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Why Marginal Revenue Equals Marginal Cost Determines Profit Maximization

ByMike Fladlien

Muscatine High School

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Total Cost

Quantity Fixed Cost Variable Cost Total Cost Total Revenue Profit

0 1 0 1 0 -1.00

0.25 1 0.02 1.02 0.3125 -0.70

0.5 1 0.06 1.06 0.625 -0.44

0.75 1 0.14 1.14 0.9375 -0.20

1 1 0.25 1.25 1.25 0.00

1.25 1 0.39 1.39 1.5625 0.17

1.5 1 0.56 1.56 1.875 0.31

1.75 1 0.77 1.77 2.1875 0.42

2 1 1.00 2.00 2.5 0.50

2.25 1 1.27 2.27 2.8125 0.55

2.5 1 1.56 2.56 3.125 0.56

2.75 1 1.89 2.89 3.4375 0.55

3 1 2.25 3.25 3.75 0.50

3.25 1 2.64 3.64 4.0625 0.42

3.5 1 3.06 4.06 4.375 0.31

3.75 1 3.52 4.52 4.6875 0.17

4 1 4.00 5.00 5 0.00

4.25 1 4.52 5.52 5.3125 -0.20

4.5 1 5.06 6.06 5.625 -0.44

Fixed Cost (FC) – Constant Costs regardless of output level

Variable Cost (VC) – Costs that change over output such as labor

Total Cost (TC) – The total of FC + VC

The Data

FC = $1

VC = .25Q^2

Profit is maxed at 2.5 units (the difference between total revenue and total cost is the greatest)

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The GraphProfit is maximized at 2.5 units

Now, let’s show that at 2.5 units, marginal revenue equals marginal cost

Marginal Revenue – The change in total revenue that results from selling an addition unit of ouput

Marginal Cost – The change in total cost that results from a change in output. dTC/dQ

Marginal Cost (Calculus) is the derivative of the total cost function. In this case, .5Q

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MR = MCThe slope of the Total Revenue, TR, curve is the Marginal Revenue, MR.

The Slope of the Total Cost, TC, curve is the Marginal Cost curve.

Let’s look at the slope of the Total Revenue, TR, curve.

The price of the product is $1.25

Perfectly Competitive so the firm can sell all they want at $1.25

Price Taker selling a homogenous good with many buyers and sellers

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MR = MCSlope of TC is Marginal Cost

At $1.25 the quantity is 2.5

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MR = MCThe intersection of the Marginal Revenue and Marginal Cost curves is the profit maximization point.

Why?

Because the distance between total revenue and total cost is the greatest at that point.

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But Why Does This Work?When I show this to students, they still don’t get it.

To convince your students that MR = MC maximizes profits, you have to show that the slopes are equal.

At 2.5 units the distance between the two curves is the farthest so profit is maximized.

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The End

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