For each of the following production functions, please do the following: i) graph the isoquant curve corresponding to Q = 100 (Tip: you don't need to use the same scale on all your graphs); ii) for each of labour and capital, use the corresponding marginal product functions to describe whether diminishing marginal returns exist; iii) find the marginal rate of technical substitution of labour for capital; iv) describe if there are increasing, constant, or decreasing returns to scale.

Microeconomics A Contemporary Intro
10th Edition
ISBN:9781285635101
Author:MCEACHERN
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Chapter7: Production And Cost In The Firm
Section7.A: Appendix: A Closer Look At Production And Cost
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For each of the following production functions, please do the following:
i) graph the isoquant curve corresponding to Q = 100 (Tip: you don't need to use
the same scale on all your graphs);
ii) for each of labour and capital, use the corresponding marginal product functions
to describe whether diminishing marginal returns exist;
iii) find the marginal rate of technical substitution of labour for capital;
iv) describe if there are increasing, constant, or decreasing returns to scale.
(a) Q = 3√L+ √K, MPL = 2 MPK = 2√/K
L'
(b) Q = 10√/KL, MPL = 5V, MPK = 5
(c) Q = VKL, MP₁ =
MPK =
(d) Q = 3L + 2K, MPL = 3, MPK = 2
(e) Q = K²√L, MPL = K2, MPK = 2K√L
1
Transcribed Image Text:For each of the following production functions, please do the following: i) graph the isoquant curve corresponding to Q = 100 (Tip: you don't need to use the same scale on all your graphs); ii) for each of labour and capital, use the corresponding marginal product functions to describe whether diminishing marginal returns exist; iii) find the marginal rate of technical substitution of labour for capital; iv) describe if there are increasing, constant, or decreasing returns to scale. (a) Q = 3√L+ √K, MPL = 2 MPK = 2√/K L' (b) Q = 10√/KL, MPL = 5V, MPK = 5 (c) Q = VKL, MP₁ = MPK = (d) Q = 3L + 2K, MPL = 3, MPK = 2 (e) Q = K²√L, MPL = K2, MPK = 2K√L 1
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