Download Intermediate Micro Theory - Claremont Mckenna College

Intermediate Micro Theory
Firm Supply
Firm Supply

We assume firms make decisions to
maximize profits
π(q) = pq – c(q)

Therefore, how much should a profit
maximizing firm supply of that output?

Hint: at what point should they choose to
not produce any more units?
Firm Supply

Profit maximizing firm wants to
maximize difference between total
Revenue and Total costs.

This will be where slope of cost
function (i.e. MC) equals the price of
the output

Or equivalently, where the slope of
the profit function equals zero
(“First Order Condition” or FOC)
pq
$
C(q)
$
π(q)= pq-C(q)
q*
Firm Supply

So a necessary condition for profit maximization is that chosen output (q*)
is such that:
MC(q*) = p

What if MC(q*) = p at more than one q?

What if p < AC(q*) (where q* is such that MC(q*) = p)?

What if p < AVC(q*) (where q* is such that MC(q*) = p)?

Given these results, can we derive the firm’s supply curve?
Firm Supply

So, in short run, Firm supply
curve is implicitly given by
MC(q) curve above AVC(q)
curve.
$
AC(q)
MC(q)
AVC(q)
p

What about in Longer run?

Before moving on to analytic
details, what will total profit
look like graphically, for any
given p?
q
Firm Supply Analytically

Analytically, short-run firm supply curve derived as
follows:

Given any price p, let q*(p) be the quantity such that
MC(q*(p)) = p

Then:
qs(p) = 0
= q*(p)
if p < min AC(q)
if p > min AC(q)
Firm Supply Analytically

Ex: Consider Firm’s (short-run) cost function from
before:
C(q) = q2/3 + 48

What will be equation for firm’s supply curve?
Long-Run vs. Short-Run Supply Curve

Recall from before that the Short-run
MC(q) curve was the MC(q) curve that
held when at least one factor was fixed at
some level.

Alternatively, in Longer-run, more factors
become variable.

This meant any Short-run MC curve lies
above the Longer-run MC curves at any
given q.

What does this imply about relative slopes
of short-run vs. longer-run supply curves?
Bringing it all together:

Suppose a firm producing widgets operated using a Cobb-Douglas
technology such that q = L0.25K0.25, where the going wage rates are
wL = $4/hr and wK = $4/hr.

How much would a profit maximizing firm supply if each widget could
be sold for $160? How about if it could be sold for $192?
Bringing it all together:

How would we sketch this all graphically?
Bringing it all together:

Substitution Effects vs. Scale Effects



Consider a price change for one of the inputs in the production of some
output.
Substitution Effect (for input x1) – change in firm’s demand for x1 due
to change in cost-minimizing way to produce any given level of output
(e.g., if firm kept producing the same quantity after the input price
change, how would their demand for input x1 change?)
Scale Effect (for input x1) – change in firm’s demand for x1 due to
change in optimal level of output.
Bringing it all together:

Consider again our firm using technology such that q = L0.25K0.25, but going
wage rates are now wL = $16/hr and wK = $4/hr.

Now what would be the cost minimizing way to make 10 units?

But now how much would a profit maximizing firm supply if each widget could
be sold for $160? How much of each input would they use?

What would be the substitution and scale effects for labor? For capital?
Bringing it all together:

Graphically?
K
p
MC(q)/q(p)
MC(q)/q(p)
200
$160
100
q=10
50
q=5
12.5 50 100
substitution
scale
5
L
10
q