<p>It is not trivial (and maybe not even possible) to find the cost function corresponding to a translog production function. And this cost function corresponding to a translog production function has not a translog functional form.<br />
If you rewrite a cost function as follow <span class="math-container">$c(w,y)=c(\exp(\ln w),\exp(\ln y)) =: C(\ln w,\ln y),$</span> then a second order Taylor development of <span class="math-container">$C$</span> around a reference point <span class="math-container">$(\ln w_0,\ln y_0)$</span> yields a translog cost function (after reparameterization).</p>

CC BY-SA 4.0
2021-06-17T19:33:33.523Z
2021-06-17T19:33:33.523Z
Bertrand
<p>I realize that the translog production function is derived as a second order taylor approximation of a production function (e.g. the CES-production function), as explained in <a href="https://economics.stackexchange.com/questions/26144/deriving-the-translog-production-function">this post</a>.</p>
<p>Is the translog <em>cost</em> function derived similarly as a taylor expansion of an arbitrary multiple product cost function? Or is it derived trough cost minimization of a translog <em>production</em> function? Or both?</p>

<production-function><cost-functions>
How is the translog cost function derived?
Freddy
# How is the translog cost function derived?

(Asked by: username_0 on 2021-06-17)

I realize that the translog production function is derived as a second order taylor approximation of a production function (e.g. the CES-production function), as explained in [this post](https://economics.stackexchange.com/questions/26144/deriving-the-translog-production-function).

Is the translog *cost* function derived similarly as a taylor expansion of an arbitrary multiple product cost function? Or is it derived trough cost minimization of a translog *production* function? Or both?

**Tags:** production-function, cost-functions

---

## 1 answers

### Answer by username_1 on 2021-06-17. Score: 0 | Accepted answer

It is not trivial (and maybe not even possible) to find the cost function corresponding to a translog production function. And this cost function corresponding to a translog production function has not a translog functional form.  
If you rewrite a cost function as follow $c(w,y)=c(\exp(\ln w),\exp(\ln y)) =: C(\ln w,\ln y),$ then a second order Taylor development of $C$ around a reference point $(\ln w\_0,\ln y\_0)$ yields a translog cost function (after reparameterization).


---

