<p>I'm trying to derive the example function used in a paper I am reading and am stuck. Please help. Below is the equation. For now, all I am requesting is someone to help me solve for p. More details included below the image.
<a href="https://i.sstatic.net/irjfY.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/irjfY.png" alt="mathematical equations" /></a></p>
<p>q is always &gt;= 0; Ti is always &gt;= 0; Ti^h is the max value Ti can take; C is always &gt;= 0; and p is always &gt;= 0.</p>
<p>Additional info you might want to know... f(x) and F(x) are the pdf and CDF of the uniform distribution respectively from Ti^l to Ti^h where 3Ti^l &gt; Ti^h. Also, p is actually the partial derivative of t with respect to q. My ultimate goal is to solve for t (so obviously I was trying to solve for p first, and then just integrate p with respect to q).</p>
<p>This is taken from: Martimort, D., &amp; Moreira, H. (2010). Common agency and public good provision under asymmetric information. Theoretical Economics, 5(2), 159–213. <a href="https://doi.org/10.3982/TE507" rel="nofollow noreferrer">https://doi.org/10.3982/TE507</a></p>
<p>I'm trying to figure out how they got their example t2 function. So, bonus points if you understand that / this paper!</p>

CC BY-SA 4.0
2023-10-27T13:37:51.073Z
Could you specify the page of the integral in the Martimort's paper? It is a long paper. Thanks!
BakerStreet
CC BY-SA 4.0
2023-10-27T21:20:39.560Z
Sure! Admitting this is my re-typing of it, but it's equation 14 on page 174. As you can see, I've gone ahead and substituted in equation 10 for psi in order to start solving for p. My ultimate goal is to eventually arrive at equation 4 (t2 and t20) on page 169.
KatLeigh11
<optimization><contract-theory>
help with nested integrals in common agency public goods paper
KatLeigh11
# help with nested integrals in common agency public goods paper

(Asked by: username_0 on 2023-10-27)

I'm trying to derive the example function used in a paper I am reading and am stuck. Please help. Below is the equation. For now, all I am requesting is someone to help me solve for p. More details included below the image.
[![mathematical equations](https://i.sstatic.net/irjfY.png)](https://i.sstatic.net/irjfY.png)

q is always >= 0; Ti is always >= 0; Ti^h is the max value Ti can take; C is always >= 0; and p is always >= 0.

Additional info you might want to know... f(x) and F(x) are the pdf and CDF of the uniform distribution respectively from Ti^l to Ti^h where 3Ti^l > Ti^h. Also, p is actually the partial derivative of t with respect to q. My ultimate goal is to solve for t (so obviously I was trying to solve for p first, and then just integrate p with respect to q).

This is taken from: Martimort, D., & Moreira, H. (2010). Common agency and public good provision under asymmetric information. Theoretical Economics, 5(2), 159–213. <https://doi.org/10.3982/TE507>

I'm trying to figure out how they got their example t2 function. So, bonus points if you understand that / this paper!

**Tags:** optimization, contract-theory

> **Comments:**
> **username_1**: Could you specify the page of the integral in the Martimort's paper? It is a long paper. Thanks!  
> **username_0**: Sure! Admitting this is my re-typing of it, but it's equation 14 on page 174. As you can see, I've gone ahead and substituted in equation 10 for psi in order to start solving for p. My ultimate goal is to eventually arrive at equation 4 (t2 and t20) on page 169.  

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## 0 answers

