# Intuition: Why does perfectly elastic supply imply no producer surplus?

Foreword: I ask NOT about the whole question; so I quote only the following part of the answer.

Source: p 153, Question 7c, Principles of Microeconomics, 7 Ed, 2014, by NG Mankiw
= Chapter 7, Question 6c, Principles of Microeconomics, 4 Ed, 2008, by NG Mankiw

... To take the most dramatic case, suppose the supply curve were horizontal, as shown in Figure 12. Then there is no producer surplus at all. ...

From the graph, I see that perfectly elastic supply $\iff$ a flat supply curve
$\iff$ producer surplus := Amount received by sellers $-$ Cost to sellers $\qquad = 0$.

If it costs you 50 cents a bag to make popcorn and you sell it for 50 cents a bag, you come out ahead by 0 cents a bag.

Since you understand the graph, let us note for casual viewers that the supply curve is perfectly flat. As such, we can see clearly the area of the consumer surplus, (the triangle between the equilibrium $p*$ and the supply curve) is 0. So the producer surplus, (and profits) are zero.

Intuition: The scenario must be one where the entire quantity demanded can be satisfied without having any diminishing marginal returns. Marginal costs and average costs across the industry must be flat along the relevant range. If you assume a linear production function, you may get this result.

But one must first understand that the supply curve is the same thing as the cost curve. If the supply curve is perfectly elastic (horizontal), that's because the cost of production is constant. Let's say this constant cost of production is \$0.50. And so in equilibrium, the good must be traded at \$0.50. That's because if the price were >\$0.50, then quantity supplied (QS) > quantity demanded (QD). Conversely, if the price were <\$0.50, then QS < QD.

Altogether then, we have

• The cost of producing every unit of the good is \$0.50. • The good is traded at \$0.50.

Therefore, producer surplus for every unit of the good is \$0.50 - \$0.50 = \$0. Therefore, (total) producer surplus is \$0.

For a fuller understanding, contrast this to the more typical scenario where the supply curve is upward-sloping.

• The cost of producing the marginal unit of the good is \$0.50. However, the cost of producing earlier units of the good is <\$0.50.
• The good is traded at \$0.50. Therefore, producer surplus for the marginal unit of the good is \$0.50 - \$0.50 = \$0. However, producer surplus for earlier units of the good is >\$0 (we produce them at <\$0.50 but sell them at \$0.50). Therefore, (total) producer surplus (which is the sum of producer surplus for each unit of the good) must be >\$0.

(Here I would also draw the graphs to illustrate but "ain't nobody got the time for that".)

The thing is, since the producer's curve is elastic, any producer necessary trades at equilibrium price. If my competitor try to earn more by elevating his prices, I will produce at the same price and kick him out of the market. In order to stay on the game, every producer sells at equilibrium price, no more, no less. Therefore, the producer surplus is 0.

The intuition of the consumer surplus is "the gain of the consumer who were willing to pay a high value for something sold at a low value". The producer surplus express the same idea for the producer.

But, the life of the perfectly-elastic-curve-producer is not bad everytime. If the government imposes a production tax, the cost will be indirectly payed by the consumer. You see, having an elastic curve has its advantages too sometimes.