Chapter 7 1 ©2005 Pearson Education, Inc. Product Curves 10 30 q/L 8 0 2 3 4 5 6 7 9 10 1 Labor q 112 Labor 0 2 3 4 5 6 7 8 9 10 1 C 60 B 20 AP is slope of line from origin to point on TP curve TP MP AP
Dec 22, 2015
Chapter 7 1©2005 Pearson Education, Inc.
Product Curves
10
30
q/L
80 2 3 4 5 6 7 9 101Labor
q
112
Labor
0 2 3 4 5 6 7 8 9 101
C
60 B20
AP is slope of line from origin to point on TP curve
TP
MP
AP
Chapter 7 2©2005 Pearson Education, Inc.
Practice
Bridget's Brewery production function is given by
where K is the number of vats she uses and L is the number of labor hours. Does this production process exhibit increasing, constant or decreasing returns to scale? Holding the number of vats constant at 4, is the marginal product of labor increasing, constant or decreasing as more labor is used?
, 2 ,y K L KL
Chapter 7 3©2005 Pearson Education, Inc.
Solution
Multiplying the K and L by 2 yields:we know the production process exhibits
constant returns to scale. Holding the number of vats constant at 4 will still result in a downward sloping marginal product of labor curve. That is the marginal product of labor decreases as more labor is used.
Chapter 7 5©2005 Pearson Education, Inc.
Measuring Cost:Which Costs Matter?
Accountants tend to take a retrospective view of firms’ costs, whereas economists tend to take a forward-looking view
Accounting Cost Actual expenses plus depreciation charges
for capital equipmentEconomic Cost
Cost to a firm of utilizing economic resources in production, including opportunity cost
Chapter 7 6©2005 Pearson Education, Inc.
Measuring Cost:Which Costs Matter?
Economic costs distinguish between costs the firm can control and those it cannot Concept of opportunity cost plays an
important role
Opportunity cost Cost associated with opportunities that are
foregone or the value of the next best alternative use of a resource
Chapter 7 7©2005 Pearson Education, Inc.
Opportunity Cost
An Example A firm owns its own building and pays no rent
for office space Does this mean the cost of office space is
zero? The building could have been rented instead Foregone rent is the opportunity cost of using
the building for production and should be included in the economic costs of doing business
Chapter 7 8©2005 Pearson Education, Inc.
Opportunity Cost
A person starting their own business must take into account the opportunity cost of their time Could have worked elsewhere making a
competitive salary
Accountants and economists often treat depreciation differently as well
Chapter 7 9©2005 Pearson Education, Inc.
Measuring Cost:Which Costs Matter?
Although opportunity costs are hidden and should be taken into account, sunk costs should not
Sunk Cost Expenditure that has been made and cannot
be recovered Should not influence a firm’s future economic
decisions
Chapter 7 10©2005 Pearson Education, Inc.
Sunk Cost
Firm buys a piece of equipment that cannot be converted to another use
Expenditure on the equipment is a sunk cost Has no alternative use so cost cannot be
recovered – opportunity cost is zero Decision to buy the equipment might have
been good or bad, but now does not matter
Chapter 7 11©2005 Pearson Education, Inc.
Prospective Sunk Cost
An Example Firm is considering moving its headquarters A firm paid $500,000 for an option to buy a
building The cost of the building is $5 million for a
total of $5.5 million The firm finds another building for $5.25
million Which building should the firm buy?
Chapter 7 12©2005 Pearson Education, Inc.
Prospective Sunk Cost
Example (cont.)The first building should be purchasedThe $500,000 is a sunk cost and should
not be considered in the decision to buyWhat should be considered is
Spending an additional $5,250,000 or Spending an additional $5,000,000
Chapter 7 13©2005 Pearson Education, Inc.
Measuring Cost:Which Costs Matter?
Some costs vary with output, while some remain the same no matter the amount of output
Total cost can be divided into:
1. Fixed Cost Does not vary with the level of output
2. Variable Cost Cost that varies as output varies
Chapter 7 14©2005 Pearson Education, Inc.
Fixed and Variable Costs
Total cost of production equals the fixed cost (the cost of the fixed inputs) plus the variable cost (the cost of the variable inputs), or…
Short time horizon – most costs are fixedLong time horizon – many costs become
variable
VC FC TC
Chapter 7 15©2005 Pearson Education, Inc.
Fixed Cost Versus Sunk Cost
Fixed cost and sunk cost are often confused
Fixed Cost Cost paid by a firm that is in business
regardless of the level of output
Sunk Cost Cost that has been incurred and cannot be
recovered
Chapter 7 16©2005 Pearson Education, Inc.
Measuring Costs
Marginal Cost (MC): The cost of expanding output by one unit Fixed costs have no impact on marginal cost,
so it can be written as:
Δq
ΔTC
Δq
ΔVC MC
Chapter 7 17©2005 Pearson Education, Inc.
Measuring Costs
Average Total Cost (ATC) Cost per unit of output Also equals average fixed cost (AFC) plus
average variable cost (AVC)
q
TVC
q
TFC
q
TC ATC
AVCAFC q
TC ATC
Chapter 7 19©2005 Pearson Education, Inc.
Determinants of Short Run Costs – An Example
Assume the wage rate (w) is fixed relative to the number of workers hired
Variable costs is the per unit cost of extra labor times the amount of extra labor: wL
q
Lw
q
VC MC
Chapter 7 20©2005 Pearson Education, Inc.
Determinants of Short Run Costs – An Example
Remembering that
LMP L
Q
L
L 1L for a 1 unit Q
Q MP
And rearranging
Chapter 7 21©2005 Pearson Education, Inc.
Determinants of Short Run Costs – An Example
We can conclude:
LMP MC
w
…and a low marginal product (MPL) leads to a high marginal cost (MC) and vice versa
Chapter 7 22©2005 Pearson Education, Inc.
Determinants of Short Run Costs
Consequently (from the table): MC decreases initially with increasing returns
0 through 4 units of output MC increases with decreasing returns
5 through 11 units of output
Chapter 7 23©2005 Pearson Education, Inc.
Cost Curves for a Firm
Output
Cost($ peryear)
100
200
300
400
0 1 2 3 4 5 6 7 8 9 10 11 12 13
VC
Variable costincreases with production and
the rate varies withincreasing and
decreasing returns.
TC
Total costis the vertical
sum of FC and VC.
FC50
Fixed cost does notvary with output
Chapter 7 24©2005 Pearson Education, Inc.
Cost Curves
0
20
40
60
80
100
120
0 2 4 6 8 10 12
Output (units/yr)
Co
st (
$/u
nit
)
MC
ATC
AVC
AFC
Chapter 7 25©2005 Pearson Education, Inc.
Cost Curves for a FirmThe line drawn from
the origin to the variable cost curve: Its slope equals AVC The slope of a point
on VC or TC equals MC
Therefore, MC = AVC at 7 units of output (point A)
1 2 3 4 5 6 7 8 9 10 11 12 13
Output
P
100
200
300
400
FC
VC
TC
A
Chapter 7 26©2005 Pearson Education, Inc.
Cost in the Long Run
In the long run a firm can change all of its inputs
In making cost minimizing choices, must look at the cost of using capital and labor in production decisions
Now: The firms’ long-run cost minimizing decision
Chapter 7 27©2005 Pearson Education, Inc.
Cost in the Long Run
Capital is either rented/leased or purchasedAssume Delta is considering purchasing an
airplane for $150 million Plane lasts for 30 years – economic depreciation for
the plane = $5 million per year
If the firm had not purchased the plane, it would have earned interest on the $150 million (of 10%)
Forgone interest is an opportunity cost that must be considered also
Chapter 7 28©2005 Pearson Education, Inc.
Cost in the Long Run
User cost of capital, then, can be described as: r = Depreciation Rate + Interest Rate
In our example, depreciation rate was 3.33% and interest was 10%, so r = 3.33% + 10% = 13.33%
Chapter 7 29©2005 Pearson Education, Inc.
Cost Minimizing Input Choice
How does a firm select inputs to produce a given output at minimum cost?
Assumptions Two Inputs: Labor (L) and capital (K) Price of labor: wage rate (w) The price of capital
r = depreciation rate + interest rate
Chapter 7 30©2005 Pearson Education, Inc.
Cost in the Long Run
The Isocost Line A line showing all combinations of L & K that
can be purchased for the same cost Total cost of production is sum of firm’s labor
cost, wL, and its capital cost, rK:
C = wL + rK For each different level of cost, the equation
shows another isocost line
Chapter 7 31©2005 Pearson Education, Inc.
Cost in the Long Run
Rewriting C as an equation for a straight line: K = C/r - (w/r)L Slope of the isocost:
-(w/r) is the ratio of the wage rate to rental cost of capital.
This shows the rate at which capital can be substituted for labor with no change in cost
rw
LK
Chapter 7 32©2005 Pearson Education, Inc.
Choosing Inputs
We will address how to minimize cost for a given level of output by combining isocosts with isoquants
We choose the output we wish to produce and then determine how to do that at minimum cost Isoquant is the quantity we wish to produce Isocost is the combination of K and L that
gives a set cost
Chapter 7 33©2005 Pearson Education, Inc.
Producing a Given Output at Minimum Cost
Labor per year
Capitalper
year
Isocost C2 shows quantity Q1 can be produced with
combination K2,L2 or K3,L3.However, both of these
are higher cost combinationsthan K1,L1.
Q1
Q1 is an isoquant for output Q1.
There are three isocost lines, of which 2 are possible choices in
which to produce Q1.
C0 C1 C2
AK1
L1
K3
L3
K2
L2
Chapter 7 34©2005 Pearson Education, Inc.
Input Substitution When an Input Price Change
If the price of labor changes, then the slope of the isocost line changes, -(w/r)
It now takes a new quantity of labor and capital to produce the output
If price of labor increases relative to price of capital, then capital is substituted for labor
Chapter 7 35©2005 Pearson Education, Inc.
Input Substitution When an Input Price Change
C2
The new combination of K and L is used to produce Q1.
Combination B is used in place of combination A.K2
L2
B
C1
K1
L1
A
Q1
If the price of laborrises, the isocost curve
becomes steeper due to the change in the slope -(w/L).
Labor per year
Capitalper
year
Chapter 7 36©2005 Pearson Education, Inc.
Cost in the Long Run
How does the isocost line relate to the firm’s production process?
K
LMP
MP- MRTS L
K
rw
LK
lineisocost of Slope
costminimizesfirmwhenrw
MPMP
K
L
Chapter 7 37©2005 Pearson Education, Inc.
Cost in the Long Run
The minimum cost combination can then be written as:
Minimum cost for a given output will occur when each dollar of input added to the production process will add an equivalent amount of output.
rwKL MPMP
Chapter 7 38©2005 Pearson Education, Inc.
Cost in the Long Run
If w = $10, r = $2, and MPL = MPK, which input would the producer use more of?
Chapter 7 39©2005 Pearson Education, Inc.
Example
If MPL = 10, MPK = 5 and w= r = $10
Which input should the firm increase/decrease usage?
What if w increased to $20?
Chapter 7 40©2005 Pearson Education, Inc.
Long Run VersusShort Run Cost Curves
Long-Run Average Cost (LAC) Most important determinant of the shape of
the LR AC and MC curves is relationship between scale of the firm’s operation and inputs required to minimize cost
1. Constant Returns to Scale If input is doubled, output will double AC cost is constant at all levels of output
Chapter 7 41©2005 Pearson Education, Inc.
Long Run Versus Short Run Cost Curves
2. Increasing Returns to Scale If input is doubled, output will more than
double AC decreases at all levels of output
3. Decreasing Returns to Scale If input is doubled, output will less than
double AC increases at all levels of output
Chapter 7 42©2005 Pearson Education, Inc.
Long Run Versus Short Run Cost Curves
In the long run: Firms experience increasing and decreasing
returns to scale and therefore long-run average cost is “U” shaped.
Source of U-shape is due to returns to scale instead of diminishing returns to a factor of production (labor) like the short-run curve
Long-run marginal cost curve measures the change in long-run total costs as output is increased by 1 unit
Chapter 7 43©2005 Pearson Education, Inc.
Economies and Diseconomies of Scale
Economies of Scale Can double output for less than double the
original costDiseconomies of Scale
Doubling the output costs more than twice the original cost
U-shaped LAC shows economies of scale for relatively low output levels and diseconomies of scale for higher levels
Chapter 7 44©2005 Pearson Education, Inc.
Long Run Costs
Increasing Returns to Scale Output more than doubles when the
quantities of all inputs are doubledEconomies of Scale
Doubling of output requires less than a doubling of cost
Why the difference: can have constant returns to scale but still have economies of scale:
Chapter 7 45©2005 Pearson Education, Inc.
Long Run Versus Short Run Cost Curves
We will use short and long run costs to determine the optimal plant size
We can show the short run average costs for 3 different plant sizes
This decision is important because once built, the firm may not be able to change plant size for a while
Chapter 7 47©2005 Pearson Education, Inc.
Long Run Cost withConstant Returns to Scale
What is the firm’s long run cost curve? Firms can change scale to change output in
the long run The long run cost curve is the dark blue
portion of the SAC curve which represents the minimum cost for any level of output
Firm will always choose plant that minimizes the average cost of production
Chapter 7 48©2005 Pearson Education, Inc.
Long Run Cost withConstant Returns to Scale
The long-run average cost curve envelops the short-run average cost curves
The LAC curve exhibits economies of scale initially but exhibits diseconomies at higher output levels
Chapter 7 49©2005 Pearson Education, Inc.
Production with Two Outputs – Economies of Scope
Many firms produce more than one product and those products are closely linked
Examples: Chicken farm--poultry and eggs Automobile company--cars and trucks University--teaching and research
Chapter 7 50©2005 Pearson Education, Inc.
Production with Two Outputs – Economies of Scope
Advantages
1. Both use capital and labor
2. The firms share management resources
3. Both use the same labor skills and types of machinery
Chapter 7 51©2005 Pearson Education, Inc.
Production with Two Outputs – Economies of Scope
Firms must choose how much of each to produce
The alternative quantities can be illustrated using product transformation curves Curves showing the various combinations of
two different outputs (products) that can be produced with a given set of inputs
Chapter 7 52©2005 Pearson Education, Inc.
Product Transformation Curve
Number of cars
Numberof tractors
O1 illustrates a low levelof output. O2 illustrates
a higher level of output withtwo times as much labor
and capital.
Each curve showscombinations of output
with a given combination of L & K.
O2
O1
Chapter 7 53©2005 Pearson Education, Inc.
Product Transformation Curve
Product transformation curves are negatively sloped To get more of one output, must give up
some of the other outputConstant returns exist in this example
Second curve lies twice as far from origin as the first curve
Curve is concave/bowed-outward Joint production has advantages
Chapter 7 54©2005 Pearson Education, Inc.
Production with Two Outputs – Economies of Scope
There is no direct relationship between economies of scope and economies of scale May experience economies of scope and
diseconomies of scale May have economies of scale and not have
economies of scope
Chapter 7 55©2005 Pearson Education, Inc.
Production with Two Outputs – Economies of Scope
The degree of economies of scope (SC) can be measured by percentage of cost saved producing two or more products jointly:
C(q1) is the cost of producing q1
C(q2) is the cost of producing q2
C(q1,q2) is the joint cost of producing both products
)qC(q
)qC(q)C(q)C(q SC
,
,
21
2121
Chapter 7 56©2005 Pearson Education, Inc.
Production with Two Outputs – Economies of Scope
With economies of scope, the joint cost is less than the sum of the individual costs
Interpretation: If SC > 0 Economies of scope If SC < 0 Diseconomies of scope The greater the value of SC, the greater the
economies of scope