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I'm taking introductory microeconomics, and I'm trying to consolidate my understanding by looking at some real world examples.

In a perfectly competitive market, there are many consumers and suppliers who are price takers. They are constrained to buy or sell at the accepted equilibrium price due to many competitors.

Therefore, we should expect $P^* = P_D = P_S$ for a certain good or service in a perfectly competitive market. However, having been to a foreign currency exchange at an airport, this does not seem to be the case! They are willing to buy an item (eg: USD) at a lower rate, but they sell it at a higher rate. So it seems that $P_D < P_S$ for the traders (looks similar to a tax wedge), assuming they are both buyers and sellers of the US dollar in the same market.

This example confuses me, as there seems to be two prices instead of one. In the textbook, if I were to buy $Q^*$ items at $P^*$, I should be able to also sell $Q^* $ items at $P^*$, not $Q^*$ items at $P < P^*$. Other examples of this can be seen whenever sellers and buyers are allowed to post their own listings; there always appears to be a price gap.

How do I explain these real world examples using the concept of supply and demand in a perfectly competitive market (and on the graph)?

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    $\begingroup$ Is the airport currency exchange market perfectly competitive? Have you tried exchanging currency with other travellers? $\endgroup$ – user253751 Mar 30 at 9:35
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    $\begingroup$ Retail currency exchange is a combination of a market and a service: a small part of the margin between buy and sell prices is to cover the risk of market movements but the large part is payment for a service, including the costs of handling of different types of money and the costs of being in a prime location, plus the profits of the dealer. So it is a market with frictions rather than a perfectly competitive market - you would not use it for day-trading speculation, but instead to have some liquid cash available for your travel. $\endgroup$ – Henry Mar 30 at 11:26
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    $\begingroup$ @Henry you should consider expanding this comment as an answer $\endgroup$ – 1muflon1 Mar 31 at 7:07
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    $\begingroup$ You may be interested in checking out "price dispersion". $\endgroup$ – Herr K. Mar 31 at 20:44
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    $\begingroup$ P.S. I've literally never exchanged currency at an airport. My bank, and other local banks, will provide this service and although I was not careful to compare the rates, I expect the banks provide better rates. $\endgroup$ – user253751 Mar 31 at 22:08
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In the comments @henry already provided you with the correct conceptual answer, I will try to offer some extra intuition and way how this could be modeled. Currency exchange is a combination of a retail market with service market so here if you would want to visualize it with supply and demand you would have to use two diagrams for both parts of the market.

If that still sounds too exotic just imagine classical retail. A supermarkets will first purchase its produce (let us say carrots) from carrot farmers. This will be separate market where supermarkets are the buyers and where they jointly together form demand and where farmers are suppliers. On this 'market for carrots from farms' there will be supply and demand and price given by the equilibrium.

However, once supermarkets acquire carrots then they will sell them on second retail market to regular consumers. On this second market, let us call it 'market for retail carrots' supermarkets are the suppliers and regular consumers are part of the demand. This market will have its separate price that might be different from the 'market for carrots from farms'. This however does not mean that market is not competitive because supermarket has additional marginal costs for warehousing those carrots, if they sell them just for price that covers these additional cost the market would be perfect (of course, in real life the market might not be perfect, but the point is you can't just say it from the fact that there is a price differential).

In the same way the exchange window at an airport can be thought of operating at two distinct markets. At a market where it buys currency from individuals where the exchange windows are the customers and part of demand and people are the suppliers, and then second market where the exchange window operates as a retail and act as a supplier and people who buy currency are the buyers.

Again this is all consistent with perfect competition. Consider the following simple model:

Exchange window sells USD at price $P_H$, but buys currency at $P_L$ and exchange window additionally has to pay the person sitting at the window wage $w$ for facilitating intermediation (let us assume that wage is paid per unit of currency exchanged to simplify calculation). Let the quantity here be the number of USD exchanged ($Q_{USD}$). Now this can be fully consistent with perfect competition. Let us suppose market is perfectly competitive so $P_H$ is treated by firms as being exogenously set (e.g. see any introductory economics text such as Mankiw Principles of Economics). This means that the profit function of this exchange window will be given by:

$$\Pi = P_H Q_{USD} - P_L Q_{USD} - w Q_{USD}$$

Now take the FOCs and we get:

$$ P_H - P_L - w = 0 \implies \underbrace{P_H}_{\text{price}} = \underbrace{P_L + w}_{\text{Marginal Cost}} $$

Hence, here we have literally a textbook example of perfectly competitive market, where $P_H>P_L$ (e.g. a situation where firm buys low sells high). Yet there is no additional markup as price that the firm provides is exactly equal to marginal cost so the markup $\mu=1$ and we have perfectly competitive outcome.

The intuition here is that for the exchange window buying currency from people is part of their cost, but then they have other costs (e.g. wage in example above and in real life also capital costs etc) since the exchange window is in business of providing intermediation service. In perfectly competitive market price at which firms supplies product will be equal to marginal cost, but here the marginal cost equal not just the cost of accruing the currency from people in the first place but also marginal cost of intermediation.

Lastly note, that this is of course not enough to prove that exchanges are competitive, rather this is proving the opposite. Namely, a difference between price at which firm buys product and price at which it sells product in itself does not tell you anything about whether market is competitive or not. $P_H>P_L$ on both competitive and non-competitive markets. Here you would have to add more reasoning to argue it is competitive, like in a question you mention that when it comes to exchanges there are usually many firms offering the same service and so on. Or you could actually try to empirically estimate marginal costs of the firm and see if indeed firm just sells its product at marginal costs or if the prices are higher indicating both presence of markup and market power.

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Are Price-Cost Markups Rising in the United States? A Discussion of the Evidence

According to this source market power is the ability of a firm or dealer to markup prices of output goods over the marginal cost of input factors.

https://www.bc.edu/content/dam/bc1/schools/mcas/economics/pdf/jep.33.3.3.pdf

The markup of price over marginal cost is a basic measure of market power. With perfect competition in the goods market, a profit-maximizing firm will set price equal to marginal cost, and the markup will be equal to one. With imperfect competition, the firm produces at the quantity where marginal revenue equals marginal cost, and price will exceed marginal cost. In seeking to measure markups, an immediate hurdle is how to measure marginal cost—a variable that must be estimated or inferred rather than being directly observed in a market transaction like prices or revenues. Economists specializing in industrial organization have developed ways of estimating markups for particular firms and industries.

Teaching The Bid-Ask Spread And Triangular Arbitrage For The Foreign Exchange Market

https://files.eric.ed.gov/fulltext/EJ1193295.pdf

According to this source currency dealers buy currency at the bid and sell at the ask with the difference described as the bid-ask spread.

International banks serve as dealers who make a market by standing ready to buy or sell foreign currencies for their own accounts. The bid price represents the price a bank dealer is willing to buy for a currency and the ask price is the price a bank dealer is willing to sell for a currency. Therefore, bank clients buy at the ask price from the dealer and sell at the bid price to the dealer. The bid-ask spread, the difference between the ask price and the bid price, is the compensation (transaction cost) to the dealer (bank clients). The bid-ask spread and bid-ask relationship are basic parts of the FX market microstructure. Students who are familiar with these topics are able to better comprehend the theory and practice of the FX market.

Networks, Crowds, and Markets: Reasoning About a Highly Connected World

https://www.cs.cornell.edu/home/kleinber/networks-book/

https://www.cs.cornell.edu/home/kleinber/networks-book/networks-book-ch11.pdf

A trader’s payoff is the profit he makes from all his transactions: it is the sum of the ask prices of his accepted offers to buyers, minus the sum of the bid prices of his accepted offers to sellers.

In the next section, we’ll work out the set of possible equilibria for the trading network in Figures 11.3–11.5, by first dissecting the network into simpler “building blocks.” In particular, these building blocks will correspond to two of the basic structures contained within the network in Figures 11.3–11.5: buyers and sellers who are monopolized by having only a single trader they can deal with, and buyers and sellers who benefit from perfect competition between multiple traders. In the process, we’ll see that network structure and access to alternatives can significantly affect the power of participants in the market.

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  • $\begingroup$ The first half of this answer has nothing to with the question. Bid ask spread is not result of market power, in fact your second half of the question explains it. It’s the compensation for the cost of carrying out transactions that would exist even in perfectly competitive market and it is a separate topic. In fact the OP specifically asks for answer in perfectly competitive market $\endgroup$ – 1muflon1 Mar 31 at 7:02
  • $\begingroup$ "Buy low sell high" implies the ability to markup the sell price over the buy price. If no one has market power or the ability to markup prices then profits go to zero. In the quote from the first reference there are zero profits when "the markup is equal to one." $\endgroup$ – SystemTheory Mar 31 at 18:12
  • $\begingroup$ no it does not imply markup. A) most markets with markup do not have this set up. This is simply not markup as understood in economics (you can literally have look at any economics text) but intermediation fee. An intermediation fee does not mean market is not perfectly competitive. Buy low sell high can be perfectly competitive outcome if difference between buy low and sell high is equal to (economic) costs of intermediation. B) in perfect competition economic profit is zero there is still accounting profit meaning if you would actually look at firms books it would record profit $\endgroup$ – 1muflon1 Mar 31 at 18:47

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