Suppose life expectancy in years (L) is a function of two inputs, health expenditures (H) and nutrition expenditures (N) in hundreds of dollars per year. The production function is L = CH 0.40 N0.60 Beginning with a health input of $400 per year (H = 4) and a nutrition input of $400 per year (N = 4), show that the marginal product of health expenditures and the marginal product of nutrition expenditures are both decreasing. The change in the marginal product of health expenditures (MPH) is AMPH ΔΗ = and the change in the marginal product of nutrition expenditures (MPN) is AMPN ΔΝ Does this production function exhibit increasing, decreasing, or constant returns to scale? This production function exhibits A. first decreasing and then increasing returns to scale. B. constant returns to scale. C. decreasing returns to scale. D. increasing returns to scale. E. first increasing and then decreasing returns to scale.

Microeconomic Theory
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ISBN:9781337517942
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Chapter11: Profit Maximization
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Problem 11.14P
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Suppose life expectancy in years (L) is a function of two inputs, health expenditures (H) and nutrition expenditures (N)
in hundreds of dollars per year. The production function is
L = CH 0.40 N0.60
Beginning with a health input of $400 per year (H = 4) and a nutrition input of $400 per year (N = 4), show that the
marginal product of health expenditures and the marginal product of nutrition expenditures are both decreasing.
The change in the marginal product of health expenditures (MPH) is
AMPH
ΔΗ
=
and the change in the marginal product of nutrition expenditures (MPN) is
AMPN
ΔΝ
Does this production function exhibit increasing, decreasing, or constant returns to scale?
This production function exhibits
A. first decreasing and then increasing returns to scale.
B. constant returns to scale.
C. decreasing returns to scale.
D. increasing returns to scale.
E. first increasing and then decreasing returns to scale.
Transcribed Image Text:Suppose life expectancy in years (L) is a function of two inputs, health expenditures (H) and nutrition expenditures (N) in hundreds of dollars per year. The production function is L = CH 0.40 N0.60 Beginning with a health input of $400 per year (H = 4) and a nutrition input of $400 per year (N = 4), show that the marginal product of health expenditures and the marginal product of nutrition expenditures are both decreasing. The change in the marginal product of health expenditures (MPH) is AMPH ΔΗ = and the change in the marginal product of nutrition expenditures (MPN) is AMPN ΔΝ Does this production function exhibit increasing, decreasing, or constant returns to scale? This production function exhibits A. first decreasing and then increasing returns to scale. B. constant returns to scale. C. decreasing returns to scale. D. increasing returns to scale. E. first increasing and then decreasing returns to scale.
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