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Profit Maximization

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- 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 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.

- 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.

- 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.

- 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?

- 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?

- 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.