Problem 1: A firm has the following production function: f(L, M) = min{L, 3M) where L is the number of labor hours and M is the number of machines. A) Show whether this firm's technology exhibits constant, increasing, or decreasing returns to scale. B) What is the optimality condition that determines the firm's optimal level of inputs? C) Suppose the firm wants to produce exactly y units and that input L costs $w, per unit and input M costs $w, per unit. What are the firm's input demand functions? D) Using the information from part D), write down the firm's total cost function as a function of w₁, WM, and y.

Problem 1: A firm has the following production function: f(L, M) = min{L, 3M) where L is the number of labor hours and M is the number of machines. A) Show whether this firm's technology exhibits constant, increasing, or decreasing returns to scale. B) What is the optimality condition that determines the firm's optimal level of inputs? C) Suppose the firm wants to produce exactly y units and that input L costs $w, per unit and input M costs $w, per unit. What are the firm's input demand functions? D) Using the information from part D), write down the firm's total cost function as a function of w₁, WM, and y.

Microeconomics A Contemporary Intro

10th Edition

ISBN:9781285635101

Author:MCEACHERN

Publisher:MCEACHERN

Chapter7: Production And Cost In The Firm

Section7.A: Appendix: A Closer Look At Production And Cost

Problem 1AQ

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