> The production function for gadgets is: Q = Q(L, G) = L½ + G½ ne price of L is w = $2. The price of G is r = $3. Total cost is: C = 2L + 3G %3D > In this problem, first check for returns to scale. > Then find expressions for the cost-minimizing input levels (L*, G*) as functions of a target quantity of output (Qo). > Then find L* & G* for two different target levels of output. a. Prove that production of gadgets exhibits diminishing returns to scale. b. Find expressions for the marginal products of L and G. 1/2 + G MPL = %3D -/2 MPG =
> The production function for gadgets is: Q = Q(L, G) = L½ + G½ ne price of L is w = $2. The price of G is r = $3. Total cost is: C = 2L + 3G %3D > In this problem, first check for returns to scale. > Then find expressions for the cost-minimizing input levels (L*, G*) as functions of a target quantity of output (Qo). > Then find L* & G* for two different target levels of output. a. Prove that production of gadgets exhibits diminishing returns to scale. b. Find expressions for the marginal products of L and G. 1/2 + G MPL = %3D -/2 MPG =
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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How do I prove there is diminishing returns to scale?  Also is part b accurately derived? Thank you!

Transcribed Image Text:> The production function for gadgets is: Q = Q(L, G) = L½ + G½
%3D
The price ofL is w = $2. The price of G is r = $3. Total cost is:
C = 2L + 3G
> In this problem, first check for returns to scale.
* Then find expressions for the cost-minimizing input levels (L*, G*) as functions of
a target quantity of output (Qo).
> Then find L* & G* for two different target levels of output.
a. Prove that production of gadgets exhibits diminishing returns to scale.
b. Find expressions for the marginal products of L and G.
1/2
+ G
MPL =
2
MPG =
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