How much to produce: price = marginal cost
Learning goals
After this page, you can:
- Explain why a price taker faces a flat demand curve, so the extra revenue from one more unit is simply the market price.
- Find the profit-maximizing output from a cost table: keep producing while the next unit’s marginal cost is at or below the price, on the rising part of MC.
- Compute profit two ways, P × q − TC and (P − ATC) × q, and say why “lowest average cost” is not the output rule.
The idea
A wheat farmer checks the posted price at the grain elevator every morning. Today it is $8.50 a bushel. She cannot change it. If she asks for $8.60, the elevator buys from the next farm. Her only decision is how much to grow and sell.
What makes a market competitive. Three things together: many sellers, an identical product, and easy entry. Wheat fits all three. One farm’s crop is a tiny drop in the market. Buyers do not care whose wheat it is. So each farm is a price taker: it takes the market price as given. It can sell as much as it wants at that price, and nothing above it.
A flat demand curve. Draw the demand curve that one farm faces. It is a horizontal line at the market price. That is not the market demand curve, which still slopes down. It is the demand for this one farm’s wheat. Ask a cent more and sales drop to zero. Ask a cent less and you give money away, because you could sell everything at the market price anyway.
Marginal revenue equals the price. Marginal revenue (MR) is the extra revenue from one more unit. For a price taker, every extra bushel sells at the same price. So MR = P. The next thousand bushels at $8.50 bring in $8,500. Always. That leaves only one question: how many units should you produce?
The output rule: compare the next unit’s cost with the price. Marginal cost (MC) is the extra cost of one more unit. If the next unit costs less than the price, making it adds to profit. If it costs more, it lowers profit. So keep going while MC ≤ P, and stop just before MC climbs above the price. In a cost table, this means: read down the MC column. Find the last row where MC is at or below the price. That row is your output.
One detail. MC often falls at first (the first few units are awkward and expensive) and then rises. Use only the rising part of MC. A low MC on the falling part does not mean “stop there”. The units after it are even cheaper.
On a graph, this is the point where the flat price line meets the rising MC curve. That is why economists write the rule as P = MC for a price taker. It is the same idea as MR = MC, which works for every firm. Only the price taker gets to replace MR with P.
Profit is a rectangle. Profit is revenue minus total cost: P × q − TC. You can also write it per unit. Average total cost (ATC) is total cost divided by output. Each unit earns P − ATC. So profit = (P − ATC) × q. On the graph it is a rectangle. Its height is the gap between the price line and the ATC curve. Its width is the output. When the price is above ATC, the rectangle is a profit. When it is below, the rectangle is a loss.
Why “lowest average cost” is the wrong target. Many managers think the best output is where average cost is lowest. It is not. The average tells you whether you make money overall. It does not tell you whether the next unit pays for itself. Suppose the price is well above your lowest average cost. Then units past that point can still cost less than the price. Each one adds a bit more profit. A price taker should grow until MC reaches the price, even if the average starts to creep up.
A loss can be the best result. Sometimes the price is below ATC at every output. Then the best the farm can do is a loss. The output rule still finds the smallest loss. Whether the farm should operate at all is the next question — the shutdown rule on the next page.
Price taker: MR = P · Output rule: the largest q with MC ≤ P on the rising part of MC (P = MC)
Profit = P × q − TC(q) = (P − ATC) × q · If you produce nothing, you still pay the fixed cost.
Try it
The chart uses a fictional farm, Cedar Ridge. Output is in thousand bushels. Costs are in $ thousand, so MC and the averages read as dollars per bushel. You can edit any total-cost cell.
- Press Price $8.50. Find the chosen row in the table. Check that the profit bar is highest there.
- Press One more thousand bushels several times. At which step does profit start to fall?
- Press Price $6.50. The rectangle turns red. Is the loss bigger or smaller than the $20,000 fixed cost?
- Slide the price down to $3.50. Read the message under the chart.
Worked example
Problem. Cedar Ridge farm has a fixed cost of $20 thousand (land lease and equipment loan). Its total cost for 0 to 10 thousand bushels is 20, 26, 30, 32.5, 36, 41, 46.5, 53, 60, 68.5, 78.5 ($ thousand). The market price is $8.50 a bushel. How much should it grow, and what is its profit?
Step 1. Marginal cost. Subtract each total cost from the next one. MC for the 1st to the 10th thousand bushels: 6, 4, 2.5, 3.5, 5, 5.5, 6.5, 7, 8.5, 10. MC is lowest at the 3rd thousand and rises after that.
Step 2. Read down the MC column. The 9th thousand bushels costs $8.50 a bushel. That is equal to the price, so grow it. The 10th would cost $10.00, more than the price. Stop. Grow 9 thousand bushels.
Step 3. Profit, way one. Revenue = 8.50 × 9 = $76.5 thousand. Total cost = $68.5 thousand. Profit = $8.0 thousand ($8,000).
Step 4. Profit, way two. ATC at 9 = 68.5 ÷ 9 = $7.61. Profit = (8.50 − 7.61) × 9 = $8.0 thousand. Same answer. (Profit at 8 thousand is also $8.0 thousand. The 9th thousand exactly pays for itself. The rule produces it anyway.)
Step 5. Not the lowest average. ATC is lowest at 8 thousand bushels ($7.50). The farm does not aim for the lowest average. It aims for the most profit.
Step 6. A lower price. At $6.50 the 7th thousand costs $6.50 and the 8th costs $7.00. Grow 7. Revenue = 6.50 × 7 = $45.5 thousand. Total cost = $53 thousand. Profit = −$7.5 thousand. That is a loss — but smaller than the −$20 thousand from growing nothing. The next page explains why that matters.
Check yourself
A wheat farm sells its crop at the market price of $8.50 a bushel. If it grows 9,000 bushels instead of 8,000, how much extra revenue does the extra 1,000 bushels bring in?
A price taker’s marginal revenue is the market price.
A farm’s marginal cost for q = 1 to 10 thousand bushels is 6, 4, 2.5, 3.5, 5, 5.5, 6.5, 7, 8.5, 10 ($ per bushel). The market price is $5.50. If the farm operates, how many thousand bushels should it grow?
Grow the largest quantity whose marginal cost is at or below the price, on the rising part of MC.
A barley farm sells 12,000 bushels at $5.00 a bushel. Its average total cost at that output is $4.25 a bushel. What is its profit?
Profit = (P − ATC) × q, the rectangle between the price and average total cost.
At its current output, the next 1,000 bushels would cost a farm $9.20 a bushel to grow. The market price is $8.50 and its average total cost is $7.60. What should it do?
Use marginal cost to choose quantity; averages only tell you whether you make money.
A farm wants to sell 2,000 more bushels this season. A neighbor suggests pricing its wheat 10 cents below the market price to attract buyers. Good advice?
A price taker faces a flat demand curve: it never needs to cut price to sell more.
Video
Video coming soon.