<p>The maximisation problem is :
<span class="math-container">$\max_{K,L}$</span> <span class="math-container">$\pi =PL^{a}K^{b}R^{c}-wL-rK-vR$</span></p>

<p>The arguments will be only <span class="math-container">$K,L$</span>,so <span class="math-container">$F.O.Cs$</span> will only include <span class="math-container">$\pi _{K},\pi _L$</span></p>

<p>The profit function will be a function of <span class="math-container">$(P,w,r,v)$</span>. Finding <span class="math-container">$F.O.Cs$</span> will give us the <span class="math-container">$\pi (P,w)$</span> function where <span class="math-container">$w$</span> denotes all the input prices. </p>

CC BY-SA 4.0
2018-11-07T05:37:43.490Z
2018-11-07T05:37:43.490Z
Henam
<p>Suppose that a competitive firm receives a price of <span class="math-container">$P$</span> for its output, and pays prices of w, r and v for its labor <span class="math-container">$(L)$</span>, capital <span class="math-container">$(K)$</span> and natural resources <span class="math-container">$(R)$</span> inputs, respectively. The firm operates with the production function
<span class="math-container">$Q = L^aK^bR^c$</span>. <strong>The firm chooses labor and capital to maximize profit.</strong></p>

<p>a. Derive the firm’s profit function. <span class="math-container">$\pi$</span></p>

<p>b. Derive the first-order conditions FOC for profit maximization. </p>

<p>My Question is regarding FOC, since the firm chooses labor and capital to maximize profit, do I look at this as a problem with simply two endogenous variables mainly labor <span class="math-container">$(L)$</span>, capital <span class="math-container">$(K)$</span>, hence the FOC are the partial derivative of the proofit function <span class="math-container">$w.r.t. L$</span> and <span class="math-container">$K$</span>. (<span class="math-container">$\pi_L$</span> and <span class="math-container">$\pi_K$</span>) or should I include <span class="math-container">$\pi_R$</span> in my solution</p>

<microeconomics><mathematical-economics><profit-maximization><cobb-douglas>
Maximizing a Cobb-Douglas Function
C. Master
# Maximizing a Cobb-Douglas Function

(Asked by: username_0 on 2018-11-05)

Suppose that a competitive firm receives a price of $P$ for its output, and pays prices of w, r and v for its labor $(L)$, capital $(K)$ and natural resources $(R)$ inputs, respectively. The firm operates with the production function
$Q = L^aK^bR^c$. **The firm chooses labor and capital to maximize profit.**

a. Derive the firm’s profit function. $\pi$

b. Derive the first-order conditions FOC for profit maximization.

My Question is regarding FOC, since the firm chooses labor and capital to maximize profit, do I look at this as a problem with simply two endogenous variables mainly labor $(L)$, capital $(K)$, hence the FOC are the partial derivative of the proofit function $w.r.t. L$ and $K$. ($\pi\_L$ and $\pi\_K$) or should I include $\pi\_R$ in my solution

**Tags:** microeconomics, mathematical-economics, profit-maximization, cobb-douglas


---

## 1 answers

### Answer by username_1 on 2018-11-07. Score: 0

The maximisation problem is :
$\max\_{K,L}$ $\pi =PL^{a}K^{b}R^{c}-wL-rK-vR$

The arguments will be only $K,L$,so $F.O.Cs$ will only include $\pi \_{K},\pi \_L$

The profit function will be a function of $(P,w,r,v)$. Finding $F.O.Cs$ will give us the $\pi (P,w)$ function where $w$ denotes all the input prices.


---

