Cost and Marginal Benefit
Explore: How much compost should you put on your garden?

The following interactive graph shows the concept of marginal cost and marginal benefit by asking how many pounds of compost to use on a tomato patch to generate the highest possible amount of profit.

The first two columns in the table show how tomato production changes as the amount of compost applied changes. The box below the table provides the prices of compost and tomatoes and an adjustment slider for productivity. For this example, the marginal cost of compost is fixed at the price of compost. In addition, the marginal benefit and marginal cost information is presented graphically. You can change the price of compost and the price of tomatoes and both the table and the graph will respond accordingly. Try a quick change in the price of tomatoes, to $0.30 a pound and observe the new values in the table and the new marginal benefit curve in the graph. Once you are comfortable with how the graph reflects changes in the table, click the Reset button to return to the original settings. This setting is for a mythical student named Heather, so let's use her case as the example. Finally, keep in mind that you can use either the table or the graph to answer the following questions.

1. How much compost Heather should use on her tomatoes, based on the information presented? Explain how you arrived at your answer.
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2. Verify that the quantity of compost you selected results in the highest level of profit. To do this copy the first two columns in the table (the compost and tomato production information) on a piece of paper and for each quantity of compost added, determine the total cost of the compost used, the total revenue generated from tomato sales, and the amount of profit (total cost – total revenue). (Assume that Heather sells all of the tomatoes she grows.) Which level of compost use leads to the highest profit? How is this analysis using total costs and total revenue related to your analysis using marginal costs and marginal benefits?
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3. Assuming Heather continues to maximize profit, how much compost will Heather add to her tomato garden if the price of compost falls to $.75 per pound (keeping the price of tomatoes at $.20 per pound)? To begin, change the price of compost in the table to $.75 per pound. Notice how the table and graph changes. Then determine the amount of compost Heather will use if her goal is to make as much money as possible. Compare this amount to your original answer. Did it increase or decrease? Why?
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4. How much compost will Heather add to her tomato garden if instead the price of tomatoes rises to $.40 per pound, while the price of compost remains at its original level of $1.40 per pound? To begin, click the Reset button to reset the original values in the table. Next, change the price of tomatoes in the table to $.40 and notice how the table values and graph change. Then determine the amount of compost Heather will use if her goal is to make as much money as possible. Compare this amount to your original answer. Did it increase or decrease? Why?
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5. What if Heather takes a gardening class that teaches her better tomato growing techniques (weeding, watering, and pruning tips, for example) that lead to a dramatic increase in tomato production? For example, if Heather can now produce 100% more tomatoes for any given level of compost, how will this affect the amount of compost Heather uses, if her goal is to make as much money as possible? To begin, click the Reset button to reset the original values in the table. Next, slide the productivity index to 100%. See how the values in the table change.
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6. As an extension of this idea, what if Heather could buy compost in units smaller than one pound?
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