. Apple uses labour and machines to produce iPhones according to the production function y = LM, where L is the number of units of labour used and M is the number of machines. The cost of labour is w = 4 per unit and the cost of using a machine is wM = 16. Apple faces a fixed cost of F = 25 for renting its factory. Given these input prices, Apple chooses how much labour and machines to employ in order to minimize the cost of producing any given amount of iPhones y. Apple is therefore solving a cost-minimization problem. (a) If Apple is cost-minimizing, how many workers will it use for each machine? That is, find the number of workers per machine that Apple will employ. (Hint: setup the tangency condition.) (b) Continuing to assume that Apple produces any given number of iPhones y in the cheapest way possible, use the equation defining the number of workers per machine from part (a) and Apple's production function to find expressions for the cost-minimizing choices of labour and machines as functions of output produced y. (c) Now use your answers to part (b) to derive Apple's total cost for producing iPhones as a function of the number of units produced y.

. Apple uses labour and machines to produce iPhones according to the production function y = LM, where L is the number of units of labour used and M is the number of machines. The cost of labour is w = 4 per unit and the cost of using a machine is wM = 16. Apple faces a fixed cost of F = 25 for renting its factory. Given these input prices, Apple chooses how much labour and machines to employ in order to minimize the cost of producing any given amount of iPhones y. Apple is therefore solving a cost-minimization problem. (a) If Apple is cost-minimizing, how many workers will it use for each machine? That is, find the number of workers per machine that Apple will employ. (Hint: setup the tangency condition.) (b) Continuing to assume that Apple produces any given number of iPhones y in the cheapest way possible, use the equation defining the number of workers per machine from part (a) and Apple's production function to find expressions for the cost-minimizing choices of labour and machines as functions of output produced y. (c) Now use your answers to part (b) to derive Apple's total cost for producing iPhones as a function of the number of units produced y.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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