<p>Why do we assume convex transaction costs in theoretic models? What is the intuition and the strict definition of this assumption?</p>

<p>Well, I have in mind the Glosten model in 1994. Neither he provides some details, nor it is obvious why he defines convex transaction costs. He only claims that the quasi-concavity of the utility function, ismplied by the concavity of some function <span class="math-container">$U(\cdot)$</span> and the convexity of the transaction costs function <span class="math-container">$TC(\cdot)$</span>. This is a link of <a href="https://www0.gsb.columbia.edu/mygsb/faculty/research/pubfiles/1537/is.pdf" rel="nofollow noreferrer">the Glosten 1994 article</a>, you can see in page <span class="math-container">$1132$</span>. I wonder does he assumes convexity because this comes from any micro foundation assumption, or it is just for solving the problem, because he can not solve it differently. Why not assuming that the function of transaction costs is a linear function which in fact is a convex and a concave function simultaneousely.</p>

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2020-03-20T01:42:28.837Z
Please provide some context to your question. Different models have different justifications for convex costs.
Herr K.
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2020-03-20T08:47:25.843Z
Well, I have in mind the Glosten model in 1994. Neither he provides some details, nor it is obvious why he defines convex transaction costs. He only claims that the quasi-concavity of the utility function, ismplied by the concavity of some function $U(\cdot)$ and the convexity of the transaction costs function $TC(\cdot)$
Hunger Learn
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2020-03-20T18:18:40.600Z
Convexity of transaction cost seems like a pretty innocuous assumption there. As you yourself noted, a linear cost function does not contradict the convexity requirement.
Herr K.
<microeconomics><financial-markets>
Convex transaction costs
Hunger Learn
# Convex transaction costs

(Asked by: username_0 on 2020-03-19)

Why do we assume convex transaction costs in theoretic models? What is the intuition and the strict definition of this assumption?

Well, I have in mind the Glosten model in 1994. Neither he provides some details, nor it is obvious why he defines convex transaction costs. He only claims that the quasi-concavity of the utility function, ismplied by the concavity of some function $U(\cdot)$ and the convexity of the transaction costs function $TC(\cdot)$. This is a link of [the Glosten 1994 article](https://www0.gsb.columbia.edu/mygsb/faculty/research/pubfiles/1537/is.pdf), you can see in page $1132$. I wonder does he assumes convexity because this comes from any micro foundation assumption, or it is just for solving the problem, because he can not solve it differently. Why not assuming that the function of transaction costs is a linear function which in fact is a convex and a concave function simultaneousely.

**Tags:** microeconomics, financial-markets

> **Comments:**
> **username_1**: Please provide some context to your question. Different models have different justifications for convex costs.  
> **username_0**: Well, I have in mind the Glosten model in 1994. Neither he provides some details, nor it is obvious why he defines convex transaction costs. He only claims that the quasi-concavity of the utility function, ismplied by the concavity of some function $U(\cdot)$ and the convexity of the transaction costs function $TC(\cdot)$  
> **username_1**: Convexity of transaction cost seems like a pretty innocuous assumption there. As you yourself noted, a linear cost function does not contradict the convexity requirement.  

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