Isocosts and isoquants.

1
Isocosts and isoquants.
2
The behavior of the firm

• Firms are assumed to attempt to maximize profits.
• First, the firm must identify the profit
  maximizing level of output the quantity where
  marginal revenue equals marginal cost.
• Next, the firm must minimize the cost of
  producing that level of output.
• It must choose the appropriate technology and
  apply it correctly. As a part of this, it must
  combine resources according to the least-cost
  recipe.

3
Learning Objectives

• Calculate and graph a firms isocost line
• Work out how the isocost line changes when
  resource prices or total cost change
• Make a map of production recipes (technology)
  using isoquants
• Explain the choices that firms make

4
Learning Objectives

• Calculate and graph a firms isocost line
• Work out how the isocost line changes when
  resource prices or total cost change
• Make a map of production recipes (technology)
  using isoquants
• Explain the choices that firms make

5
A Cost Function Two Resources

• Assume that there are two resources, Labor (L)
  and Capital (K).
• The money payments to these resources are Wages
  (W) and Rent (R). An isocost line is similar to
  the budget line. Its a set of points with the
  same cost, C. Lets plot K on the y axis and L on
  the x axis.
• WL RK C solve for K by first subtracting WL
  from both sides.RK C - WL next divide both
  sides by R.K C/R (W/R)L note that C/R is
  the y intercept and W/R is the slope.

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An isocost line
C/R
C/W
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A Numerical Example

• Bundles of Labor Machine rental
• with C 30 (6 per labor hour) (3 per
  machine hour)
• a 0 10
• b 1 8
• c 2 6
• d 3 4
• e 4 2
• f 5 0

Points a through f lie on the isocost line for C
30/hour.
8
The Isocost Line
a
10
b
Capital, K (machines rented)
8
c
6
d
4
e
2
f
0 1 2 3 4 5 6 7 8 9
10
Labor, L (worker-hours employed)
9
The Isocost Line
Cost 30 R 3/machine W 6/hour
a
10
b
Capital, K (machines rented)
8
c
6
d
4
e
2
f
0 1 2 3 4 5 6 7 8 9
10
Labor, L (worker-hours employed)
10
Learning Objectives

• Calculate and graph a firms isocost line
• Work out how the isocost line changes when
  resource prices or total cost change
• Make a map of production recipes (technology)
  using isoquants
• Explain the choices that firms make

11
The Isocost Line

• Wage-rental ratio
• With K on the y axis and L on the x axis, the
  slope of any isocost line equals W/R, the
  wage-rental ratio. It is also the relative price
  of labor.
• The y-intercept shows the number of units of K
  that could be rented for C.
• The x-intercept shows the number of units of L
  that could be hired for C.

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Changes in One Resource Price
Cost 30 R 3/machine The money wage, W ...
a
10
Capital, K (machines rented)
8
6
A Change in W
4
6
2
10
f
h
0 1 2 3 4 5 6 7 8 9
10
Labor, L (worker-hours employed)
13
Changes in One Resource Price
Cost 30 R 3/machine The money wage, W ...
a
10
Capital, K (machines rented)
8
6
A Change in W
4
6
2
10
3
f
h
0 1 2 3 4 5 6 7 8 9
10
Labor, L (worker-hours employed)
14
Changes in Cost
10
Capital, K (machines rented)
A Change in Cost every pointbetween g and h
costs 18.
8
g
6
4
2
W 6 R 3C 30
h
0 1 2 3 4 5 6 7 8 9
10
Labor, L (worker-hours employed)
15
Changes in Cost
10
Capital, K (machines rented)
A Change in Cost every pointbetween g and h
costs 18.
8
g
6
4
2
W 6 R 3C 30
C 18
h
0 1 2 3 4 5 6 7 8 9
10
Labor, L (worker-hours employed)
16
Learning Objectives

• Calculate and graph a firms isocost line
• Work out how the isocost line changes when
  resource prices or total cost change
• Make a map of production recipes (technology)
  using isoquants
• Explain the choices that firms make

17
An Isoquant
Each point on a given isoquant represents
different recipes for producing the same level of
output.
12
10
Capital, K (machines rented)
8
i
6
Quantity of Soybeans 1 (kg./hour)
4
2
j
0 1 2 3 4 5 6 7 8 9
10
Labor, L (worker-hours employed)
18
An Isoquant Map
Different isoquants represents different levels
of output.
m
Quantity of Soybeans 2 (kg./hour)
Capital, K (machines rented)
0 1 2 3 4 5 6 7 8 9
10
k
j
Quantity of Soybeans 1 (kg./hour)
0 1 2 3 4 5 6 7 8 9
10
Labor, L (worker-hours employed)
19
An Isoquant Map
These isoquants exhibit Constant Returns to Scale
double the input, get double the output.
K/L 2
m
Quantity of Soybeans 2 (kg./hour)
Capital, K (machines rented)
0 1 2 3 4 5 6 7 8 9
10
K/L 1/2
k
j
Quantity of Soybeans 1 (kg./hour)
0 1 2 3 4 5 6 7 8 9
10
Labor, L (worker-hours employed)
20
Learning Objectives

• Calculate and graph a firms isocost line
• Work out how the isocost line changes when
  resource prices or total cost change
• Make a map of production recipes (technology)
  using isoquants
• Explain the choices that firms make

21
Cost Minimization
Choose the recipe where thedesired isoquant is
tangent tothe lowest isocost.
12
a
10
Capital, K (machines rented)
8
C 36
6
W 6 R 3C 30
4
equ.
2
C 18
0 1 2 3 4 5 6 7 8 9
10
Labor, L (worker-hours employed)
22
Conclusion Buy resources such that the last
dollar spent on K adds the same amount to output
as the last dollar spent on L.

• The slope of the isocost line W/R.
• The slope of the isoquant MPL/MPK