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victus00 [196]
4 years ago
11

​Vasco's utility function​ is: Upper U equals 10 Upper X squared Upper ZU = 10X2Z The price of X is px​ = ​$55​, the price of Z

is pz​ = ​$2020​, and his income is ​$150150. What is his optimal​ bundle? ​(round your answer to two decimal​ places)
Business
1 answer:
disa [49]4 years ago
6 0

Answer:

Explanation:

U = 10 X²Z

Given

150 = 5X + 20Z

30 = X + 4Z

To maximise utility

differentiating partially wrt X

MU_x = dU/ dX = 20XZ

differentiating partially wrt Y

MU_y = dU/dY = 10X²

For optimal bundle

MU_x / MU_y = P_x / P_y

20XZ /  10X² = 5 / 20

2Z / X = 1/4

X = 8Z

30 = X + 4Z

30 = 8Z + 4Z

12Z = 30

Z = 2.5

X =  8 X 2.5

= 20

X = 20

Z = 2.5

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3 years ago
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jek_recluse [69]

Answer:

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1. Differential Analysis as of April 30:

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Annual revenue                              $74,200          $74,200

Annual depreciation (straight-line)    8,900             19,950  

Annual manufacturing

costs, excluding depreciation        23,600              6,900

Annual nonmanufacturing

operating expenses                         6,100                6,100

Total expenses                            $38,600           $32,950

Annual net income                      $35,600           $41,250         $5,650

Net income for 6 six years        $213,600        $247,500       $33,900

2. Other factors that should be considered are:

B. What effect does the federal income tax have on the decision?

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E. Are there any improvements in the quality of work turned out by the new machine?

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a) Dat and Calculations:

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Annual depreciation (straight-line) 8,900

Annual manufacturing costs, excluding depreciation 23,600

Annual nonmanufacturing operating expenses 6,100

Annual revenue 74,200

Current estimated selling price of machine 29,700

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Purchase price of machine, six-year life $119,700

Annual depreciation (straight-line) 19,950

Estimated annual manufacturing costs, excluding depreciation 6,900

Annual nonmanufacturing operating expenses 6,100

Annual revenue 74,200

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3 years ago
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