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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.

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Profit Maximization

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  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 • 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.

  3. 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.

  4. 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.

  5. 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?

  6. 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?

  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.

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