6.4: Profit Maximization and Output

Last updated
Save as PDF

Page ID: 210849

Martin Medeiros
Chabot College

$ \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $

$ \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} $

$ \newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$

( \newcommand{\kernel}{\mathrm{null}\,}\) $ \newcommand{\range}{\mathrm{range}\,}$

$ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$

$ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$

$ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$

$ \newcommand{\Span}{\mathrm{span}}$

$ \newcommand{\id}{\mathrm{id}}$

$ \newcommand{\Span}{\mathrm{span}}$

$ \newcommand{\kernel}{\mathrm{null}\,}$

$ \newcommand{\range}{\mathrm{range}\,}$

$ \newcommand{\RealPart}{\mathrm{Re}}$

$ \newcommand{\ImaginaryPart}{\mathrm{Im}}$

$ \newcommand{\Argument}{\mathrm{Arg}}$

$ \newcommand{\norm}[1]{\| #1 \|}$

$ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$

$ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\AA}{\unicode[.8,0]{x212B}}$

$ \newcommand{\vectorA}[1]{\vec{#1}} % arrow$

$ \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$

$ \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $

$ \newcommand{\vectorC}[1]{\textbf{#1}} $

$ \newcommand{\vectorD}[1]{\overrightarrow{#1}} $

$ \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} $

$ \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} $

$ \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $

$ \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} $

$\newcommand{\avec}{\mathbf a}$ $\newcommand{\bvec}{\mathbf b}$ $\newcommand{\cvec}{\mathbf c}$ $\newcommand{\dvec}{\mathbf d}$ $\newcommand{\dtil}{\widetilde{\mathbf d}}$ $\newcommand{\evec}{\mathbf e}$ $\newcommand{\fvec}{\mathbf f}$ $\newcommand{\nvec}{\mathbf n}$ $\newcommand{\pvec}{\mathbf p}$ $\newcommand{\qvec}{\mathbf q}$ $\newcommand{\svec}{\mathbf s}$ $\newcommand{\tvec}{\mathbf t}$ $\newcommand{\uvec}{\mathbf u}$ $\newcommand{\vvec}{\mathbf v}$ $\newcommand{\wvec}{\mathbf w}$ $\newcommand{\xvec}{\mathbf x}$ $\newcommand{\yvec}{\mathbf y}$ $\newcommand{\zvec}{\mathbf z}$ $\newcommand{\rvec}{\mathbf r}$ $\newcommand{\mvec}{\mathbf m}$ $\newcommand{\zerovec}{\mathbf 0}$ $\newcommand{\onevec}{\mathbf 1}$ $\newcommand{\real}{\mathbb R}$ $\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$ $\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$ $\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$ $\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$ $\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$ $\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$ $\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$ $\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$ $\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$ $\newcommand{\laspan}[1]{\text{Span}\{#1\}}$ $\newcommand{\bcal}{\cal B}$ $\newcommand{\ccal}{\cal C}$ $\newcommand{\scal}{\cal S}$ $\newcommand{\wcal}{\cal W}$ $\newcommand{\ecal}{\cal E}$ $\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$ $\newcommand{\gray}[1]{\color{gray}{#1}}$ $\newcommand{\lgray}[1]{\color{lightgray}{#1}}$ $\newcommand{\rank}{\operatorname{rank}}$ $\newcommand{\row}{\text{Row}}$ $\newcommand{\col}{\text{Col}}$ $\renewcommand{\row}{\text{Row}}$ $\newcommand{\nul}{\text{Nul}}$ $\newcommand{\var}{\text{Var}}$ $\newcommand{\corr}{\text{corr}}$ $\newcommand{\len}[1]{\left|#1\right|}$ $\newcommand{\bbar}{\overline{\bvec}}$ $\newcommand{\bhat}{\widehat{\bvec}}$ $\newcommand{\bperp}{\bvec^\perp}$ $\newcommand{\xhat}{\widehat{\xvec}}$ $\newcommand{\vhat}{\widehat{\vvec}}$ $\newcommand{\uhat}{\widehat{\uvec}}$ $\newcommand{\what}{\widehat{\wvec}}$ $\newcommand{\Sighat}{\widehat{\Sigma}}$ $\newcommand{\lt}{<}$ $\newcommand{\gt}{>}$ $\newcommand{\amp}{&}$ $\definecolor{fillinmathshade}{gray}{0.9}$

It seems odd to discuss profit maximization when dealing with firms in a perfectly competitive industry. After all, it was established in the last section that market entry competes away all economic profit in the industry. Well, when it comes to perfect competition it may be more appropriate to change “profit maximization” to “doing the best you can.”

Firms in a perfectly competitive industry do not get to choose the price they charge for their product. The price is set by the market and individual firms take this price as given. This is why firms in this industry are called price takers.

Take selling water as an example. You are selling a product that is available for free and in many places. If you decide to ask $20 for a gallon for your water you will likely sell zero, because even if one does not drink from the faucet, he can buy a bottle of water for about $1.00. The feeling that you can't really set your own price is what a price-taker feels like to an individual or company with a very small market share amongst thousands of other suppliers!

Output

If price is a part of the business that is predetermined by the market, then what decisions are up to the managers? One very important decision a manager gets to make is the rate of output.

It is very important to note that any change in the rate of output affects revenues and costs. And anything that affects revenues and costs also impacts profit.

Profit = Total Revenue – Total Cost

The goal of any profit-maximizing firm is to choose a rate of output that brings in the most profit.

What is the rate of output that will maximize profit?

To answer this question, you need to focus on the very last unit produced rather than the entire range of output. See figure 8.

A diagram of a boxDescription automatically generated with medium confidence

Figure 8

The last unit produced is important because of its contribution to the change in total revenue and total cost. This before-and-after approach (i.e., total revenue before production compared to total revenue after production) is really a marginal analysis. A firm needs to know the marginal cost and marginal revenue of the last unit produced to discern its contribution to profit. See figure 9.

A diagram of boxes with numbers and lettersDescription automatically generated with medium confidence

Figure 9

Notice that the MR for each unit of production is the same. This is because firms in perfectly competitive industries can sell all their output at market equilibrium price. Some feel this ability to sell more without having to lower the price is a violation of the law of demand. The reason a perfectly competitive firm can sell all its output without lowering prices is because of its size. All firms are so small that an increase in output by a single firm will not affect the market supply curve. Without any change in the market supply or market demand curves, the equilibrium price will hold. And since these firms are price takers (i.e., they take the price from the market as their own), they can increase production and sell all additional units at the prevailing market price.

Now, let’s get back to finding the profit maximizing rate of output.

Whenever the marginal revenue for an additional unit of production is greater than its marginal cost, profits will increase. A profit-maximizing company will continue to increase the rate of output if there is a positive impact on profits. See figure 10.

A diagram of boxes and numbersDescription automatically generated with medium confidence

Figure 10

So, the profit maximizing rate of output in the scenario depicted in figure 5.8 is five units. Five units is the rate of output which were MR=MC. This means if this firm increased output to six units, then profits would fall because this rate of output would have a MR<MC.

Take another look at figure 5.8. Observe how MC is increasing with the rate of production while MR is constant. So, if you expand output beyond the rate where MR=MC (let’s say six units) then you will see MC grow larger than MR and profits fall. See figure 11.

A diagram of boxes on a conveyor beltDescription automatically generated

Figure 11

You can see how a mistake like overproduction could lead to a fall in profits (in this case producing six units instead of five). This is why it is important for a business, especially one in a perfectly competitive industry, to monitor and control costs.

Search

Text Color

Text Size

Margin Size

Font Type