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Alex Ar [27]
3 years ago
14

Tracy consumes dress shoes​ (D) and casual Crocs​ (C). Her marginal utility from consuming casual Crocs is MU Subscript Upper CM

UCequals=20DC and her marginal utility from consuming dress shoes is MU Subscript Upper DMUDequals=10Upper C squaredC2. Her annual shoe allowance is ​$450450​, which she spends on only dress shoes and Crocs. If she pays ​$5050 for a pair of dress shoes and ​$2525 for a pair of​ Crocs, what is her optimal consumption​ bundle?
Business
1 answer:
Llana [10]3 years ago
7 0

Answer:

The optimal bundle is 6 pairs of dress shoes and 3 pairs of Crocs.

Explanation:

From the question,

Allowance (M) = $450; Price of dress shoes, Pd = $50; Price of crocs, Pc = $50

Note: MRS-price ratio, MUC- marginal utility from consuming casual Crocs ,MUD- marginal utility from consuming dress shoes

Optimal bundle is determined where MRS = Price ratio

MRS = MUC/MUD = 20DC/10C2 = 2D/C

Price ratio = Pd/Pc = 50/50 = 1

So, 2D/C = 1

       Therefore, C = 2D

Budget constraint:  M = Pd*D + Pc*C

So, 50D + 50*(2D) = 450

      50D + 100D = 150D = 450

So, D = 450/150 = 3

C = 2D = 2*3 = 6

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a. Peabody & Peabody

Pro Forma Balance Sheet

December 31, 2021 ($000)

Cash                             480

Marketable securities 200

Accounts receivable 1,440

Inventories                2,160

Total current assets 4,280

Net fixed assets       4,820

Total assets              9,100

Liabilities and Stockholders equity:

Accounts payable          1,680

Accruals                           500

Other current liabilities     80

Total current liabilities 2,260

Long-term debt           2,000

Total liabilities             4,260

Common equity         3,900            

Total liabilities and stockholders’ equity $8,160

Required Finance         940

b. From the statement prepared in part a, it is clear that Peabody & Peabody requires new financing of $940,000 for 2020 to meet the projected assets base.

Explanation:

a) Data and Calculations:

2019 Sales = $10 million

Pro Forma Balance Sheet

December 31, 2017 ($000)

Assets:

Cash                             400

Marketable securities 200

Accounts receivable 1,200

Inventories                1,800

Total current assets 3,600

Net fixed assets       4,000

Total assets              7,600

Liabilities and Stockholders equity:

Accounts payable          1,400

Accruals                           400

Other current liabilities     80

Total current liabilities  1,880

Long-term debt           2,000

Total liabilities              3,880

Common equity           3,720

Total liabilities and stockholders’ equity $7,600

Purpose: To analyze expected performance and financing needs for 2021.

1. Percent of Sales ($12 million)

Accounts receivable, 12%  $1,440

Inventory, 18%                    $2,160

Accounts payable, 14%      $1,680

Net profit margin, 3%          $360

2. Market securities            $200

3. Cash balance (desired minimum) $480

4. Net fixed assets           4,000

New equipment in 2020    650

Depreciation, 2020           (290)

New equipment in 2021    850

Depreciation, 2021            (390)

Net fixed assets            $4,820

5. Accruals                       $500

8. Dividend payout = 50% of $360 = $180

Retained Earnings (current) = $180

Common Equity:

2019    3,720

Income   180 (Retained Earnings)

2020  3,900

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