A firm has two plants that produce identical output. The cost functions are C₁ = 129₁-12 (9₁)² + (9₁) ³ and C₂=1292-8 (92)2 + (92₂) ³. At what output level does the average cost curve of each plant reach its minimum? If the firm wants to produce 20 units of output, how much should it produce in each plant? Let q₁ be the output at plant 1 and q2 be the output at plant 2. Average cost at plant 1 reaches a minimum at (Enter your response rounded to one decimal place.) Average cost at plant 2 reaches a minimum at 9₁ = unit(s). and 92 (Enter your response rounded to one decimal place.) If the firm wants to produce 20 units of output, it should produce 91 = 92 (Enter your responses rounded to two decimal places.) unit(s). = units at plant 1 units at plant 2.
A firm has two plants that produce identical output. The cost functions are C₁ = 129₁-12 (9₁)² + (9₁) ³ and C₂=1292-8 (92)2 + (92₂) ³. At what output level does the average cost curve of each plant reach its minimum? If the firm wants to produce 20 units of output, how much should it produce in each plant? Let q₁ be the output at plant 1 and q2 be the output at plant 2. Average cost at plant 1 reaches a minimum at (Enter your response rounded to one decimal place.) Average cost at plant 2 reaches a minimum at 9₁ = unit(s). and 92 (Enter your response rounded to one decimal place.) If the firm wants to produce 20 units of output, it should produce 91 = 92 (Enter your responses rounded to two decimal places.) unit(s). = units at plant 1 units at plant 2.
Chapter6: Proudction Costs
Section: Chapter Questions
Problem 8SQ
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Transcribed Image Text:A firm has two plants that produce identical output. The cost functions are
2
3
C₁ = 129₁ - 12 (9₁)² + (9₁) ³
and
2+
C₂ = 1292-8 (92)² + (92) ³.
At what output level does the average cost curve of each plant reach its minimum? If the firm wants to produce 20 units
of output, how much should it produce in each plant? Let q₁ be the output at plant 1 and 92 be the output at plant 2.
Average cost at plant 1 reaches a minimum at
(Enter your response rounded to one decimal place.)
Average cost at plant 2 reaches a minimum at
and
91
92
91 =
92
(Enter your responses rounded to two decimal places.)
=
(Enter your response rounded to one decimal place.)
If the firm wants to produce 20 units of output, it should produce
=
=
unit(s).
unit(s).
units at plant 1
units at plant 2.
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