administrative expense $ 5 Fixed costs: Fixed manufacturing overhead $ 161,200 Fixed selling and administrative expense $ 63,700 The total contribution margin for the month under variable costing is:
Answer:
$225,400
Explanation:
The computation of total contribution margin under variable costing is shown below:-
Sales (4900 × $88) $431,200
Less:Variable cost
Direct material (4900 × $12) ($58,800)
Direct labor (4900 × 23) ($112,700)
Variable manufacturing overhead
(4900 × 2) ($9,800)
Variable selling and administrative
expenses (4900 × $5) ($24,500)
Total variable expenses ($205,800)
Contribution margin $225,400
Therefore the total contribution margin under variable costing is $225,400
Suppose that output (Y ) in an economy is given by the following aggregate production function: Yt = Kt + Nt where Kt is capital and Nt is the population. Furthermore, assume that capital depreciates at rate δ and that savings is a constant proportion s of income. You may assume that δ > s. 1. Suppose that the population remains constant. Solve for the steady-state level of capital per worker. 2. Now suppose that the population grows at rate n. Solve for the steady-state level of capital per worker. 3. Based on your answer to part 2) above, solve for the steady-state growth rates (in terms of n) of the following: (a) capital per worker (b) output per worker (c) capital (d) output
Answer:
Check the explanation
Explanation:
Yt = Kt + Nt
Taking output per worker, we divide by Nt
Yt/Nt = Kt/Nt + 1
yt = kt + 1
where yt is output per worker and kt is capital per worker.
a) With population being constant, savings rate s and depreciation rate δ.
ΔKt = It - δKt
dividing by Nt, we get
ΔKt/Nt = It/Nt - δKt/Nt ..... [1]
for kt = Kt/Nt, taking derivative
d(kt)/dt = d(Kt/Nt)/dt ... since Nt is a constant, we have
d(kt)/dt = d(Kt/Nt)/dt = (dKt/dt)/Nt = ΔKt/Nt = It/Nt - δKt/Nt = it - δkt
thus, Capital accumulation Δkt = i – δkt
In steady state, Δkt = 0
That is I – δkt = 0
S = I means that I = s.yt
Thus, s.yt – δkt = 0
Then kt* = s/δ(yt) = s(kt+1)/(δ )
kt*= skt/(δ) + s/(δ)
kt* - skt*/(δ) = s/(δ)
kt*(1- s/(δ) = s/(δ)
kt*((δ - s)/(δ) = s/(δ)
kt*(δ-s)) = s
kt* = s/(δ -s)
capital per worker is given by kt*
b) with population growth rate of n,
d(kt)/dt = d(Kt/Nt)/dt =
= [tex]\frac{\frac{dKt}{dt}Nt - \frac{dNt}{dt}Kt}{N^{2}t}[/tex]
= [tex]\frac{dKt/dt}{Nt} - \frac{dNt/dt}{Nt}.\frac{Kt}{Nt}[/tex]
= ΔKt/Nt - n.kt
because (dNt/dt)/Nt = growth rate of population = n and Kt/Nt = kt (capital per worker)
so, d(kt)/dt = ΔKt/Nt - n.kt
Δkt = ΔKt/Nt - n.kt = It/Nt - δKt/Nt - n.kt ......(from [1])
Δkt = it - δkt - n.kt
at steady state Δkt = it - δkt - n.kt = 0
s.yt - (δ + n)kt = 0........... since it = s.yt
kt* = s.yt/(δ + n) =s(kt+1)/(δ + n)
kt*= skt/(δ + n) + s/(δ + n)
kt* - skt*/(δ + n) = s/(δ + n)
kt*(1- s/(δ + n)) = s/(δ + n)
kt*((δ + n - s)/(δ + n)) = s/(δ + n)
kt*(δ + n -s)) = s
kt* = s/(δ + n -s)
.... is the steady state level of capital per worker with population growth rate of n.
3. a) capital per worker. in steady state Δkt = 0 therefore, growth rate of kt is zero
b) output per worker, yt = kt + 1
g(yt) = g(kt) = 0
since capital per worker is not growing, output per worker also does not grow.
c)capital.
kt* = s/(δ + n -s)
Kt*/Nt = s/(δ + n -s)
Kt* = sNt/(δ + n -s)
taking derivative with respect to t.
d(Kt*)/dt = s/(δ + n -s). dNt/dt
(dNt/dt)/N =n (population growth rate)
so dNt/dt = n.Nt
d(Kt*)/dt = s/(δ + n -s).n.Nt
dividing by Kt*
(d(Kt*)/dt)/Kt* = s/(δ + n -s).n.Nt/Kt* = sn/(δ + n -s). (Nt/Kt)
[tex]\frac{sn}{\delta +n-s}.\frac{Nt}{Kt}[/tex]
using K/N = k
[tex]\frac{s}{\delta +n-s}.\frac{n}{kt}[/tex]
plugging the value of kt*
[tex]\frac{sn}{\delta +n-s}.\frac{(\delta + n -s)}{s}[/tex]
n
thus, Capital K grows at rate n
d) Yt = Kt + Nt
dYt/dt = dKt/dt + dNt/dt = s/(δ + n -s).n.Nt + n.Nt
using d(Kt*)/dt = s/(δ + n -s).n.Nt from previous part and that (dNt/dt)/N =n
dYt/dt = n.Nt(s/(δ + n -s) + 1) = n.Nt(s+ δ + n -s)/(δ + n -s) = n.Nt((δ + n)/(δ + n -s)
dYt/dt = n.Nt((δ + n)/(δ + n -s)
dividing by Yt
g(Yt) = n.(δ + n)/(δ + n -s).Nt/Yt
since Yt/Nt = yt
g(Yt) = n.(δ + n)/(δ + n -s) (1/yt)
at kt* = s/(δ + n -s), yt* = kt* + 1
so yt* = s/(δ + n -s) + 1 = (s + δ + n -s)/(δ + n -s) = (δ + n)/(δ + n -s)
thus, g(Yt) = n.(δ + n)/(δ + n -s) (1/yt) = n.(δ + n)/(δ + n -s) ((δ + n -s)/(δ + n)) = n
therefore, in steady state Yt grows at rate n.
