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.
What is the marginal cost in plant 1? Findâˆ‚c₁/âˆ‚y₁.
What is the marginal cost in plant 2? Findâˆ‚c₂/âˆ‚y₂.
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?
What is the optimal production level,y₁^and y₂^, that wouldminimize cost? What is the total cost now?

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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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