4. A two-output-two-input firm has a transformation function of the type: 91 +92 = 21/42/4. where q, and q are outputs and z₁ and 2₂ are inputs. (a) Is this production function consistent with non-increasing returns to scale? Explain why or why not. (b) Fix 2₁ = 1 and 2₂ = 1. Draw the transformation function between ₁ and 2. (c) Fix q₁ q2 = 1. Draw the transformation function (isoquant) for inputs z₁ and 2₂. (d) Find profit maximising 21.22.91-92 at prices equal to: P₁ = 1, P2= 2 and ₁= 1, 2 = 2. Hint: before you set up the profit maximisation problem, think about your picture in (b). With a transformation frontier of this form and such prices, does the firm produce both outputs? If not, rephrase the maximisation problem accordingly.

Microeconomic Theory
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ISBN:9781337517942
Author:NICHOLSON
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Chapter9: Production Functions
Section: Chapter Questions
Problem 9.7P
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4. A two-output-two-input firm has a transformation function of the type:
91 + 92 = z4z4.
where q and q are outputs and z and 2z are inputs.
(a) Is this production function consistent with non-increasing returns to scale? Explain why or why not.
(b) Fix z = l and z, = 1. Draw the transformation function between g and q2.
(c) Fix q = = 1. Draw the transformation function (isoquant) for inputs z, and z2.
(d) Find profit maximising z1. z2.91.92 at prices equal to: Pi = 1, p2 = 2 and w =
maximisation problem, think about your picture in (b). With a transformation frontier of this form and such prices, does the firm
produce both outputs? If not, rephrase the maximisation problem accordingly.
1, wz = 2. Hint: before you set up the profit
Transcribed Image Text:4. A two-output-two-input firm has a transformation function of the type: 91 + 92 = z4z4. where q and q are outputs and z and 2z are inputs. (a) Is this production function consistent with non-increasing returns to scale? Explain why or why not. (b) Fix z = l and z, = 1. Draw the transformation function between g and q2. (c) Fix q = = 1. Draw the transformation function (isoquant) for inputs z, and z2. (d) Find profit maximising z1. z2.91.92 at prices equal to: Pi = 1, p2 = 2 and w = maximisation problem, think about your picture in (b). With a transformation frontier of this form and such prices, does the firm produce both outputs? If not, rephrase the maximisation problem accordingly. 1, wz = 2. Hint: before you set up the profit
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