Answer: Inventory will fluctuate significantly during the year
Explanation:
If a make-to-stock manufacturing firm with highly seasonal demand follows a level production strategy, then the inventory will fluctuate significantly during the year.
When using a level production strategy, it should be noted that there will be an increase in the inventory during when there are low demand while there'll be a reduction in the inventory during the periods of high demand.
You sold a put contract on EDF stock at an option price of $.50 and an exercise price of $21. Today, EDF stock is selling for $20 a share and your option position was closed out. Ignoring transaction costs and taxes, what is your total profit
Answer:
-$50
Explanation:
Calculation to determine your total profit on this investment
Total profit = 1 × 100 × ($.50 - $21+ $20)
Total profit = 100×(-$0.5)
Total profit = -$50
Therefore your total profit on this investment is -$50
Mickley Company’s plantwide predetermined overhead rate is $20.00 per direct labor-hour and its direct labor wage rate is $15.00 per hour. The following information pertains to Job A-500: Direct materials $ 280 Direct labor $ 150 Required: 1. What is the total manufacturing cost assigned to Job A-500? 2. If Job A-500 consists of 70 units, what is the unit product cost for this job? (Round your answer to 2 decimal places.)
Answer and Explanation:
The computation is shown below;
1.
Total hours for job A - 500
= Direct labor ÷direct labor wage rate
= $150 ÷ $15
= 10
Total over head cost = overhead cost per labor hours × no. of labor hours
= $20 × 10
= $200
total manufacturing cost = Direct materials cost + Direct labor cost + Total over head cost
= $280 + $150 + $200
= $630
2.
Cost assigned to each unit
= total manufacturing cost ÷ number of units
= $630 ÷ 70
= $9
Holling Inc. uses the weighted-average method in its process costing. The following data concern the company’s Mixing Department for the month of December. Materials Conversion Work in process, December 1 $ 8,130 $ 9,128 Cost added to production in the Mixing Department during December $ 226,500 $ 284,232 Equivalent units of production for December 9,900 9,400 Required: Compute the cost per equivalent unit for materials and conversion for the Mixing Department in December. (Round your answers to 2 decimal places.)
Answer:
Statement of Cost per equivalent unit
Particulars Materials Conversion
Cost of beginning work in process $8,130 $9,128
Add: Costs added during the month $226,500 $284,232
Total cost A $234,630 $293,360
Number of equivalent units B 9,900 9,400
Cost per equivalent unit (A/B) $23.70 $31.21
Which of the following statements about a partnership is correct? Group of answer choices The personal assets of a partner are included in the partnership accounting records. A partnership is not required to file an information tax return. Each partner's share of income is taxable to the partnership. A partnership represents an accounting entity for financial reporting purposes.
Answer:
do you have a picture I can help you
1. Jupiter Explorers has $9,800 in sales. The profit margin is 5%. There are 4,500 shares of stock outstanding. The market price per share is $1.90.
What is the price-earnings ratio?
2. A firm has a return on equity of 18%. The total asset turnover is 1.7 and the profit margin is 6%. The total equity is $7,200.
What is the amount of the net income?
Answer:
17.43
132.19
Explanation:
Net profit margin is an example of a profitability ratio. It measures he ability of a firm to earn a profit from its assets
Net profit margin = Net income / Revenue
0.05 = x / 9800
net income = 490
net income per share = 490 / 4500 = 0.109
p/e = 1.9 / 0.109 = 17.43
Using the Dupont formula, ROE can be determined using:
ROE = Net profit margin x asset turnover x financial leverage
ROE = (Net income / Sales) x (Sales/Total Assets) x (total asset / common equity)
Interest earnings of 4 percent with a $450 minimum balance; average monthly balance, $600; monthly service charge of $20 for falling below the minimum balance, which occurs five times a year (no interest earned in these months). (Do not round intermediate calculations. Round your answer to 2 decimal places. Input the amount as a positive value.)
Answer:
$86
Explanation:
Missing word "What could be the net annual cost"
Monthly fee = $20
Interest rate = 4% = 0.04
Average monthly balance = $600
Net annual cost = $20*5 - 0.04*$600*7/12
Net annual cost = $100 - $14
Net annual cost = $86
So, the net annual cost of this account is $86.
Information related to Kerber Co. is presented below.
1. On April 5, purchased merchandise from Wilkes Company for $23,000, terms 2/10, net/30, FOB shipping point.
2. On April 6, paid freight costs of $900 on merchandise purchased from Wilkes.
3. On April 7, purchased equipment on account for $26,000.
4. On April 8, returned damaged merchandise to Wilkes Company and was granted a $3,000 credit for returned merchandise.
5. On April 15, paid the amount due to Wilkes Company in full.
Collapse question
Prepare the journal entries to record these transactions on the books of Kerber Co. under a perpetual inventory system. (Credit account titles are automatically indented when amount is entered. Do not indent manually. Record journal entries in the order presented in the problem.)
No. Date Account Titles and Explanation Debit Credit
1. April 5April 6April 7April 8April 15
2. April 5April 6April 7April 8April 15
3. April 5April 6April 7April 8April 15
4. April 5April 6April 7April 8April 15
5. April 5April 6April 7April 8April 15
Answer:
Date Account titles & Explanation Debit Credit
Apr-05 Merchandise Inventory $23,000
Accounts Payable $23,000
Apr-06 Merchandise Inventory $900
Cash $900
Apr-07 Equipment $26,000
Accounts Payable $26,000
Apr-08 Accounts Payable $3,000
Merchandise Inventory $3,000
Apr-15 Accounts Payable $20,000
($23,000-$20,000)
Merchandise Inventory $400
($20,000*2%)
Cash $19.600
Using the following information, compute NET INCOME.
Cost of Goods Sold $ 6,000
Interest Expense 1,100
Selling and Administrative Expense 750
Cash 400
Sales 10,000
Accrued Wages Payable 250
Dividends 700
Retained Earnings (beginning) 1,000
Income Tax Expense 1,200
a. $1,350
b. $700
c. $1,700
d. $950
e. $1,950
Answer:
d. $950
Explanation:
Calculation to determine the NET INCOME
Sales $ 10,000.00
Cost of goods sold $ 6,000.00
Gross margin $ 4,000.00
($10,000-$6,000)
Selling and administrative expenses $ 750.00
Net operating income $ 3,250.00
($4,000-$750)
Interest expense $ 1,100.00
Net income before taxes $ 2,150.00
($3,250-$1,100)
Income taxes $ 1,200.00
Net income $ 950.00
($2,150-$1,200)
Therefore the NET INCOME will be $950
A certain smelting plant operates 24 hours per day, with three shifts of 200 workers per shift. Due to a flu epidemic, 1/4 of the workers on the first shift, 10 percent of the workers on the second shift, and 100 of the workers on the third shift are unable to work on a given day. If each worker and each shift has the same productivity, what is the approximate percent decrease in productivity due to the flu epidemic?
Answer:
35
Explanation:
12/1-34÷1 I just need points
Tech Solutions is a consulting firm that uses a job-order costing system. Its direct materials consist of hardware and software that it purchases and installs on behalf of its clients. The firm’s direct labor includes salaries of consultants that work at the client’s job site, and its overhead consists of costs such as depreciation, utilities, and insurance related to the office headquarters as well as the office supplies that are consumed serving clients. Tech Solutions computes its predetermined overhead rate annually on the basis of direct labor-hours. At the beginning of the year, it estimated that 50,000 direct labor-hours would be required for the period’s estimated level of client service. The company also estimated $225,000 of fixed overhead cost for the coming period and variable overhead of $0.50 per direct labor-hour. The firm’s actual overhead cost for the year was $238,100 and its actual total direct labor was 53,100 hours. Required: 1. Compute the predetermined overhead rate. 2. During the year, Tech Solutions started and completed the Xavier Company engagement. The following information was available with respect to this job: Direct materials $ 44,850 Direct labor cost $ 28,200 Direct labor hours worked 200 Compute the total job cost for the Xavier Company engagement.
Answer and Explanation:
The computation is shown below;
1. The predetermined overhead rate is
= $0.50 + ($225,000 ÷ 50,000 direct labor hours)
= $.50 + $4.5
= $5
2. The total job cost is
= $44,850 + $28,200 + 200 × $5
= $44,850 + $28,200 + $1,000
= $74,050
So in this way these can be calculated
What are the opportunity offers by
vocational education?
Answer:
Where I grew up, I went to a vocational school for just the beginning of the year, then left to a charter school, At a vocational school, I can choose a cooking class, welding, mechanic, and some other neat stuff, it's kinda of preparing you to be independent, but also you can do it working with other people too.
They are strict with absences and tardies, 3 tardies make one absence, and absences put penalties on your highschool resume/record, depending on how many penalties from absences and tardies you get, they kick you out of the school which is not fair if you have construction workers on the road slowing you down on your way to school for 3 months.
If you do a vocational school, collages you want to go to are more likely to take you in faster than a person who went to a regular high school.
A bank has $132,000 in excess reserves and the required reserve ratio is 11 percent. This means the bank could have __________ in checkable deposit liabilities and __________ in (total) reserves. Group of answer choices $5,000,000; $5,869,000 $1,000,000; $110,000 $4,000,000; $590,000 $4,700,000; $869,000
Answer:
$14,520 in check-able deposit liabilities and $117,480 in total reserves.
Explanation:
The bank has $132,000 in excess reserves and excess reserves ratio is 11%. The bank will have total reserves of $132,000 * 89% = $117,480. The total liabilities will be equivalent to the excess reserves which is $14,520 [$132,000 - $117,480].
Corporate decision makers and analysts often use a particular technique, called a DuPont analysis, to better understand the factors that drive a companyâs financial performance, as reflected by its return on equity (ROE). By using the DuPont equation, which disaggregates the ROE into three components, analysts can see why a companyâs ROE may have changed for the better or worse, and identify particular company strengths and weaknesses. The DuPont Equation A DuPont analysis is conducted using the DuPont equation, which helps to identify and analyze three important factors that drive a companyâs ROE.
Required:
What factors directly affect a companyâs ROE?
Answer:
DuPont Equation
The three factors that directly affect a company's ROE (Return on Equity) are:
1. Profit margin
2. Total asset turnover
3. Equity multiplier
Explanation:
The profit margin measures the operating efficiency of the company with higher sales leading to higher profit margins.
The total asset turnover is a financial measure that divides turnover by the total assets. It shows the efficiency achieved in the use of assets to generate sales revenue.
The equity multiplier measures the financial leverage of the company. It shows how the use of debts increases the value of the company's equity.
Dianne Ruth withdrew $8,000 from her educational savings account and used $6,000 to pay for qualified higher education expenses. The remaining balance of $2,000 was used to purchase clothes. On the date of the distribution, her educational savings account had $25,000 balance including $20,000 she had contributed.
How much of the $8,000 is tax free?
Answer:
$7,600
Explanation:
Calculation to determine How much of the $8,000 is tax free
Step 1 is to calculate the % using this formula
%=Savings ratio ROC Contributed/Total balance
Let plug in the formula
%=$20,000/$25,000
%= .80*100
%=80%
Step 2 is to calculate the ROC tax free using this formula
ROC tax free=% x Distribution
Let plug in the formula
ROC tax free=.80x 8000
ROC tax free=$6,400
Step 3 is to Contained earnings in distribution using this formula
Contained earnings in distribution=Distribution - ROC tax free
Let plug in the formula
Contained earnings in distribution=$8,000-$6,400
Contained earnings in distribution= $1,600
Step 4 is to calculate Excludable earning using this formula
Excludable earning=(Qualified exp/distribution ) x Earning contained
Let plug in the formula
Excludable earning=($6,000/$8,000) x $1,600
Excludable earning= $1,20/
Step 5 is to calculate the Taxable amount using this formula
Taxable =Earnings - Excludable
Let plug in the formula
Taxable=$1,600-$1,200
Taxable =$400
Now let determine the Tax free using this formula
Tax free = Distribution- Taxable
Let plug in the formula
Tax free=$8,000- $400
Tax free=$7,600
Therefore How much of the $8,000 is tax free will be $7,600
businesses do not maximise outputs from the given inputs
Answer:
Businesses that do not maximise outputs from the given inputs are inefficient, and probably have diseconomies of scale, the opposite of economies of scale, that ocurrs when output increases proportionally less than the inputs that are invested.
This situation arises as a result of an economic law, the law of diminishing retuns. According to this economic law, there is a point in the production process in which the use of additional units of input do not result in a proportional yield, in other words, when a business presents diminishing returns, the more inputs it adds, the less output grows in proportion to the inputs.
explain why it is important for marketers to be able to measure the effectiveness of marketing activities.
Kenneth Clark is saving for an Australian vacation in three years. He estimates that he will need $4,970 to cover his airfare and all other expenses for a week-long holiday in Australia. If he can invest his money in an S&P 500 equity index fund that is expected to earn an average annual return of 11.4 percent over the next three years.
Required:
How much will he have to save every year if he starts saving at the end of this year?
Answer:
$1481.37
Explanation:
Annual savings = future value / annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
[(1.114)^3 - 1 ] / 0.114 = 3.3549996
$4,970 / 3.3549996 = $1481.37
Wildhorse, Inc. had net sales in 2020 of $1,502,400. At December 31, 2020, before adjusting entries, the balances in selected accounts were Accounts Receivable $221,100 debit, and Allowance for Doubtful Accounts $3,000 credit. If Wildhorse estimates that 8% of its receivables will prove to be uncollectible.
Required:
Prepare the December 31, 2017, journal entry to record bad debt expense.
Answer and Explanation:
The journal entry is shown below:
Bad debt expense Dr $14,668 ($221,100 × 8% - $3,000)
To Allowance for doubtful debts $14,668
(Being bad debt expense is recorded)
Here the bad debt expense is debited as it increased the expense and credited the allowance for doubtful debt as it decreased the assets
Explain five planning steps that are required to have a good business communication. Take any of the business as example and implement those five planning steps on it, as answer
The correct answer to this open question is the following.
Although you did not include any specific context or references, we can say the following.
The five planning steps that are required to have good business communication are the following.
1.- Establish attainable and specific goals. You can use the SMART formula.
2.- Identify who ypur audience is and where they are so you can be effective in sending your messages.
3.- Prepare the right strategy to implement your program. Have your communication department on the same page.
4.- Prepare the proper budget so you can run your program.
5.- Perform your program, monitor it, and evaluate your results.
For instance, Walmart is a corporation that makes communication a priority and invests time and money to run communications programs so every employee in the corporation is on the same page and can perform their jobs effectively, eliminate rumors, and be productive.
Several years ago, Castles in the Sand Inc. issued bonds at face value of $1,000 at a yield to maturity of 8%. Now, with 7 years left until the maturity of the bonds, the company has run into hard times and the yield to maturity on the bonds has increased to 12%. What is the price of the bond now
Answer:
$814.10
Explanation:
Calculation to determine what the price of the bond now
Using this formula
Bond price = PV of coupon payments + PV of face value
Bond price= C×((1 / r) – {1 / [r(1 + r)t]}) + FV / (1 + r)t
Let plug in the formula
Bond price= [(.080 ×$1,000) / 2] ×[[1 / (.12 / 2)] – (1 / {(.12 / 2)[1 + (.12 / 2)](7 ×2)})] + $1,000 / [1 + (.12 / 2)](7 ×2)
Bond price= $814.10
Therefore the price of the bond now is $814.10
Interest income has been recorded during the year as interest payments have been received by Parnell. The Oracle bonds are currently valued on the financial market at $205 million.
Required:
Prepare the appropriate adjusting entry, if one is necessary.
Answer:
Interest payments (Dr.) $20.5 million
Interest Interest Income (Cr.) $20.5 million
Explanation:
Adjusting entries are prepared when there is change in the transaction after it has been recorded or if the entry is recorded incorrectly. The change in the transaction may impact the financial statements so adjusting entries are prepared which correct the impact of transaction.
The advantage to savers and investors of receiving compound interest rather than simple interest is that future values are larger because interest is earned on accumulated interest payments. Also, the difference in future values becomes smaller as time goes by.
a. True
b. False
Answer:
B. false
Explanation:
over time it becomes larger because you are bringing in more money from interest sitting there
Alternative Production Procedures and Operating Leverage Assume Sharpie, a brand of Newell Brands, is planning to introduce a new executive pen that can be manufactured using either a capital-intensive method or a labor-intensive method. The predicted manufacturing costs for each method are as follows: Capital Intensive Labor Intensive Direct materials per unit $ 10.00 $ 12.00 Direct labor per unit $ 4.00 $ 12.00 Variable manufacturing overhead per unit $ 5.00 $ 2.00 Fixed manufacturing overhead per year $ 1,800,000 $ 500,000 Sharpies market research department has recommended an introductory unit sales price of $100. The incremental selling costs are predicted to be $250,000 per year, plus $4 per unit sold. (a) Determine the annual break-even point in units if Sharpie uses the: Note: Round both answers UP to the nearest whole number.
Answer:
For Capital Incentive manufacturing method = 26,623 Units
For Labor Incentive manufacturing method = 10,714 Units
Explanation:
We are asked to find out the annual break - even point in units if Sharpie uses the Capital Intensive Method and Labour intensive Method.
Solution:
1. For Capital Intensive Method:
Direct Materials = 10
Direct Labor = 4
Variable MOH = 5
Variable Selling = 4
Total Variable Cost = T = 23
Selling Price = P = 100
Contribution Margin = M = P-T = 77
Fixed Overhead:
Fixed MOH = 1800000
Fixed Selling costs = 250000
Total Fixed Costs = 2050000
Break Even Point in Units = Total Fixed Cost / M = 26623
2. For Labor Intensive Method:
Direct Materials = 12
Direct Labor = 12
Variable MOH = 2
Variable Selling = 4
Total Variable Cost = T = 30
Selling Price = P = 100
Contribution Margin = M = P-T = 70
Fixed Overhead:
Fixed MOH = 500000
Fixed Selling costs = 250000
Total Fixed Costs = 750000
Break Even Point in Units = Total Fixed Cost / M = 10714
Wildcat, Inc., has estimated sales (in millions) for the next four quarters as follows:
Q1 Q2 Q3 Q4
Sales $165 $185 $205 $235
a. Sales for the first quarter of the year after this one are projected at $180 million. Accounts receivable at the beginning of the year were $71 million. Wildcat has a 45-day collection period.
b. Wildcat's purchases from suppliers in a quarter are equal to 45 percent of the next quarter's forecast sales, and suppliers are normally paid in 36 days. Wages, taxes, and other expenses run about 20 percent of sales. Interest and dividends are $16 million per quarter.
c. Wildcat plans a major capital outlay in the second quarter of $99 million. Finally, the company started the year with a $78 million cash balance and wishes to maintain a $40 million minimum balance.
Complete the following cash budget for Wildcat, Inc.
WILDCAT, INC. Cash Budget (in millions)
Q1 Q2 Q3 Q4
Beginning cash balance $78.00 $ $ $
Net cash inflow
Ending cash balance $ $ $ $
Minimum cash balance -30.00 -30.00 -30.0 -30.00
Cumulative surplus (deficit) $ $ $ $
Answer:
Wildcat, Inc.
WILDCAT, INC. Cash Budget (in millions)
Q1 Q2 Q3 Q4
Beginning cash balance $78.00 $115.90 $48.45 $83.40
Net cash inflow 37.90 -67.45 34.95 71.05
Ending cash balance $115.90 $48.45 $83.40 $154.45
Minimum cash balance -40.00 -40.00 -40.00 -40.00
Cumulative surplus (deficit) $75.90 $8.45 $43.40 $114.45
Explanation:
a) Data and Calculations:
Q1 Q2 Q3 Q4 Q1
Sales (in millions) $165 $185 $205 $235 $180
Accounts receivable at beginning of the year = $71 million
Collection period = 45 days = 50% in each quarter and 50% in the next
Purchases for the quarter = 45% of next quarter's forecast sales
Payment period = 36 days
Wages, taxes, etc. = 20% of sales
Q1 Q2 Q3 Q4 Q1
Sales (in millions) $165 $185 $205 $235 $180
Cash collections:
50% quarter of sales 82.50 92.50 102.50 117.50
50% next quarter 71.00 82.50 92.50 102.50
Total cash collections 153.50 175.00 195.00 220.00
Purchases 83.25 92.25 105.75 81.00
Cash Payments:
80% month of purchase 66.60 73.80 84.60 64.80
20% following purchase 16.65 18.45 21.15
Total purchases payments 66.60 90.45 103.05 85.95
Wages, taxe, etc. 33 37 41 47
Interest and dividends 16 16 16 16
Capital outlay 99
Total cash disbursements 115.60 242.45 160.05 148.95
Net cash inflow 37.90 -67.45 34.95 71.05
Cash, beginning = $78 million
Desired minimum balance = $40 million
Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 75.00. During these years of part-time work, he will neither make deposits to nor take withdrawals from his retirement account. Exactly one year after the day he turns 75.0 when he fully retires, he will wants to have $2,552,589.00 in his retirement account. He he will make contributions to his retirement account from his 26th birthday to his 65th birthday. To reach his goal, what must the contributions be
On the first day of its fiscal year, Chin Company issued $26,200,000 of five-year, 6% bonds to finance its operations of producing and selling home improvement products. Interest is payable semiannually. The bonds were issued at a market (effective) interest rate of 7%, resulting in Chin receiving cash of $25,110,559.
a. Journalize the entries to record the following:
1. Issuance of the bonds.
2. First semiannual interest payment. The bond discount amortization is combined with the semiannual interest payment. Round your answer to the nearest dollar.
3. Second semiannual interest payment. The bond discount amortization is combined with the semiannual interest payment. Round your answer to the nearest dollar.
b. Determine the amount of the bond interest expense for the first year.
c. Explain why the company was able to issue the bonds for only $9,594,415 rather than for the face amount of $10,000,000.
Solution :
a. 1). Preparing the journal entry to record the issuance of bonds.
Date Account title Debit ($) Credit ($)
Jan 1 Cash 25,110,559
Discount on bonds payable 1,089,441
Bonds payable 26,200,000
a. 2). Preparing the journal entry to record the first semi annual interest payment.
Date Account title Debit ($) Credit ($)
Jun 30 Interest expense 390559
Discount on the bonds payable 108,945
Cash ($26,200,000 x 3%) 786,000
a.3). Preparing the journal entry to record the second semi-annually interest payment.
Date Account title Debit ($) Credit ($)
Dec 31 Interest expense 390,559
Discount on bonds payable 108,945
Cash 786,000
b). Determining the amount of bond interest expense for the 1st year.
Particulars Amount ($)
Interest expense ( 786,000 + 786,000 ) 1,572,000
Add : Discount amortized (108,945 + 108,945) 217,890
Interest expense (for the 1st year) 1,789,890
c). The company issued the bonds having face value of $26,200,000 for $25,110,559. That is the bonds are issued at a discount for $1,089,441. The bonds are issued at a discount as the market interest of the bonds are higher than the bonds coupon rate.
Distribution network is not required for
product.
O Standardised
O Durable
O Unstandardised
O Perishable
Answer:
O Perishable
Explanation:
The distribution network required for the products that are standardised, durable and unstandardised that means for storage purpose
But in the case of the perishable goods, the goods that are not stored for the longer time that means it consumed immediately like milk, bread, eggs, etc
So as per the given option, the last option should be relevant
A manager hires labor and rents capital equipment in a very competitive market. Currently the wage rate is $7 per hour and capital is rented at $11 per hour. If the marginal product of labor is 65 units of output per hour and the marginal product of capital is 55 units of output per hour, should the firm increase, decrease, or leave unchanged the amount of capital used in its production process
Answer:
leave unchanged
Explanation:
because it doe snore jobs then the other one
Lottery. Your dreams of becoming rich have just come true. You have won the State of Tranquility's Lottery. The State offers you two payment plans for the $6 comma 000 comma 000 advertised jackpot. You can take annual payments of $150 comma 000 at the end of the year for the next 40 years or $1 comma 466 comma 858 today. a. If your investment rate over the next 40 years is 11%, which payoff will you choose? b. If your investment rate over the next 40 years is 9%, which payoff will you choose? c. At what investment rate will the annuity stream of $150 comma 000 be the same as the lump-sum payment of $1 comma 466 comma 858?
Answer:
A=1466858
B=$150000
C=10%
Explanation:
A)
Present value of $150000 at 11% for 40 years;
Using excel PV function: PV(11%,40,-150000) = $1342657.623
Therefore, 1466858 should be selected.
B)
Present value of $150000 at 9% for 40 years
= PV(9%,40,-150000) = $1613604.03
Therefore payment of $150000 should be selected
C)
Using excel rate function: RATE(40,-150000,1466858)
= 10%
Georgina consumes only grapefruits and pineapples. Her utility function is U (x comma y )equals x to the power of 0.8 end exponent y to the power of 0.2 end exponent, where x is the number of grapefruits consumed and y is the number of pineapples consumed. Georgina’s income is $105, and the prices of grapefruits and pineapples are $4 and $3, respectively. How many grapefruits will she consume?
Answer:
21
Explanation:
Given that:
The utility function U(x, y) = [tex]x^{0.8} y^{0.2}[/tex]
The budget line income is:
105=4x +3y
The equation MRTS is:
[tex]\dfrac{MU_x}{MU_y } =\dfrac{ Px}{Py}[/tex]
where;
[tex]MU_x(x,y) = 0.8 \times x^{0.8-1}\times y^{0.2} \\ \\ \implies 0.8 \times x^{-0.2}\times y^{0.2}[/tex]
[tex]MU_y(x,y) = 0.2 \times x^{0.8}\times y^{0.2-1} \\ \\ \implies 0.8 \times x^{0.8}\times y^{-0.8}[/tex]
and:
[tex]P_y= 3[/tex]
[tex]P_x = 4[/tex]
∴
Using the equation MRTS:
[tex]\dfrac{MU_x}{MU_y } =\dfrac{ Px}{Py}[/tex]
[tex]\dfrac{ 0.8 \times x^{-0.2}\times y^{0.2} }{0.8 \times x^{0.8}\times y^{-0.8}} = \dfrac{4}{3}[/tex]
[tex]\dfrac{4y }{x} = \dfrac{4}{3}[/tex]
4x = 12y
x = 12y/4
x = 3y
Replacing the value of x into the budget line income, we have:
105 = 4x + 3y
105 = 4(3y) + 3y
105 = 12y + 3y
105 = 15y
y = 105/15
y = 7
Then, from x = 3y
x = 3(7)
x = 21
Thus, she will consume 21 gapefruits