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.

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Profit Maximization

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Profit maximization

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

Profit

  • Profits=revenue-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.


One input one output

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

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

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

  • What happens to output when p and w1 change?


In the long run

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

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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