3) A paper factory signed contract to produce 1000 reams of paper each week for a customer. The paper plant's production function is Q = 4K0.75 L0.25, where Q is output (reams produced), K is the quantity of capital rented, and L is the quantity of labor hired. Each worker is paid $10 per hour and each machine rents for $60 per hour. a. What is the MRTSLK? Demonstrate. b. Find the optimal amount of Labor and capital that is needed to produce 1,000 reams per week. c. What is the firms' total cost of producing the 1,000 reams?
3) A paper factory signed contract to produce 1000 reams of paper each week for a customer. The paper plant's production function is Q = 4K0.75 L0.25, where Q is output (reams produced), K is the quantity of capital rented, and L is the quantity of labor hired. Each worker is paid $10 per hour and each machine rents for $60 per hour. a. What is the MRTSLK? Demonstrate. b. Find the optimal amount of Labor and capital that is needed to produce 1,000 reams per week. c. What is the firms' total cost of producing the 1,000 reams?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
![3) A paper factory signed contract to produce 1000 reams of paper each week for a customer. The paper
plant's production function is Q = 4K0.75 L0.25, where Q is output (reams produced), K is the quantity of capital
rented, and L is the quantity of labor hired. Each worker is paid $10 per hour and each machine rents for $60 per
hour.
a. What is the MRTSLK? Demonstrate.
b. Find the optimal amount of Labor and capital that is needed to produce 1,000 reams per week.
c. What is the firms' total cost of producing the 1,000 reams?
d. Draw a diagram of the iso-quant and the iso-cost lines and identify the optimal input combination.
e. Suppose the firm needs to increase production to 1,100. Without redoing the full analyses, determine how
much additional labor and capital will be needed to achieve this. (This is a one-line answer).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7b9ef3af-1bb5-4398-94ba-7d8c1b3fd143%2Fc8e312ae-247c-4ead-b6aa-5d22637f0542%2Ftw91p7q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3) A paper factory signed contract to produce 1000 reams of paper each week for a customer. The paper
plant's production function is Q = 4K0.75 L0.25, where Q is output (reams produced), K is the quantity of capital
rented, and L is the quantity of labor hired. Each worker is paid $10 per hour and each machine rents for $60 per
hour.
a. What is the MRTSLK? Demonstrate.
b. Find the optimal amount of Labor and capital that is needed to produce 1,000 reams per week.
c. What is the firms' total cost of producing the 1,000 reams?
d. Draw a diagram of the iso-quant and the iso-cost lines and identify the optimal input combination.
e. Suppose the firm needs to increase production to 1,100. Without redoing the full analyses, determine how
much additional labor and capital will be needed to achieve this. (This is a one-line answer).
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