A production function expresses the relationship between inputs, such as capital (K) and labor (L), and output (q). The following equation represents the functional form for a production function: q = f (K, L). If a production function exhibits constant returns to scale, this means that if you double the amount of capital and labor used, output is twice its original amount. Suppose the production function is as follows: f(K, L) = 4K +9L. Prove that this production function exhibits constant returns to scale by completing the following algebraic equations. Assume that z is a positive number. f(zK, zL) = 1 111. =zq Which of the following production functions exhibit constant returns to scale? Check all that apply. Of(K, L) = KL Of(K, L) = 7K0.5 10.5 Of(K, L) = 3K0.5 10.1
A production function expresses the relationship between inputs, such as capital (K) and labor (L), and output (q). The following equation represents the functional form for a production function: q = f (K, L). If a production function exhibits constant returns to scale, this means that if you double the amount of capital and labor used, output is twice its original amount. Suppose the production function is as follows: f(K, L) = 4K +9L. Prove that this production function exhibits constant returns to scale by completing the following algebraic equations. Assume that z is a positive number. f(zK, zL) = 1 111. =zq Which of the following production functions exhibit constant returns to scale? Check all that apply. Of(K, L) = KL Of(K, L) = 7K0.5 10.5 Of(K, L) = 3K0.5 10.1
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.9P
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Transcribed Image Text:5. Proving constant returns to scale
A production function expresses the relationship between inputs, such as capital (K) and labor (L), and output (q). The following equation represents
the functional form for a production function: q= f (K, L).
If a production function exhibits constant returns to scale, this means that if you double the amount of capital and labor used, output is
twice its original amount.
Suppose the production function is as follows:
ƒ (K, L) = 4K +9L.
Prove that this production function exhibits constant returns to scale by completing the following algebraic equations. Assume that z is a positive
number.
f (zK, zL)
111.
= 2q
Which of the following production functions exhibit constant returns to scale? Check all that apply.
f (K, L) = KL
f (K, L) 7K0.5 10.5
□ f (K, L) = 3K0.5 L0.1
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