Managerial Economics

1
Law of Diminishing Marginal returns As units of
one input are added (with all other inputs held
constant), a point will be reached where the
resulting additions to output will begin to
decrease (marginal product will decline). Here
diminishing returns will occur for any workers
beyond 40.
MP Increasing
Total Product Increasing
MP Decreasing
Decreasing
2
Optimal Use of an Input
When adding an additional unit of an input, firm
will face additional benefit (increased output)
and additional cost. We know profit max is where
MR MC, or marginal profit zero. BUT, in
production, were changing input amounts, not
prices or quantity. Must find where marginal
profit of adding another input zero. (where
marginal revenue product MC).
3
Optimal Use of an Input
Marginal Benefit Side Marginal Revenue Product
of Labor (MRPL) Extra revenue resulting from an
increase in labor. MRPL (Price of output) x
(marginal output / unit of labor) MRPL
(MR)(MPL) (how many Qs will each additional unit
of labor produce times how much can we sell each
for) Example When increasing labor from 20 to
30 workers, marginal product per worker is 4.5
(from table). We can sell each unit of output
for 40. MRPL (40)(4.5) 180
per worker
4
Optimal Use of an Input
Marginal Cost Side Marginal Cost of an
input Amount an additional unit of input adds to
firms costs. Marginal cost of labor is
typically the wage. Profit maximizing workforce
is M ? L MRPL MCL Labor should be increased
until MRPL MCL
5
Optimal Use of an Input
Example 1 Production function Q 60L
L2 Price of output 2 per unit Price of
labor 16/hour How many workers should the
firm hire? MPL ?Q/ ?L 60 2L MRPL
(2)(60-2L) 120- 4L Setting MRPL MC, 120-
4L 16 L 26
6
Optimal Use of an Input
Example 2 Production function Q 10L
.5L2 Price of output 10 per unit Price of
labor 40/hour How many workers should the
firm hire?
Example 3 Production function Q 10L .5L2
24K K2 Price of output 10 per unit Price
of labor 40/hour Price of K 80 What is the
optimal quantity of each input?
7
Long Run Production
IN LR, all inputs are variable. With variable K,
firms can make decisions about scale (size) of
their production facility. Returns to
Scale Measure of the percentage change in an
output resulting from a given percentage change
in inputs.
8
Returns to Scale

• Constant Returns to Scale
• When a given percentage change in inputs results
  in an equal percentage change in outputs.
• If inputs are doubled, output is doubled.
• 10 increase in inputs results in 10 increase in
  output.
• Firms inputs are equally productive whether
  smaller or larger levels of output are produced.

9
Returns to Scale

• Increasing Returns to Scale
• When a given percentage change in inputs results
  in greater percentage change in outputs.
• If inputs are doubled, output is more than
  doubled.
• 10 increase in inputs results in a greater than
  10 increase in output.
• Firms inputs are more productive when producing
  larger levels of output.

10
Returns to Scale

• Decreasing Returns to Scale
• When a given percentage change in inputs results
  in a smaller percentage change in outputs.
• If inputs are doubled, output is less than
  doubled.
• 10 increase in inputs results in a less than 10
  increase in output.
• Firms inputs are more productive when producing
  smaller levels of output.

11
Least-Cost Production
With both inputs variable, firm must decide how
much L and how much K to use for minimizing cost
of producing a given level of output. Least cost
production is where ratios of marginal products
to input costs are equal across all inputs.
(Extra output per dollar of input must be the
same for all inputs). MPL/PL MPK/PK
12
Least-Cost Production
Example 1 Production function Q 10L .5L2
24K K2 Price of labor 40/hour Price of K
80 What is the optimal combination of K and L?
MPL/PL MPK/PK
MPL ?Q/ ? L (10 L)/40 MPK ?Q/ ? K
(24 - 2K)/80 10 L 24 2K 40 80 L K
2
13
Least-Cost Production
Example 2 Production function Q 40L L2
54K 1.5K2 Price of labor 10/hour Price of K
15 What is the optimal combination of K and L?
MPL/PL MPK/PK
MPL ?Q/ ?L (40 - 2L)/10 MPK ?Q/ ?K
(54 3K)/15 40 2L 54 3K 10 15 L K
2
14
Cobb-Douglas Production Function
Most common form of production function
Q cLaKß
Where C is constant, and a and ß are between
zero and 1.

• MPL decreases as L increases, but increases as K
  increases. (vice versa for K)
• Nature of returns to scale can be seen in sum of
  the exponents
• If a ß 1 Constant returns
• If a ß lt 1 Decreasing returns
• If a ß gt 1 Increasing returns

15
Cobb-Douglas Production Function
Example
Q L.5K.5

• Constant returns to scale
• Both inputs exhibit diminishing returns as
  quantity of the input is increased.

Q L.7K.4

• Increasing returns to scale
• Both inputs exhibit diminishing returns as
  quantity of the input is increased.