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Sladkaya [172]
3 years ago
7

There are two people in the economy: Martha and Charlie. There are two goods in the economy: books and wine. Martha is endowed w

ith 110 books and 20 wine bottles, while Charlie is endowed with 20 books and 45 wine bottles. Denote books with, b, and wine with, w. Martha has the utility function: U(b,w) = 6b+24w. Charlie has the utility function: U(b,w) = bw. At a pareto optimal allocation, the price of books is $1, while the price of wine is $4. How many books does Charlie consume at a pareto-optimal allocation in the exchange equilibrium?
Business
1 answer:
balu736 [363]3 years ago
3 0

Answer:

Charlie consumes 100 books and 25 wines at pareto-optimal allocation, is the right answer.

Explanation:

According to the question, book is denoted with b whereas, wine is denoted with w.

The Utility function of Martha is-  U\left ( b,w \right )=6b+24w

The Utility function for Charlie is- U\left ( b,w \right )=bw

P_{b} = $1 : P_{w} = $4

At pareto-optimality,

MRS_{bw}=\frac{P_{b}}{P_{w}}\\\frac{w}{b}=\frac{1}{4}\\4w=b\\

The budget constraint,

1.b+4.w=m=1\left ( 20 \right )+4\left ( 45 \right )\\b+4w=20+180\\4w+4w=200\\w=\frac{200}{8}=25\\\therefore b=100

Therefore, it may be said that Charlie must consume 100 books and 25 wine at pareto-optimal allocation.

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Sales and costs are projected to grow at 20% a year for at least the next 4 years. Both current assets and accounts payable are
shusha [124]

Question Completion:

The 2017 financial statements for Growth Industries are presented below  

INCOME STATEMENT, 2017  

Sales $ 380,000  

Costs 240,000  

EBIT $ 140,000  

Interest expense 28,000  

Taxable income $ 112,000  

Taxes (at 35%) 39,200

Net income $ 72,800  

Dividends 21,840

Addition to retained earnings 50,960  

BALANCE SHEET, YEAR -END, 2017  

Assets    

Current assets  

Cash      $ 7,000      

Accounts receivable 12,000

Inventories 31,000

Total current assets $ 50,000  

Net plant and equipment 320,000

Total assets $ 370,000

Liabilities

Current liabilities

Accounts payable $ 14,000

Total current liabilities $14,000

Long-term debt Stockholders' equity 280,000

Common stock plus additional paid-in capital 15,000

Retained earnings 61,000  

Total liabilities and stockholders' equity $ 370,000

Answer:

Growth Industries

The required external financing over the next year is:

= $16,600.

Explanation:

a) Data and Calculations:

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Fixed assets growth rates = 20%

Interest expense = 10% of long-term debt outstanding

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INCOME STATEMENTs,               2017        Projected

Sales                                      $ 380,000   $456,000 ($380,000 * 1.2)

Costs                                        240,000      288,000 ($240,000 * 1.2)

EBIT                                        $ 140,000    $168,000

Interest expense                       28,000        28,000

Taxable income                     $ 112,000    $140,000

Taxes (at 35%)                          39,200        49,000

Net income                            $ 72,800      $91,000

Dividends                                   21,840       36,400

Addition to retained earnings 50,960    $54,600

Retained earnings, 2017  $61,000

Projected addition             54,600

Retained earnings,         $115,600

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Assets                                                                2017   Projected

Current assets  

Cash                                                               $ 7,000      $8,400 ($7,000*1.2)

Accounts receivable                                       12,000       14,400 (12,000*1.2)

Inventories                                                      31,000      37,200 (31,000*1.2)

Total current assets                                   $ 50,000   $60,000

Net plant and equipment                           320,000    384,000 ($320,000*1.2)

Total assets                                             $ 370,000 $ 444,000

Liabilities

Current liabilities

Accounts payable                                     $ 14,000      $16,800 ($14,000*1.2)

Total current liabilities                               $14,000      $16,800

Long-term debt Stockholders' equity     280,000     280,000

Common stock plus

additional paid-in capital                           15,000        15,000

Retained earnings                                      61,000      115,600

Total liabilities

and stockholders' equity                    $ 370,000  $427,400

External Financing Required = Assets - Liabilities & equity

Assets =                    $444,000

Liabilities + Equity = $427,400

External financing      $16,600

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