Transcript L - City University of Hong Kong

Producer Theory
Tutorial 6
The Production Functions
 Firms
- A firm is an organization that turns inputs into outputs.
- The major assumption: Profit maximization
  TR  TC
- where TR = P x Q is the total revenue; TC is the total cost of production
- Two decisions:
• Input Choice: Choose the input that will minimize cost to produce any given
output.
• Output Choice: Choose the amount of output produced and hence the price
of the product.
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Production Function
 Production function: shows the relationship between the maximum
amount of output a firm can produce and the amount inputs used, given
the current technology.
Q  f ( L, K )
where L is the quantity of labor used; K is the quantity of capital used.
 The production function can be represented in a 3-D diagram.
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The Production Functions
Q
L
K
L2
K1
Keep K constant
0
L1
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Short-run Production
 Input flexibility
- Short run: a period of time that at least one factor of production is fixed, i.e.
the fixed input.
- Long run: a period of time, which is long enough that all inputs can be variable.
How long does it take for all inputs to be variable?
 Short-run production: One variable Input
- In the short run, economists usually assume that capital is fixed.
- If we were to cut the hill vertically at a particular level of K, we can study how
output level varies with the change in L, keeping K constant.
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Total Product Curve
Q  Marginal product of labor (MPL): the additional output that
can be produced by employing one more unit of labor,
keeping the amount of capital used constant.
B
TPL
Q2
ΔQ
Law of diminishing marginal returns:
If a firm increases an input
successively, keeping all other inputs
constant, the marginal product of the
variable input will eventually diminish.
A
Q1
0
L
L1
L2
ΔL
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Q
D
C
B
Q1
A
0
L
Q
Average product of
labor (APL): the average
amount of output per unit
of labor
b
c
MPL1
APL1 = Q1/L1
APL
d
L1 L2
L3
L
L4
MPL
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Long-run Production: Isoquants
 In the long run, both K and L are variable. A firm, therefore, is possible to
produce a particular output level with different combinations of inputs.
 If we were to cut the hill horizontally at a particular level of output, and project the
outside edge of the hill on the floor. We derive a curve that shows all the
combinations of labor and capital that can be used to produce the same level of
output. This is called the isoquant.
Q
Q2
Q1
L
K
0
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Contour Lines
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Isoquants
 Isoquant map: a graphical representation of a set of isoquants.
K
K1
a
b
K1
Q3
Q2
Q1
L
L1
L2
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Isocost Lines
 The total cost of production is the sum of the labor cost and capital cost:
C  wL  rK
 Isocost Line: It shows all the combinations of inputs that incur the same cost for
the firm.
 Derive another isocost line that represents
a lower total cost.
 Suppose the wage rate increases, with the
rental price of capital remains unchanged.
Derive the isocost line that represents the
same total cost.
K
TC
r
Slope  
w
r
IL
TC
w
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L
The Firm’s Optimal Input Choice
 A consumer’s optimal choice is the input combination that minimizes its
total cost to produce a given output level.
- Put the isoquant curves and isocost line together!
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Firm Optimal Choice
 Which point is
the firm’s optimal
input choice?
- Must lie on the
isoquant
- The point where
the isoquant is
tangent to the
lowest attainable
isocost line.
K
C1
r
C
C1
r
A
E
B
D
Q1
IL2
IL1
L
Page 13
Application: Minimum Wage in Shenzhen
 “Shenzhen Municipal Government raised the minimum wage by 17.6%
starting 1 July, 2008. (Source: Hong Kong Economic Times, 26 June, 2008)
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Comparative Statics Analysis:
Changes in Input Prices
 Suppose wage rate increases
from w1 to w2.
 The firm will substitute capital
for labor to produce Q1, so as
to reduce the costs.
K
TC1
r
E2
E1
 Change in cost?
Q1
 What if the firm do not change
its input combination?
IC2
TC1
w2
IC3
TC 2
w2
IC1
TC1
w1
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L
Discussion Question 1: Minimum Wage in
Shenzhen
 “Shenzhen Municipal Government raised the minimum wage by 17.6%
starting 1 July, 2008. (Source: Hong Kong Economic Times, 26 June, 2008)
 Hong Kong factories decided to install more machines to automate
simple production procedures (replacing low-skilled labor) in order to cut
costs”
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Application: Nothing to Lose but their Chains
• (Source: “Nothing to lose but their chains,”
The Economist, 21st June 2008. )
- “… Some factory robots are now smart
enough top be released from their safety
cages to work among humans. And as they
become cleverer and more dexterous, they
are starting to move from factories to offices
and homes …”
- “…Eventually, advanced humanoid robots
will escape from the laboratory. Indeed,
Toyota and Honda expect domestic robots to
become a huge market in the future, with
machines working as a family helper.”
- “… Four trends were on show: robots are
rapidly becoming more responsive, cheaper,
simpler to program and safer…”
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Discussion Question 3
 What is the difference between decreasing returns to scale and diminishing
marginal returns? Can a production function exhibit diminishing marginal returns
but not decreasing returns to scale?
 Returns to scale: to measure how output responds to increases in all inputs
together.
 If the production function is given by q  ( L, K ) and all inputs are multiplied by
the same positive constant, e.g. 2, we describe the returns to scale of the
production function:
- Constant returns to scale:
f (2 L,2 K )  2Q
- Increasing returns to scale:
f (2 L,2 K )  2Q
- Decreasing returns to scale:
f (2 L,2 K )  2Q
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Returns to Scale
K
K
K
3q
2K
2K
2K
2q
3q
K
2q
K
K
q
L
2L
Increasing
Returns to Scale
2q
q
L
L
2L
Constant
Returns to Scale
q
L
L
2L
L
Decreasing
Returns to Scale
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Returns to Scale
 Note that decreasing
returns to scale is
different from the
diminishing marginal
returns.
K
E
3
D
2
q=1500
A
1
C
B
1
2
q=1000
q=750
q=650
q = 500
3
L
Page 20
Discussion Question 4
 Suppose the firm wants to increase its output level in the short run,
compare its optimal input choice in the short run and long run.
 Short-run cost will never be lower than the long-run cost!
K
e2
K
e1
e5
e4
e3
Q2
Q1
Q3
L
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