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DigiWatch plans to open a new production facility to produce digital watches. Based on previous experience,...

  1. DigiWatch plans to open a new production facility to produce digital watches. Based on previous experience, the firm estimates that the fixed costs of the plant will be $366,000 per year, and that average variable cost will be:

AVC = 7.00 + .002Q.

(a) Compute the total cost and average cost for the first year of production at an output of 6,000 watches.

(b) In the second year of production, DigiWatch revamped its assembly operations to improve efficiency. The firm produced 8,000 watches at a total cost of $498,000. How much did the revamp reduce average cost in the second year?

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Answer #1

FC = 366000 per year

AVC = 7 + 0.002Q

VC = 7Q + 0.002Q^2

TC = 366000 + 7Q + 0.002Q^2

a) When Q = 6000,

TC = 366000 + 7*6000 + 0.002*6000^2

= 480000

ATC = 480000 / 6000 = 80

b) TC with out improvement at Q = 8000

TC = 366000 + 7*8000 + 0.002*8000^2

TC = 550000

ATC = 550000 / 8000 = 68.75

ATC with improvement = 498000 / 8000 = 62.25

ATC decreased by = 68.75 - 62.25 = 6.50

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