Download NOTE ON PRODUCER SURPLUS1

Department of Managerial Economics and Decision Sciences
NOTE ON PRODUCER SURPLUS1
We have seen that the area between the market price and a demand curve corresponds to
what we have called consumer surplus, a measure of the net benefit to consumers from
their purchase consumption activity. You might wonder: Does the area between the
market price and the supply curve have a similar interpretation? The answer is yes. It
corresponds to what we will call producer surplus. Analogous to consumer surplus,
producer surplus measures the net benefit accruing to firms from their production and
sales activity.
To illustrate the concept of producer surplus, let us begin with a simple example. Suppose
that a shipbuilder can either build one ship in the upcoming year or no ships at all. The
firm would be willing to supply this ship as long it receives at least $50 million, the
marginal cost that the firm incurs if it builds the ship (or equivalently, the cost that it
avoids if it does not build the ship). If the market price for ships of this type is $75
million, the firm would be willing to supply a ship. By doing so, it receives $75 million in
additional revenue, while incurring $50 million in additional cost, thus increasing its total
profit. The firm’s producer surplus would be $75 million - $50 million = $25 million.
Notice that producer surplus for the ship is the difference between the market price and
the marginal cost of the ship. But because the firm is producing just one unit, producer
surplus is also the difference between the firm’s total revenue and its total variable cost.
Of course, firms typically would be willing to supply more than one unit. For example,
suppose that our shipbuilder could potentially build as many as four ships during a
particular year. The firm’s short-run supply curve ss is shown in the figure below. It
shows that the firm must receive at least $50 million per ship in order to be willing to
supply the first ship. The lowest price at which it would be willing to supply a second
ship would be $60 million. The minimum price at which it would supply a third ship
would be $70 million, and the minimum price at which it would supply a fourth ship
would be $80 million. As in our initial example, the minimum price at which the
shipbuilder would be willing to supply ships reflects the marginal cost of producing a
ship. The shipbuilder requires a higher price in order to supply the second ship because if
it builds two ships in the upcoming year rather than one, it must utilize an older portion of
its shipyard with less modern equipment (which in turn makes its workers less
productive), causing it to incur a higher marginal cost on the second ship. The shipbuilder
requires a higher price still in order to be willing to supply the third and fourth ships for
the same reason.
1
© Professor David Besanko, These notes were prepared for use in class discussion in MECN 430 Microeconomic
Analysis. Do not copy this document for any other use without my explicit permission. Version of January 14, 2004.
Price (millions of $ per unit)
Producer Surplus
ss
80
75
70
60
50
1
2
3
4
Quantity (ships per year)
Suppose that the market price of ships is $75 million per ship. At this price, the
shipbuilder’s supply curve indicates that it would supply three ships in the upcoming
year. What is the shipbuilder’s producer surplus? To find out, you would add the
producer surplus of each of the individual ships built. The producer surplus of the first
ship is (as before) $25 million: the market price of $75 million minus the marginal cost of
$50 million of building that ship. The producer surplus of the second ship is the $75
million market price minus the $60 million marginal cost, or $15 million, while the
producer surplus of the third ship is $75 million minus $70 million, or $5 million. The
shipbuilder’s producer surplus is thus $25 million + $15 million + $5 million = $45
million (the sum of the producer surpluses for each of the ships supplied). If you add up
the individual producer surpluses what do you get? You get the sum total of the firm’s
revenues minus the firm’s total variable costs. Producer surplus for an individual firm
equals total revenue minus total variable cost.
As the figure above shows, the shipbuilder’s producer surplus corresponds to the area
between the firm’s supply and the market price. In this example, the firm’s supply curve
was a series of “steps,” which makes it easy to see the producer surplus of each unit
produced. However, the concept of producer surplus readily applies to the case in which a
firm has a smooth supply curve. The concept also readily applies when we consider an
entire market of firms. The overall producer surplus for a market of firms is the area
between the market price and the market supply curve.
2
In the short run, when some of the firm’s fixed costs might be sunk, a firm’s producer
surplus (area between its short-run supply curve and the market price) differs from its
economic profit. In particular, economic profit equals total revenue minus total
reinvestment costs (total variable costs plus total fixed costs plus the firm’s total capital
charge). By contrast, producer surplus equals total revenue minus total variable costs.
3