<p>If bidders have quasilinear preferences and monetary transfers are possible, then the two notions are equivalent: If <span class="math-container">$x$</span> is an allocation of the object and <span class="math-container">$t$</span> is a vector of monetary transfers with a balanced budget (so the sum of all transfers is 0), then the pair <span class="math-container">$(x,t)$</span> is Pareto efficient if and only if <span class="math-container">$x$</span> is the utilitarian allocation (object goes to the bidder with the highest valuation).</p>

<p>If monetary transfers are not possible, every allocation of the object to some bidder is Pareto efficient.</p>

CC BY-SA 4.0
2020-05-12T09:31:06.890Z
Interesting, do notions of efficiency for auctions ever consider the seller's utility as well as buyers? (I don't mean revenue maximisation, I mean buyer's and seller's combined utility). In this conversation, they have been referring only to buyers.
Student
CC BY-SA 4.0
2020-05-12T13:16:22.423Z
@Student: Yes, but mostly in a trivial sense where the seller is assumed to have a zero valuation of the object.
VARulle
CC BY-SA 4.0
2020-05-12T08:59:30.647Z
2020-05-12T08:59:30.647Z
VARulle
<p>Consider a finite number of bidders, each bidding for a single indivisible object, with private independent values from some probability distribution.
There are 2 intuitive notions of (ex-post) efficiency: Pareto efficiency and the notion of efficiency that the bidder with the highest value receives the object.</p>

<p>Are the two ever equivalent? I can see that the second notion implies Pareto efficiency, but not the converse.</p>

<microeconomics><auctions><pareto-efficiency><mechanism-design>
Efficiency in Auctions
Student
# Efficiency in Auctions

(Asked by: username_0 on 2020-05-11)

Consider a finite number of bidders, each bidding for a single indivisible object, with private independent values from some probability distribution.
There are 2 intuitive notions of (ex-post) efficiency: Pareto efficiency and the notion of efficiency that the bidder with the highest value receives the object.

Are the two ever equivalent? I can see that the second notion implies Pareto efficiency, but not the converse.

**Tags:** microeconomics, auctions, pareto-efficiency, mechanism-design

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## 1 answers

### Answer by username_1 on 2020-05-12. Score: 1

If bidders have quasilinear preferences and monetary transfers are possible, then the two notions are equivalent: If $x$ is an allocation of the object and $t$ is a vector of monetary transfers with a balanced budget (so the sum of all transfers is 0), then the pair $(x,t)$ is Pareto efficient if and only if $x$ is the utilitarian allocation (object goes to the bidder with the highest valuation).

If monetary transfers are not possible, every allocation of the object to some bidder is Pareto efficient.

> **Comments:**
> **username_0**: Interesting, do notions of efficiency for auctions ever consider the seller's utility as well as buyers? (I don't mean revenue maximisation, I mean buyer's and seller's combined utility). In this conversation, they have been referring only to buyers.  
> **username_1**: @Student: Yes, but mostly in a trivial sense where the seller is assumed to have a zero valuation of the object.  

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