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 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

• 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

• What happens to output when p and w1 change?

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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.