Suppose you run a factory whose short-run production function is given by f (L) = 180L² – 3L³. (a) Find mathematical expressions for the total product of labor, the average product of labor and the marginal product of labor. (b) On two separate axes, graph T P,, APı, and M PL. The diagrams do not need to be scale, but be sure they are internally consistent. In other words, make sure that all relevant relationships between the three lines are correct. If you have trouble figuring out what the graph looks like, feel free to use a graphing calculator or an online graphing tool to find the basic shape. Find the quantity of labor associated with each of the following points and label it on your diagram: (i) the maximum value of T PL, (ii) the maximum value of APL, (iii) the maximum value of M PL. (c) For what values of L does the production function exhibit each of the following: i. increasing marginal labor productivity ii. diminishing marginal labor productivity iii. negative marginal labor productivity Your answers for part (c) should be in the form of an inequality.

Suppose you run a factory whose short-run production function is given by f (L) = 180L² – 3L³. (a) Find mathematical expressions for the total product of labor, the average product of labor and the marginal product of labor. (b) On two separate axes, graph T P,, APı, and M PL. The diagrams do not need to be scale, but be sure they are internally consistent. In other words, make sure that all relevant relationships between the three lines are correct. If you have trouble figuring out what the graph looks like, feel free to use a graphing calculator or an online graphing tool to find the basic shape. Find the quantity of labor associated with each of the following points and label it on your diagram: (i) the maximum value of T PL, (ii) the maximum value of APL, (iii) the maximum value of M PL. (c) For what values of L does the production function exhibit each of the following: i. increasing marginal labor productivity ii. diminishing marginal labor productivity iii. negative marginal labor productivity Your answers for part (c) should be in the form of an inequality.

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

Suppose you run a factory whose short-run production function is given by
f (L) = 180L² – 3L³.
(a) Find mathematical expressions for the total product of labor, the average product of
labor and the marginal product of labor.
(b) On two separate axes, graph T PL, APL, and MPt. The diagrams do not need to be scale,
but be sure they are internally consistent. In other words, make sure that all relevant
relationships between the three lines are correct. If you have trouble figuring out what
the graph looks like, feel free to use a graphing calculator or an online graphing tool to
find the basic shape. Find the quantity of labor associated with each of the following
points and label it on your diagram: (i) the maximum value of TPL, (ii) the maximum
value of APL, (ii) the maximum value of M PL.
(c) For what values of L does the production function exhibit each of the following:
i. increasing marginal labor productivity
ii. diminishing marginal labor productivity
iii. negative marginal labor productivity
Your answers for part (c) should be in the form of an inequality.

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