# What does perfectly inelastic demand imply about gains from trade and domestic consumers?

Source: p 191, Question 9.7b, 9.7c, Principles of Microeconomics, 7 Ed, 2014, by NG Mankiw

Consider a country that imports a good. True or false. Explain your answer.
b) “If demand is perfectly inelastic, there are no gains from trade.”
c) “If demand is perfectly inelastic, consumers do not benefit from trade.”

Please explain if this Best Answer is wrong? It claims that b) and c) are true. Yet my own work below shows a surplus of $+B$ after imports $\implies$ Gains from importing $\implies$ B and C are false.
Please feel free to correct my graph, but please also explain the intuition.
I wish to develop intuition, rather than be mechanically engrossed in graphs.

• I agree with you. As shown in your graph, consumer surplus increases by A+B. Producer surplus decreases by A. Total domestic surplus increases by B. – NickJ Mar 18 '15 at 3:48
• It is strange that this has not yet come up, but I would not know how to define consumer surplus in this case as it seems to be infinite. Inelastic demand implies an infinitely large reservation price which means that given any finite price results in an infinite surplus. – Giskard Aug 26 '15 at 22:06

@VicAche this is incorrect. While the consumer may be willing to pay a large amount, consumer surplus is defined as the willingness to pay minus the price she pays. So if the willingness to pay is infinite as you correctly asserted, then the consumer surplus is also infinite. See my answer to this question.

Perfectly inelastic demand means the consumer has no choice about buying the product or not: for some reason, he has to buy it. This means that consumer surplus is steady at 0: the consumer never pays less than he would be ready to pay, he always pays what he is asked to.

According to your (wrong) graph, the quantity reached would be at the intersection of WP and Supply. While this is true for producers, it is not for consumers: the supply curve should be bent to follow WP when crossing it.

You are right about producer surplus, which means we get a total surplus of $-A$, and a consumer surplus of $0$. There are no gains from trade and consumers do not benefit from trade.

• Is the consumer surplus 0 or is it infinitely large? – Giskard Aug 26 '15 at 22:07
• @denesp I've always seen it to be 0. One should decide given the background case, one common, real-life case of inelastic demand where surplus really should be 0 are nails in the car industry. Nails are necessary in car making but come at a price that is negligible so car makers are ready to pay a lot more for the same daily amount of nails when big suppliers encounter shutdowns. But giving a split of the profits in car making to nails seems pretty strange. – VicAche Aug 27 '15 at 7:47
• I don't know, I am still not entirely convinced. Splitting the profits in a particular way seems to me to be more of a bargaining issue, not necessarily a reflection on the surplus. – Giskard Aug 27 '15 at 8:04
• @denesp it is a reflection on the surplus because it decides on a hard limit for the buying price of the given good. – VicAche Aug 27 '15 at 8:43
• It is a reflection on both the surplus and the bargaining power hence it is not necessarily a reflection on the surplus. Consider that in Bertrand price competition the costs fully determine the prices. – Giskard Aug 27 '15 at 8:52
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