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Exercise 2. Two plants A firm has two plants, both with increasing marginal costs. Plant 1 is...

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Economics

Exercise 2. Two plants

A firm has two plants, both with increasing marginal costs.Plant 1 is more efficient than plant 2. Specifically, the costfunction in plant 1 isc1(y1)=2y12, while thecost function in plant 2 isc2(y2)=3y22. Outputproduced in plant 1, y1, is identical to output producedin plant 2, y2. For any overall output levelY=y1+y2the firm wants to minimize costs.

  1. What is the marginal cost in plant 1? Find∂c1/∂y1.

  1. What is the marginal cost in plant 2? Find∂c2/∂y2.

  1. The firm needs to produce a total of Y=10 units. If it decidesto produce all of them in plant 1 (y1=100 andy2=0), what is the total cost?

  1. What is the optimal production level,y1*and y2*, that wouldminimize cost? What is the total cost now?

Answer & Explanation Solved by verified expert
3.9 Ratings (455 Votes)
a Total Cost of plani 1 c1y1 2y12 Marginal cost in plant 1 MC1 c1y1 2y12y1 4y1 b Total Cost of plani 2 c2y2 3y22 Marginal cost in plant 2 MC2 c2y2 3y22y2 6y2 c    See Answer
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