AGEC 2003 : Agec Exam 2 Notes
Notes for exam 2 3/27/2012 1:35:00 AM
Chapter 5: Producer Decision Making – Two Variable Inputs Part 1
Understanding Producer Decisions
• In the previous chapter, we evaluated how changing one variable
input while holding all other inputs constant affected the level of
output produced and net revenue generated
• This relationship is described in the textbook as a factor-product
relationship
• In many cases, a producer faces the decision of varying multiple
inputs to produce a given output
• The beginning of this chapter will address what is described in the
textbook as the factor-factor relationship
Mathematical Two Variable Production Function
• Using the same symbols as in Chapter 4, we can define a
production function with only two inputs as Y = f(X1,X2)
• Or as a production function with two variable inputs and all other
inputs fixed Y = f(X1,X2|X3,X4,…,Xn)
Graphical Two Variable Production Function
• As the TPP curve was the graphical representation of the one
variable input production function, the isoquant is the graphical
representation of the two variable input production function
Terms
• Isoquant
o A curve that shows all combinations of the two variable inputs
that can be used to produce a given quantity of output
• An isoquant is the graphical equivalent in production economics to
what the indifference curve is to consumption economics
Slide 2 on chapter 5 graphs
Terms
• Resource Substitution
o The technical relationship that occurs when one input can be
substituted for another in production while yielding the same
level of output
Special Forms of Resource Substitution
• Perfect substitutes
o A form of resource (input) substitution where one input can
be exactly substituted for another in production
• Perfect compliments
o A form of resource (input) substitution where two inputs can
only be used in production in a fixed ratio and cannot be
substituted for one another
• Imperfect substitutes
o A form of resource (input) substitution where larger and
larger amounts of a second variable resource (input) are
required to replace equal incremental reductions of the first
resource (input) while maintaining the same level of output
Slide 3 on chapter 3 graphs
Marginal Rate of (Technical) Substitution
• Mathematically, MRSx1x2 = ∆X2/∆X1
• Interpreted, the number of units of X2 that X1 can replace without
changing output
• This is analogous to the indifference curve where we choose
different consumption bundles but the level of utility is held
constant
Understanding Marginal Rate of (Technical) Substitution
• As we move downward and to the right along the isoquant, we
must compensate the loss of the use of input X2 in production with
additional use of the input X1 in order to produce the same level of
output (that is, stay on the same isoquant)
• What happens if we reduce the input X2 without increasing X1?
• When we reduce the use of one input without increasing the other
input in production, we reduce the level of output by the Marginal
Physical Product (MPP) of the reduced input multiplied by the
magnitude change of that reduced input
• In the case of reduced X2, the change in output equals
(mathematically) ∆Y = MPPx2 * ∆X2
Slide 4-8 on chapter 5 graphs
Understanding the Marginal Rate of Substitution
• Similarly, if we increase the use of one input while holding the other
input constant, the increase in output is equal to the Marginal
Physical Product of that input multiplied by the magnitude change
of the increased input
• In the case of an increased X1, ∆Y = MPPx1 * ∆X1
• As we move along an isoquant, the reduced level of output resulting
from decreased use of X2 is compensated by increased output from
the use of X1
• Mathematically, MPPx2 * ∆X2 = MPPx1 * ∆X1
o Rearranged ∆X2/∆X1 = MPPx1/MPPx2
o Just as it was in consumption in chapter 3 (we just
substituted MPP for MU)
Slide 9 on chapter 5 graphs
Isocost Curve
• The isocost curve identifies all the combinations of the two given
inputs that can be afforded to produce a given level of output
• Three pieces of information required – price of input X1, Px1, the
price of input X2, Px2, and the total amount of money to be spent on
inputs
• Like the budget line, the points where the isocost line intersect the
vertical and horizontal axis are calculated by the total amount of
money to be spent on inputs divided by the price of the input X2,
Px2, and the total amount of money to be spent on inputs divided by
the price of the input X1, Px1 respectively
Slide 10-11 on chapter 5 graphs
Document Summary
Chapter 5: producer decision making two variable inputs part 1. Graphical two variable production function: as the tpp curve was the graphical representation of the one variable input production function, the isoquant is the graphical representation of the two variable input production function. Terms: resource substitution, the technical relationship that occurs when one input can be substituted for another in production while yielding the same level of output. Physical product (mpp) of the reduced input multiplied by the magnitude change of that reduced input: in the case of reduced x2, the change in output equals (mathematically) y = mppx2 * x2. Understanding the marginal rate of substitution: similarly, if we increase the use of one input while holding the other input constant, the increase in output is equal to the marginal. Px2, and the total amount of money to be spent on inputs divided by the price of the input x1, px1 respectively.
