Please solve sub question (5) ONLY A company that produces healthcare services (patient visits) operates with the followingproduction function where q denotes the weekly output level in terms of the number ofpatients, L represents the hours of human intelligence (doctors and nurses) employed perweek, and K denotes the hours of artificial intelligence utilized per week:q=L0.5 K0.25The cost per hour for artificial intelligence is represented by r, and the cost per hour forhuman intelligence is denoted by w, both expressed in dollars per hour.1) Determine the optimal levels of L and K that minimize the firm's costs given a target levelof production q. Express the cost-minimizing levels of Land K as two functions of q, w, andr. Show your work carefully.For the following questions, for simplicity, assume that w=1 and r=1.2) Suppose the firm aims to produce eight visits this week (q=8), calculate the optimal hoursof human intelligence Land artificial intelligence K. Also find the total cost of producingthose eight patient visits.3) Considering the firm has the flexibility to adjust L and K (we are in the long run of thefirm), what is the firm's supply curve?4) Suppose the firm decides on a new production level of 12 patients seen per week but hasalready committed to 9 hours of artificial intelligence K and cannot change this input. Howmany hours of human intelligence L will the firm need to employ to achieve this newproduction level in the short run of the firm? What will be the cost of reaching this newoutput?5) Intuitively, with words, briefly discuss what would happen with your answers in (1), and(2) if there is technological change and now the production function becomes:q=L0.25 K0.5

New Production function : q = L0.25 K0.5Price of K = rPrice of L = w Cost constraint : C = wL +…

A company that produces healthcare services (patient visits) operates with the following production function where q denotes the weekly output level in terms of the number of patients, L represents the hours of human intelligence (doctors and nurses) employed per week, and K denotes the hours of artificial intelligence utilized per week: q=L0.5 K0.25

A company that produces healthcare services (patient visits) operates with the following production function where q denotes the weekly output level in terms of the number of patients, L represents the hours of human intelligence (doctors and nurses) employed per week, and K denotes the hours of artificial intelligence utilized per week: q=L0.5 K0.25

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter16: Labor Markets

Section: Chapter Questions

Problem 16.7P

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A company that produces healthcare services (patient visits) operates with the following production function where q denotes the weekly output level in terms of the number of patients, L represents the hours of human intelligence (doctors and nurses) employed per week, and K denotes the hours of artificial intelligence utilized per week: 9 L0.5 K0.25 = The cost per hour for artificial intelligence is represented by r, and the cost per hour for human intelligence is denoted by w, both expressed in dollars per hour. 1) Determine the optimal levels of L and K that minimize the firm's costs given a target level of production q. Express the cost-minimizing levels of L and K as two functions of q, w, and r. Show your work carefully.
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