. Apple uses labour and machines to produce iPhones according to the production f y = L&M, where L is the number of units of labour used and M is the number of m The cost of labour is w₁ = 4 per unit and the cost of using a machine is wM = 16. faces a fixed cost of F = 25 for renting its factory. Given these input prices, Apple cl how much labour and machines to employ in order to minimize the cost of producin, given amount of iPhones y. Apple is therefore solving a cost-minimization problem.
. Apple uses labour and machines to produce iPhones according to the production f y = L&M, where L is the number of units of labour used and M is the number of m The cost of labour is w₁ = 4 per unit and the cost of using a machine is wM = 16. faces a fixed cost of F = 25 for renting its factory. Given these input prices, Apple cl how much labour and machines to employ in order to minimize the cost of producin, given amount of iPhones y. Apple is therefore solving a cost-minimization problem.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
can you explain the solution for part b like for example how did they get M=y^2/2 and L=2y^2
![15. Apple uses labour and machines to produce iPhones according to the production
y = LAM, where L is the number of units of labour used and M is the number of me
The cost of labour is w₁ = 4 per unit and the cost of using a machine is wWM = 16.
faces a fixed cost of F = 25 for renting its factory. Given these input prices, Apple cl
how much labour and machines to employ in order to minimize the cost of producin,
given amount of iPhones y. Apple is therefore solving a cost-minimization problem.
Solution: a) We have the technical rate of substitution is equal to the ratio of input
{M}
= so that L = 4M and
LM
prices: MPL
WL. Here, that implies:
MPM WM
Apple will use 4 workers for each machine.
PERDRY
I
=
b) We have y LM and L= 4M. Solving them together gives: M =
and L = 2y².
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06207e20-a3f2-4f4e-b190-212fd3381778%2Fc5616024-d321-4252-a53c-1e1c010925c1%2F6mvsnwu_processed.png&w=3840&q=75)
Transcribed Image Text:15. Apple uses labour and machines to produce iPhones according to the production
y = LAM, where L is the number of units of labour used and M is the number of me
The cost of labour is w₁ = 4 per unit and the cost of using a machine is wWM = 16.
faces a fixed cost of F = 25 for renting its factory. Given these input prices, Apple cl
how much labour and machines to employ in order to minimize the cost of producin,
given amount of iPhones y. Apple is therefore solving a cost-minimization problem.
Solution: a) We have the technical rate of substitution is equal to the ratio of input
{M}
= so that L = 4M and
LM
prices: MPL
WL. Here, that implies:
MPM WM
Apple will use 4 workers for each machine.
PERDRY
I
=
b) We have y LM and L= 4M. Solving them together gives: M =
and L = 2y².
=
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