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frez [133]
3 years ago
13

​U(X,Y)equals=20Xplus+80Yminus−Upper X squaredX2minus−2Upper Y squaredY2 where X is his consumption of CDs with a price of ​$11

and Y is his consumption of movie​ videos, with a rental price of ​$22. He plans to spend ​$6565 on both forms of entertainment. Determine the number of CDs and video rentals that will maximize​ Maurice's utility.
Business
1 answer:
ankoles [38]3 years ago
7 0

Answer:

The number of CDs = 111.36

The number of movie videos = 242.72

N/B: I choose not to round up the answers.

Explanation:

The method used is the Lagrangian method. Basically, the optimization problem we are trying to solve is  the utility function u(x,y) = 20x+80y -x^2 -y^2

subject to the constraint

11x + 22y = 6565.

So the optimization problem(Lagrangian) is

\Delta = 20x + 80y -x^2 -y^2- \lambda(11x+22y-6565),

where \lambda is a constant called the Lagrange multiplier.

To find the optimal consumption, we need to maximize the Lagrangian with respect to the variables x,y,\lambda. This we do by differentiating \Delta with respect to each variable and then equate to 0.

\Delta_x : 11\lambda = 20 - 2x ........................(1) \\\Delta_y: 11\lambda = 40 -y .........................(2) \\\Delta_\lambda = 11x + 22y = 6565............................(3) \\

Equate (1) and (2), to get y = 20+2x and substitute into (3) to get x = 111.36. Substituting x = 111.36 into 20+2x to get the corresponding value of y.

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3 years ago
Which of the following is a microeconomic topic? A) the unemployment rate of the United. States economy as a whole. B) the rate
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Answer:

The correct answer is C, the advertising strategy of a particular company.

Explanation:

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3 years ago
Read 2 more answers
omparative Income Statement For the Years Ended December 31, 20Y6 and 20Y5 1 20Y6 20Y5 Amount Increase (Decrease) Percentage Inc
ElenaW [278]

Answer:

The question is incomplete. Here is the complete question:

 

Liquidity and Solvency Measures Computations

Current ratio $3,093,000 ÷ $840,000

Working capital $3,093,000 – $840,000

Accounts receivable turnover $8,280,000 ÷ [($714,000 + $740,000) ÷ 2]

Ratio of fixed assets to long-term liabilities $2,690,000 ÷ $1,690,000

Inventory turnover $4,100,000 ÷ [($1,072,000 + $1,100,000) ÷ 2]

Number of days' sales in receivables [($714,000 + $740,000) ÷ 2] ÷ ($8,280,000 ÷ 365)

Number of days' sales in inventory [($1,072,000 + $1,100,000) ÷ 2] ÷ ($4,100,000 ÷ 365)

Times interest earned ($989,400 + $127,000) ÷ $127,000

Ratio of liabilities to stockholders' equity $2,530,000 ÷ $4,077,000

Quick ratio $1,866,000 ÷ $840,000

Profitability Measures Computations

Asset turnover $8,280,000 ÷ [($5,783,000 + $5,593,000) ÷ 2]

Return on total assets ($801,420 + $127,000) ÷ [($6,607,000 + $6,417,000) ÷ 2]

Return on stockholders’ equity $801,420 ÷ [($4,077,000 + $3,873,150) ÷ 2]

Return on common stockholders’ equity ($801,420 – $65,000) ÷ [($3,589,500 + $3,445,920) ÷ 2]

Earnings per share on common stock ($801,420 – $65,000) ÷ 250,000 shares

Price-earnings ratio $35 ÷ $3.05

Dividends per share $175,000 ÷ 250,000 shares

Dividend yield $0.70 ÷ $35

Two of the computations use shares.

Use the following comparative income statement form to enter amounts you identify from the computations on the Liquidity and Solvency Measures panel and on the Profitability Measures panel. Compute any missing amounts and complete the horizontal analysis columns. Enter percentages as decimal amounts, rounded to one decimal place. When rounding, look only at the figure to the right of one decimal place. If < 5, round down and if ≥ 5, round up. For example, for 32.048% enter 32.0%. For 32.058% enter 32.1%.

Comparative Income Statement    

For the Years Ended December 31, 20Y6 and 20Y5

 

1   20Y6 20Y5 Amount Increase (Decrease) Percentage Increase (Decrease)

2 Sales   $7,287,000.00    

3 Cost of goods sold   3,444,000.00    

4 Gross profit   $3,843,000.00    

5 Selling expenses   $1,457,600.00    

6 Administrative expenses 1,242,000.00 1,106,000.00    

7 Total operating expenses   $2,563,600.00    

8 Income from operations   $1,279,400.00    

9 Interest expense   120,600.00    

10 Income before income tax   $1,158,800.00    

11 Income tax expense   181,980.00    

12 Net income   $976,820.00    

Explanation:

Items Computations value

1. Sales: Sales are taken from number of days' sales in receivables or accounts  

receivable turnover ratio, with assuming that all sales are credit sales 8,280,000.00

2. Cost of goods sold:  Cost of goods sold is taken from number of days' sales in inventory or Inventory turnover 4,100,000.00

3. Gross profit:  Gross profit = Sales - Cost of goods sold 4,180,000.00

4. Selling expenses:  Selling expenses = Total operating expenses - Cost of goods sold - Administrative expenses 1,821,600.00

5. Administrative expenses:  available 1,242,000.00

6. Total operating expenses: Total operating expenses = Sales - Income from operations 7163600

7. Income from operations: Income from operations (or is also known EBIT) = Income before income tax + Interest expense 1,116,400.00

8. Interest expense: Interest expense is taken from Times interest earned and Return on total assets 127,000.00

9. Income before income tax: Income before income tax is taken from Times interest earned and Interest expense being specified already 989,400.00

10. Income tax expense: Income tax expense = Income before income tax - Net income 187,980.00

11. Net income: Net income is taken from Return on total assets and Return on common stockholders’ equity 801,420.00

Download docx
4 0
3 years ago
Which of the following activities describes the opportunity cost of attending an economics class?
zhuklara [117]

Answer:

C is the correct option

Explanation:

Opportunity cost is a concept of Macroeconomic theory. It is also known as an alternative cost. It is the value of what one gives up to choose something else. In simple terms, we can say that it is the value of the road not taken. In the above question, the value of the activities one had to leave to attend the economics class woul be known as the Opprtunity cost.

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3 years ago
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