; Profit Maximization
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Profit Maximization


  • pg 1
									           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).
• 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
• A competitive firm takes prices as given.
• What are profits?
• Note that inputs and outputs can be internal to the
          One input, one output
• There is one output y and one input x where
• 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
• 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
           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
  (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
• 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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