; Profit Maximization
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# Profit Maximization

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```									           Profit Maximization
• What is the goal of the firm?
–   Expand, expand, expand: Amazon.
–   Earnings growth: GE.
–   Produce the highest possible quality: this class.
–   Many other goals: happy customers, happy
workers, good reputation, etc.
• It is to maximize profits: that is, present
value of all current and future profits (also
known as net present value NPV).
Profit
• Profits=revenue-costs
• Two inputs x1 and x2 with input prices w1 and
w2. Inputs can be labour, rent, parts, etc.
• Two outputs y1 and y2 with output prices p1 and
p2.
• A competitive firm takes prices as given.
• What are profits?
• Note that inputs and outputs can be internal to the
firm.
One input, one output
• There is one output y and one input x where
y=f(x).
• The firms problem is the maximize
Max x,y p*y-w*x s.t. y=f(x).
• Two ways:
1. Draw isoprofit lines (where profit is constant). Find
which is the highest profit line that can be reached with
the production function.
2. Substitute in for y and take FOC and solve.
Past, Present and Future
• What happens if some decisions are already
made in the past?
• Remember one can’t change the past.
• Euro-tunnel: spend billions to build it.
Does this mean that prices have to be higher
for tickets?
• Similar for Airwave Auctions, Iridium and
many other cases.
Past costs are sunk.
• y=f(x1,x2), but x2 is already paid for and
fixed.
• This problem is the same as our problem
with just one variable.
• Try this w/ Cobb-Douglas f ( x1, x2 )  x1x2
• What happens to output when p and w1
change?
In the Long run..
• We can choose both variables. We then
need to take FOCs of both.
• Focs are p*f1(x1,x2)=w1 and
p*f2(x1,x2)=w2.
(remember f1(x1,x2)= MP1)
• What is output in the C-D case as a function
of prices?
Returns to Scale
• If production is decreasing-RS, then solution is
simple.
• If production is increasing-RS then “Houston, we
have a problem.”
• If production is constant-RS, then
– If profits are negative then firms produce zero.
– If profits are positive then firms can keep
producing to increase profits. Result output
prices decrease and input prices increase.
– Result: if market is competitive w/ CRS there
are zero profits for each firm!!
• Some economists claim any DRS is just CRS with
less inputs. Think of CD.

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