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 labour, rent, parts, etc. Two outputs y1 and y2 with output prices p1 and p2. A competitive firm takes prices as given. What are 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?

In the Long run.. We can choose both variables. We then need to take FOCs of both. Focs are p*f 1 (x1,x2)=w1 and p*f 2 (x1,x2)=w2. (remember f 1 (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.