Economics 103
Lecture # 15
Price Searching
Here we are going to make another minor adjustment to our model.
Rather than assume firms face a perfectly elastic (flat) demand
curve, now we assume firms face a downward sloping demand.
Why might that be?
a. People are often ignorant of many things
b. A firm may have a great location.
c. Your product might be slightly different from the competition.
d. Sellers might act strategically
We’ll leave this one
until next chapter.
e. The firm might be a … monopolist.
The KEY to understanding a price searching firm, is to understand
the marginal revenue curve.
Clearly marginal
revenue is falling
Recall when a firm was
a price taker the marginal
revenue curve equaled
the price.
Now marginal revenue is less than the price.
For those of you who have had some calculus. Suppose the
demand curve is given by the formula: p = a – b Q.
If we multiply both sides by Q we get:
PQ = aQ – bQ2
Note the left hand side is the Total Revenue.
Now take the derivative with respect to Q.
MR = a – 2bQ.
So the marginal revenue
curve falls twice as
fast as the demand curve.
Graphically we have:
When MR=0, then TR is
maximized, and the
elasticity of demand is
equal to –1.
MR is negative in
the inelastic region of
the demand curve.
This is the only adjustment we make for price searching.
If the firm has ordinary cost curves, what price would the firm
set?
Notice the firm
uses the same idiots
rule of thumb
This leads to a lower
level of output, and
a higher price than the
price taking model.
NB: The price searching firm DOES NOT maximize total revenue.
Bono gets paid based on royalties, which are a share of the
total revenues.
A revenue maximizer
wants to lower the
price and raise the
quantity to P’ and Q’.
P’
Q’
Notice Bono never
has said he wants
to give his albums
away.
The same disputes arises between authors and publishers. In fact,
between anyone who is paid a royalty vs. someone who has
to bear the full costs.
How much
profit is this firm
earning?
We need to know
the average costs.
Suppose the average costs looked like this:
Is this firm making
a profit or loss?
It would be
making a profit
equal to the shaded
area.
What if the average costs looked like this:
Is the firm making a
profit or loss, and by
how much?
The loss would equal the green area.
If the price searching firm was making zero profits, then
the average costs would look:
This would have to
be the equilibrium.
If the price searcher was
earning a profit, the
price of the factor making
it a price searcher would
have to rise.
The opposite would happen if the firm was making a loss.
Natural Monopoly.
For us this is a minor digression.
What if a firm, had declining costs over the range of the demand
curve?
Why would costs
look like this?
How many firms
could survive?
If you forced the firm
to set P=MC, what
would the profit be?