Profit Maximization

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).

2
Profit

• Profitsrevenue-costs
• Two inputs x1 and x2 with input prices w1 and w2.
  Inputs can be labor, rent, parts, etc.
• Two outputs y1 and y2 with output prices p1 and
  p2.
• A competitive firm takes prices as given.
• What is profits?
• Note that inputs and outputs can be internal to
  the firm.

3
One input, one output

• There is one output y and one input x where
  yf(x).
• The firms problem is the maximize
• Max x,y py-wx s.t. yf(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.

4
Past, Present and Future

• What happens if some decisions are already made
  in the past?
• Remember one cant 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.

5
Past costs are sunk.

• yf(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
• What happens to output when p and w1 change?

6
In the Long run..

• We can choose both variables. We then need to
  take FOCs of both.
• Focs are pf1(x1,x2)w1 and pf2(x1,x2)w2.
• (remember f1(x1,x2) MP1)
• What is output in the C-D case as a function of
  prices?

7
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.