Oftentimes I hear conservatives argue for freer markets on efficiency grounds. Typically this will take the form of a pseudo-counterfactual, along the lines of “Well if there were profits to be made in this market, why didn’t some firm come in and earn them?” People sometimes assume that the freer the market, the greater the efficiency.
On the other hand, liberals will often assert that economists have an uncritical, ideological lust for the free market.
Neither of these things are true. Here’s a simple example.
Let Sam (the seller) own an item that he values somewhere between $0 and $100. My example of this is an autographed portrait of Tom Hanks — nobody really knows how much it’s worth, but it’s definitely worth less than $100. Let’s call his valuation of the portrait \(v_s\). If the seller receives a bid greater than or equal to \(v_s\), he will sell it.
Barry (the buyer) comes along. He too values the portrait somewhere between $0 and $100. He values it at \(v_b\). Sam and Barry agree to simultaneously write down their offers (the lowest price Sam will accept, and how much Barry bids) and then to reveal their prices. If the bid is greater than the price, Barry buys the portrait.
To make the maths a little easier to grasp, let’s assume the valuations are uniform, continuous, and iid. This means that 1% of people value the portrait at $1 or less; 30% value is at $30 or less; 99.99% value it at $99.99 or less, etc.
Note that this is a free market situation. There is no government intervention or taxation. There is no large corporation acting anti-competitively. There are no externalities. It’s two guys negotiating on a price.
How much does Barry bid? To get the intuitive idea, let’s say his valuation is $60. If he bids $60, even if that bid is accepted he gets no “profit” since $60 was really the most he would pay anyway. However if he bids e.g. $55 although he decreases his chances (by 5%) of winning, he stands to make a $5 profit if he does win. Thus he may have an incentive to bid below his true valuation. You can skip this if you like, but denoting \(b\) as how much Barry should bid, here’s the mathsy bit:
\(\pi_B = \text{prob(}b>v_s) (v_s – b) + \text{prob}(b<v_s)(0) \\\pi_B = F(b)(v_s – b) \\
\pi_B = b(v_s – b) \\
\displaystyle \frac{\partial \pi_B}{\partial b} = v_s – 2b = 0 \\
b = \frac{1}{2} v_s\\\)
Thus the optimal bid for Barry is exactly half his valuation. What does this tell us?
In the original setting, trade should happen if Barry’s valuation is greater than Sam’s. By our assumption, that happens half the time. However Barry, behaving rationally, will lower his bid in the hope of maximising his expected profits. This means that trade will happen only one quarter of the time.
This implies that even in this very simple no-frills no-government setting, the free market will only work efficiently 50% of the time.
So no, the free market will not definitely realise all potential gains from trade and no, economists do not think that free markets will cure all of the world’s problems.
(This is based on a microeconomic theory question that I think was written by Lones Smith. It is an application of the Myerson-Satterthwaite theorem.)