Assume instead that pharmacists and robots dispense prescriptions according to the following production function: Y = 10*KO.8L0.2 where Y is the number of prescriptions dispensed; L is the number pharmacist hours, and K is the number of robot hours. In addition, $10 worth of materials is used for each prescription. a. What is this type of production function called, and what are we assuming about the relationship between robots and pharmacists by using this production function? b. Derive the cost-minimizing demands for K and L as a function of output, the wage rate and the rental rate of capital. c. Use these results to derive the total cost function: costs as a function of y, r, w, and the $10 materials cost. d. Pharmacists earn $32 per hour. The rental rate for robots is $64 per hour. What are total costs as a function of Y? e. Does this technology exhibit decreasing, constant, or increasing returns to scale? f. The pharmacy plans to produce 40,000 prescriptions per week. At the prices given in part d), how many pharmacists should the pharmacy hire? How many robots should it rent? (Assume that pharmacists and robots work 40 hours/week each.) g. What are the marginal and average costs at this level of production?

Assume instead that pharmacists and robots dispense prescriptions according to the following production function: Y = 10*KO.8L0.2 where Y is the number of prescriptions dispensed; L is the number pharmacist hours, and K is the number of robot hours. In addition, $10 worth of materials is used for each prescription. a. What is this type of production function called, and what are we assuming about the relationship between robots and pharmacists by using this production function? b. Derive the cost-minimizing demands for K and L as a function of output, the wage rate and the rental rate of capital. c. Use these results to derive the total cost function: costs as a function of y, r, w, and the $10 materials cost. d. Pharmacists earn $32 per hour. The rental rate for robots is $64 per hour. What are total costs as a function of Y? e. Does this technology exhibit decreasing, constant, or increasing returns to scale? f. The pharmacy plans to produce 40,000 prescriptions per week. At the prices given in part d), how many pharmacists should the pharmacy hire? How many robots should it rent? (Assume that pharmacists and robots work 40 hours/week each.) g. What are the marginal and average costs at this level of production?

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Assume instead that pharmacists and robots dispense prescriptions according to the following production function: Y
= 10*KO.8L0.2 where Y is the number of prescriptions dispensed; L is the number pharmacist hours, and K is the
number of robot hours. In addition, $10 worth of materials is used for each prescription. a. What is this type of
production function called, and what are we assuming about the relationship between robots and pharmacists by using
this production function? b. Derive the cost - minimizing demands for K and L as a function of output, the wage rate and
the rental rate of capital. c. Use these results to derive the total cost function: costs as a function of y, r, w, and the $10
materials cost. d. Pharmacists earn $32 per hour. The rental rate for robots is $64 per hour. What are total costs as a
function of Y? e. Does this technology exhibit decreasing, constant, or increasing returns to scale?f. The pharmacy
plans to produce 40,000 prescriptions per week. At the prices given in part d), how many pharmacists should the
pharmacy hire? How many robots should it rent? (Assume that pharmacists and robots work 40 hours/week each.) g.
What are the marginal and average costs at this level of production?

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