# Week5 ProductionandCosts 2007

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```					ECMA04H
Week 5
Production, Productivity and Costs

Tight week
…and our midterm test coming up (20%)

When? Friday Oct. 26 at 3 p.m.

Where? Soon, find out at:
www.utsc.utoronto.ca/~cleveland/ECMA04H

What if you miss it?

What’s on the test?
Up to end of Week 6 – short run and long run
costs faced by perfectly competitive firms
Second test – Friday, November 16th at 3 p.m.
(makeup test for those attending LIVE!)

First, finish up material on excess burden of
taxation…..from last week.
Production, productivity and costs
Basic objective of this week….understand
diminishing marginal productivity and the
shapes of typical cost curves in short run.

General objective: to understand the supply
curve. Decisions by firms about how much to
produce/supply.
We assume that the objective of firms is
to maximize profits!

They hire labour and purchase (or rent)
capital equipment and other inputs. These
inputs combine together to produce
output. Output is sold to earn a profit (or
loss….)

Most firms, most of the time, have no
control over the production technology

We write this as       q = f(K,L)

K = inputs of capital (machinery,
buildings, etc)

L = inputs of labour (hours of
standardized worker)

5/7
An example of a production function:

q = KαLβ (called “Cobb-Douglas”
function)

even simpler version of Cobb-Douglas
function is to choose
α = β = 0.5

[Note: α and β are parameters of the
Cobb-Douglas function]

so we have q = (KL)0.5
Now define time period: short run, long run, very
long run

Short run = period too short for firms to
change production capacity (K)
Long run = period long enough for firms to
change plant capacity, and for new firms to
enter industry (or exit)

SR (K is fixed in amount)

5/8

technology capital     labour
short run

long run

very long run
e.g.,     long run:
q = (KL)0.5

in short run, we would have to assume K =
constant

e.g., K = 9, so q = 3L0.5

Now define
marginal product of labour = MPL =
dq/dL

In example we used earlier

K = 9, so q = 3L.5

we get MPL = dq/dL = 1.5L-0.5 =
1.5/L.5
We assume that dMPL/dL < 0
This is called diminishing marginal product

“Law of Diminishing Returns” (or law of
diminishing marginal product, or law of
variable proportions)

Malthus (Malthusian economics)
NOW we go to the next stage: we want

TC = PKK + PLL

PKK = (rental) cost of capital equipment
PLL = cost of labour
In short run, K fixed and L variable,
so

PKK = fixed cost
PLL = variable cost

TC =    PKK + PLL

=   FC + VC
discuss the characteristic shapes of the
cost curves in the short run
Why is the MC curve J-shaped and upward-
sloping?

Why are the AVC and the AC curves U-
shaped and reach their minimum just as
they cross MC?

Why is AFC shaped like a lazy L?
Notes for you to look at on your own

Assume simple pizza firm uses K and L to
produce Q.

Q = f(K, L)          production function

K is fixed, so

Assume
Q = 28L + 4L2 – L3

This production function represents the
best available pizza production technology,
showing output of pizzas as a function of
the amount of labour inputs (with K fixed).
We can show the choices we have available
in the SR for our pizza firm

Q = 28L + 4L2 – L3

Labour Input (# of   Pizza Output
workers)
0                     0
1                   31
2                    64
3                    93
4                    112
5                    115
6                    96
7                    49
Q
(Output)

125

100

75

50

25

0       1     2    3   4    5    6     7    L (Labour Inputs)

Production Function or Total Product Curve
If Q = 28L + 4L2 – L3,

Then dQ/dL = 28 + 8L –3L2
dQ/dL is marginal product of labour
rate of change of output as labour is added

Also worth noting:
Average product of labour = Q/L
Q/L = 28 + 4L – L2
Average output per worker (i.e., per unit of
labour)
Labour   Pizza  Marginal   Average
Input    Output Product of Product of
Labour     Labour
0         0      28         --
1        31      33         31
2        64      32         32
3        93      25         31
4        112     12         28
5        115     -7         23
6        96     -32         16
7        49     -63          7
Output
per unit
of labour

50

40

30

20

10

0       1     2   3    4   5    6     7   L (Labour Inputs)

Marginal Product and Average Product Curves
Law of Diminishing Marginal Product

As more and more of a variable input is
combined with a fixed input, marginal
product will inevitably decline
What about the costs of production?
Where do our cost curves come from?

Assume PL = \$100/day
Assume PK = \$500/day
Small competitive firm is a price taker in
the market for inputs

FC = fixed costs (overhead costs; costs
that do not vary with output)

VC = variable costs (costs that vary with
output; avoidable costs)

TC = FC + VC
TC = (PK x K) + (PL x L)
MC = dTC/dq
Rate of change of firm’s costs as output
increases; incremental cost
(use small q from now on for the output of
the firm; big Q for output of industry)

Sometimes we use MC = ΔTC/Δq
(an approximation, when we don’t have a
function for TC to differentiate)

AC = TC/q
AC = (FC + VC)/q = AFC + AVC
Look at the table below

What are the shapes of the curves?
Labour Pizza Marginal Average   FC     VC    TC     MC      AC      AVC     AFC
Input Output Product Product
of       of
Labour   Labour
0      0       28     --       500    0    500              --      --      --
1      31      33     31       500   100   600    3.23    19.35    3.23   16.13
2     64       32     32       500   200   700    3.03    10.94    3.13    7.81
3     93       25     31       500   300   800    3.45     8.60    3.23   5.38
4     112      12     28       500   400   900    5.26     8.04    3.57   4.46
5     115      -7     23       500   500   1000   33.33    8.70    4.35   4.35
6     96      -32     16       500   600   1100           11.45    6.25     --
7     49      -63      7       500   700   1200           24.49   14.29     --

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