Please solve sub questions 3 and 4 ONLY. (3) and (4) 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:9 L0.5 K0.25=The 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 L and 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 L and 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?

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

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

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Please solve sub questions 3 and 4 ONLY. (3) and (4)

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.
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 hours
of human intelligence L and artificial intelligence K. Also find the total cost of producing
those eight patient visits.
3) Considering the firm has the flexibility to adjust L and K (we are in the long run of the
firm), what is the firm's supply curve?
4) Suppose the firm decides on a new production level of 12 patients seen per week but has
already committed to 9 hours of artificial intelligence K and cannot change this input. How
many hours of human intelligence L will the firm need to employ to achieve this new
production level in the short run of the firm? What will be the cost of reaching this new
output?

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