2. Indira runs a bakery using labor (L, measured in hours of her time) and capital (K, measuredin ovens). Indira's production function (measured in loaves of bread) is given byf (L, K) = 4L}K³.(a) Indira currently has 8 ovens.i. Find an expression for her (short-run) average and marginal product of labor.ii. In two separate diagrams, graph Indira's total, average, and marginal product oflabor. Do these curves follow all the rules we discussed about the relationshipsbetween curves? Does Indira's production technology satisfy the law of diminishingmarginal returns?(b) Suppose Indira is trying to decide whether to buy more ovens or sell some of the ones shehas and wants to understand the tradeoffs between more ovens and her time. If Indirawants to produce 100 loaves a week, help her find out how many ovens she’ll need forvarious amounts of her time. That is, find an expression for the number of ovens she'llneed to produce 100 loaves as a function of the number of hours she works. (Hint: ifre stuck, trying picking a couple specific numbers of hours she might work and seehow many ovens she’d need to get 100 loaves. Then try to generalize to get an expressionthat will work for any amount of time. ).(c) Plot your equation from part (b). What does this line represent?(d) Find an expression for Indira's marginal rate of technical substitution between ovensand labor as a function of K and L. What is the connection between your answer tothis question and the picture you drew in part (c).you

The production function gives the different output levels that get produced when production inputs…

2. Indira runs a bakery using labor (L, measured in hours of her time) and capital (K, measured in ovens). Indira's production function (measured in loaves of bread) is given by f (L, K) = 4L}K³. %3D (a) Indira currently has 8 ovens. i. Find an expression for her (short-run) average and marginal product of labor. ii. In two separate diagrams, graph Indira's total, average, and marginal product of labor. Do these curves follow all the rules we discussed about the relationships between curves? Does Indira's production technology satisfy the law of diminishing marginal returns?

2. Indira runs a bakery using labor (L, measured in hours of her time) and capital (K, measured in ovens). Indira's production function (measured in loaves of bread) is given by f (L, K) = 4L}K³. %3D (a) Indira currently has 8 ovens. i. Find an expression for her (short-run) average and marginal product of labor. ii. In two separate diagrams, graph Indira's total, average, and marginal product of labor. Do these curves follow all the rules we discussed about the relationships between curves? Does Indira's production technology satisfy the law of diminishing marginal returns?

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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Concept explainers

Isocost and Isoprofit Curve Analysis

An isocost curve in the production theory that is a crucial part of economics depicts different combinations of factor inputs at a given market cost. In other words, this shows all the combinations of production factors that cost the same for the firm to employ. Usually, this can be depicted as a downward sloping straight line when the firms act as the price-takers in the factor markets. The slope of this mainly depicts the relative prices of different production factors.

Question

2. Indira runs a bakery using labor (L, measured in hours of her time) and capital (K, measured
in ovens). Indira's production function (measured in loaves of bread) is given by
f (L, K) = 4L}K³.
(a) Indira currently has 8 ovens.
i. Find an expression for her (short-run) average and marginal product of labor.
ii. In two separate diagrams, graph Indira's total, average, and marginal product of
labor. Do these curves follow all the rules we discussed about the relationships
between curves? Does Indira's production technology satisfy the law of diminishing
marginal returns?
(b) Suppose Indira is trying to decide whether to buy more ovens or sell some of the ones she
has and wants to understand the tradeoffs between more ovens and her time. If Indira
wants to produce 100 loaves a week, help her find out how many ovens she’ll need for
various amounts of her time. That is, find an expression for the number of ovens she'll
need to produce 100 loaves as a function of the number of hours she works. (Hint: if
re stuck, trying picking a couple specific numbers of hours she might work and see
how many ovens she’d need to get 100 loaves. Then try to generalize to get an expression
that will work for any amount of time. ).
(c) Plot your equation from part (b). What does this line represent?
(d) Find an expression for Indira's marginal rate of technical substitution between ovens
and labor as a function of K and L. What is the connection between your answer to
this question and the picture you drew in part (c).
you

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