Week 3 managerial economics
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6ech06_rev.pptChapter Six
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
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Chapter 6
The Theory
and
Estimation of Production
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
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Overview
- The production function
- Short-run analysis of average and marginal product
- Long-run production function
- Importance of production function in managerial decision making
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
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Learning objectives
- define the production function
- explain the various forms of production functions
- provide examples of types of inputs into a production function for a manufacturing or service company
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
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Learning objectives
- understand the law of diminishing returns
- use the Three Stages of Production to explain why a rational firm always tries to operate in Stage II
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
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Production function
- Production function: defines the relationship between inputs and the maximum amount that can be produced within a given period of time with a given level of technology
Q=f(X1, X2, ..., Xk)
Q = level of output
X1, X2, ..., Xk = inputs used in
production
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
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Production function
- Key assumptions
- given ‘state of the art’ production technology
- whatever input or input combinations are included in a particular function, the output resulting from their utilization is at the maximum level
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
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Production function
- For simplicity we will often consider a production function of two inputs:
Q=f(X, Y)
Q = output
X = labor
Y = capital
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
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Production function
- Short-run production function shows the maximum quantity of output that can be produced by a set of inputs, assuming the amount of at least one of the inputs used remains unchanged
- Long-run production function shows the maximum quantity of output that can be produced by a set of inputs, assuming the firm is free to vary the amount of all the inputs being used
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
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Short-run analysis of Total,
Average, and Marginal product
- Alternative terms in reference to inputs
- ‘inputs’
- ‘factors’
- ‘factors of production’
- ‘resources’
- Alternative terms in reference to outputs
- ‘output’
- ‘quantity’ (Q)
- ‘total product’ (TP)
- ‘product’
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
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Short-run analysis of Total,
Average, and Marginal product
- Marginal product (MP) = change in output (Total Product) resulting from a unit change in a variable input
- Average product (AP) = Total Product per unit of input used
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
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Short-run analysis of Total,
Average, and Marginal product
- if MP > AP then AP is rising
- if MP < AP then AP is falling
- MP=AP when AP is maximized
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
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Short-run analysis of Total,
Average, and Marginal product
- Law of diminishing returns: as additional units of a variable input are combined with a fixed input, after some point the additional output (i.e., marginal product) starts to diminish
- nothing says when diminishing returns will start to take effect
- all inputs added to the production process have the same productivity
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
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Short-run analysis of Total,
Average, and Marginal product
- The Three Stages of Production in the short run:
- Stage I: from zero units of the variable input to where AP is maximized (where MP=AP)
- Stage II: from the maximum AP to where MP=0
- Stage III: from where MP=0 on
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
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Short-run analysis of Total,
Average, and Marginal product
- In the short run, rational firms should be operating only in Stage II
Q: Why not Stage III? firm uses more variable inputs to produce less output
Q: Why not Stage I? underutilizing fixed capacity, so can increase output per unit by increasing the amount of the variable input
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
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Short-run analysis of Total,
Average, and Marginal product
- What level of input usage within Stage II is best for the firm?
answer depends upon:
how many units of output the firm can sell
the price of the product
the monetary costs of employing the variable input
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
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Short-run analysis of Total,
Average, and Marginal product
- Total revenue product (TRP) = market value of the firm’s output, computed by multiplying the total product by the market price
TRP = Q · P
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
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Short-run analysis of Total,
Average, and Marginal product
- Marginal revenue product (MRP) = change in the firm’s TRP resulting from a unit change in the number of inputs used
MRP = MP · P =
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
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Short-run analysis of Total,
Average, and Marginal product
- Total labor cost (TLC) = total cost of using the variable input labor, computed by multiplying the wage rate by the number of variable inputs employed
TLC = w · X
- Marginal labor cost (MLC) = change in total labor cost resulting from a unit change in the number of variable inputs used
MLC = w
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
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Short-run analysis of Total,
Average, and Marginal product
- Summary of relationship between demand for output and demand for a single input:
A profit-maximizing firm operating in perfectly competitive output and input markets will be using the optimal amount of an input at the point at which the monetary value of the input’s marginal product is equal to the additional cost of using that input
MRP = MLC
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
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Short-run analysis of Total,
Average, and Marginal product
- Multiple variable inputs
- Consider the relationship between the ratio of the marginal product of one input and its cost to the ratio of the marginal product of the other input(s) and their cost
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
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Long-run production function
- In the long run, a firm has enough time to change the amount of all its inputs
- The long run production process is described by the concept of returns to scale
Returns to scale = the resulting increase
in total output as all inputs increase
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
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Long-run production function
- If all inputs into the production process are doubled, three things can happen:
- output can more than double
‘increasing returns to scale’ (IRTS)
- output can exactly double
‘constant returns to scale’ (CRTS)
- output can less than double
‘decreasing returns to scale’ (DRTS)
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
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Long-run production function
- One way to measure returns to scale is to use a coefficient of output elasticity:
if EQ > 1 then IRTS
if EQ = 1 then CRTS
if EQ < 1 then DRTS
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
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Long-run production function
- Returns to scale can also be described using the following equation
hQ = f(kX, kY)
if h > k then IRTS
if h = k then CRTS
if h < k then DRTS
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
Chapter Six
Copyright 2009 Pearson Education, Inc. Publishing as Prentice Hall.
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Long-run production function
- Graphically, the returns to scale concept can be illustrated using the following graphs
Q
X,Y
IRTS
Q
X,Y
CRTS
Q
X,Y
DRTS
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X
Q
MP
X
D
D
=
X
Q
AP
X
=
X
TRP
D
D
k
k
w
MP
w
MP
w
MP
=
=
2
2
1
1
inputs
all
in
change
Percentage
Q
in
change
Percentage
=
Q
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